Bridge model solving method, system, device and computer-readable storage medium
By using the target parameters and dichotomous method of the target bridge damper iteratively calculates the spring displacement in the bridge model solution, the problem of low resolution efficiency of the bridge model is solved, and a more efficient calculation process is achieved.
Patent Information
- Application Number
- CN202410681704.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-29
- Publication Date
- 2025-07-01
- Estimated Expiration
- 2044-05-29
AI Technical Summary
In the prior art, the bridge model has low calculation efficiency, especially when dealing with the nonlinear structure of large cable-stayed bridges. The traditional solution method has limitations on load and step size, and the calculation efficiency is low.
The first and second function values are determined based on the target parameters of the target bridge damper and the preset lower and upper bounds of the spring displacement, and the spring displacement is iteratively calculated using dichotomy, and the equilibrium equation is solved based on the explicit integral method to construct the nonlinear damping force of the bridge model.
It improves the efficiency of bridge model solution, breaks through the traditional method's limitations on load and step size, reduces the number of iterations, and significantly improves the calculation speed.
Smart Images
Figure CN118656889B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of engineering structure tests, and particularly to a bridge model solving method, system, device and computer-readable storage medium. Background Art
[0002] Earthquakes can bring huge disasters to mankind. As the traffic lifeline in earthquake-prone areas, if bridges are damaged during earthquakes, it will bring great difficulties to disaster relief work, aggravate secondary disasters, and cause huge economic losses. Therefore, the safety of bridges under earthquakes has gradually attracted social attention. Bridge seismic analysis is a prerequisite for improving bridge safety, but earthquakes have very strong uncertainties, which bring great difficulties to bridge seismic analysis.
[0003] In existing bridge seismic analysis, bridge models are built through visual finite element models or through programming languages on real-time platforms. However, due to the generally non-linear structures of large cable-stayed bridges to a certain extent, how to consider their non-linearity when solving the model is an unavoidable problem. The traditional method for solving bridge models is the fast non-linear method, but the fast non-linear method has certain limitations in load terms and integration step sizes and requires multiple iterations, with low computational efficiency. Therefore, how to improve the efficiency of bridge model solving is an urgent problem to be solved currently. Summary of the Invention
[0004] The present application provides a bridge model solving method, system, device and computer-readable storage medium, which can solve the technical problem of low efficiency in solving bridge models in the prior art.
[0005] In a first aspect, an embodiment of the present application provides a bridge model solving method, and the bridge model solving method includes:
[0006] Determining a first function value based on target parameters of a target bridge damper and a preset lower bound of spring displacement, where the target parameters include a target total displacement, a damping section displacement at the previous moment, a preset target step size, a preset damping coefficient, a preset reference speed, and a preset spring stiffness;
[0007] Determining a second function value based on the target parameters and a preset upper bound of spring displacement;
[0008] Determining spring displacement based on the bisection method, the target parameters, the first function value and the second function value, and determining non-linear damping force based on the spring displacement and the spring stiffness;
[0009] Construct an equilibrium equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset nodal parameters of the target bridge damper, and the nonlinear damping force, where the preset nodal parameters include nodal acceleration, nodal velocity, and nodal displacement;
[0010] Perform mode decomposition on the equilibrium equation to obtain modal equations of each order of the target bridge damper, and solve the modal equations of each order based on the explicit integration method to obtain modal displacements of each order of the target bridge damper.
[0011] Combined with the first aspect, in one implementation, the determining the first function value based on the target parameters of the target bridge damper and a preset lower bound of the spring displacement includes:
[0012] Determine a lower bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the lower bound of the spring displacement;
[0013] Determine the first function value based on the lower bound of the damping section velocity, the lower bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness.
[0014] Combined with the first aspect, in one implementation, the determining the second function value based on the target parameters and a preset upper bound of the spring displacement includes:
[0015] Determine an upper bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the upper bound of the spring displacement;
[0016] Determine the second function value based on the upper bound of the damping section velocity, the upper bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness.
[0017] Combined with the first aspect, in one implementation, before the step of determining the spring displacement based on the bisection method, the target parameters, the first function value, and the second function value, further includes:
[0018] Judge whether the first function value and the second function value have different signs;
[0019] If so, execute the step of determining the spring displacement based on the bisection method, the target parameters, the first function value, and the second function value;
[0020] If not, update the upper bound and the lower bound of the spring displacement to make the first function value and the second function value have different signs, and execute the step of determining the spring displacement based on the bisection method, the target parameters, the first function value, and the second function value.
[0021] In combination with the first aspect, in one embodiment, determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value includes:
[0022] Determining the spring displacement midpoint based on the dichotomy method, the upper bound of the spring displacement, and the lower bound of the spring displacement;
[0023] Determining the midpoint of the damping section velocity based on the spring displacement midpoint, the target total displacement, the target step size, and the damping section displacement at the previous moment;
[0024] Determining the third function value based on the midpoint of the damping section velocity, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness;
[0025] Determining the spring displacement based on the first function value, the second function value, the third function value, and the spring displacement midpoint.
[0026] In combination with the first aspect, in one embodiment, determining the spring displacement based on the first function value, the second function value, the third function value, and the spring displacement midpoint includes:
[0027] If the first function value and the third function value have different signs, then determining the fourth function value based on the upper bound of the damping section velocity, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness;
[0028] When the absolute value of the difference between the fourth function value and the first function value is less than a preset difference threshold, taking the spring displacement midpoint as the spring displacement;
[0029] If the second function value and the third function value have different signs, then determining the fifth function value based on the lower bound of the damping section velocity, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness;
[0030] When the absolute value of the difference between the fifth function value and the second function value is less than a preset difference threshold, taking the spring displacement midpoint as the spring displacement.
[0031] In a second aspect, an embodiment of the present application provides a bridge model solving system, and the bridge model solving system includes:
[0032] A first processing module, which is used to determine the first function value based on the target parameter of the target bridge damper and the preset lower bound of the spring displacement, and the target parameter includes the target total displacement, the damping section displacement at the previous moment, the preset target step size, the preset damping coefficient, the preset reference velocity, and the preset spring stiffness;
[0033] A second processing module, which is used to determine a second function value based on the target parameter and a preset upper bound of spring displacement;
[0034] A third processing module, which is used to determine spring displacement based on the bisection method, the target parameter, the first function value and the second function value, and determine a non-linear damping force based on the spring displacement and the spring stiffness;
[0035] A fourth processing module, which is used to construct a balance equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset node parameters of a target bridge damper and the non-linear damping force, where the preset node parameters include node acceleration, node velocity, and node displacement;
[0036] A fifth processing module, which is used to perform mode decomposition on the balance equation to obtain modal equations of each order of the target bridge damper, and solve the modal equations of each order based on the explicit integration method to obtain modal displacements of each order of the target bridge damper.
[0037] Combined with the second aspect, in an implementation manner, the first processing module is specifically used for:
[0038] Determine a lower bound of damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the lower bound of spring displacement;
[0039] Determine a first function value based on the lower bound of damping section velocity, the lower bound of spring displacement, the damping coefficient, the reference velocity, and the spring stiffness.
[0040] In a third aspect, an embodiment of the present application provides a bridge model solving device, where the bridge model solving device includes a processor, a memory, and a bridge model solving program stored on the memory and executable by the processor. When the bridge model solving program is executed by the processor, the steps of the bridge model solving method as described in any one of the foregoing are implemented.
[0041] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, on which a bridge model solving program is stored. When the bridge model solving program is executed by a processor, the steps of the bridge model solving method as described in any one of the foregoing are implemented.
[0042] The beneficial effects brought by the technical solution provided by the embodiment of the present application include:
[0043] The first function value and the second function value are respectively determined by the target parameter, the preset lower bound of the spring displacement, and the preset upper bound of the spring displacement. Then, the spring displacement is determined according to the bisection method, the first function value, and the second function value. The calculation by the bisection method reduces the number of iterations. The nonlinear damping force is determined according to the spring displacement and the spring stiffness. An equilibrium equation is constructed based on the preset mass matrix, the preset proportional damping matrix, the preset stiffness matrix, the preset node parameters, and the nonlinear damping force. Then, the equilibrium equation is solved according to the explicit integration method, which breaks through the limitations of the traditional method on the load term and the step size to a certain extent, thereby improving the solution efficiency of the bridge model. Description of the Drawings
[0044] Figure 1 It is a schematic flowchart of the implementation example of the bridge model solution method of this application;
[0045] Figure 2 It is a Maxwell model diagram of the bridge nonlinear damper of this application;
[0046] Figure 3 It is a schematic framework flowchart of the bridge model solution of this application;
[0047] Figure 4 For this application Figure 1 It is a refined flowchart of step S10 in this application;
[0048] Figure 5 It is a schematic flowchart of the bridge model calculation of this application;
[0049] Figure 6 It is a schematic architecture diagram of the implementation example of the bridge model solution system of this application;
[0050] Figure 7 It is a schematic hardware structure diagram of the bridge model solution device involved in the solution of the embodiment of this application. Detailed Implementation Modes
[0051] In order to enable those skilled in the art to better understand the solution of this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this application.
[0052] To make the purpose, technical solution, and advantages of this application clearer, the implementation mode of this application will be further described in detail below in conjunction with the accompanying drawings.
[0053] In the first aspect, the embodiment of this application provides a bridge model solution method.
[0054] In one embodiment, with reference to Figure 1 , Figure 1 , which is a schematic flowchart of an embodiment of the bridge model solving method of the present application. As Figure 1 shown, the bridge model solving method includes:
[0055] Step S10: Determine a first function value based on the target parameters of the target bridge damper and the preset lower bound of the spring displacement. The target parameters include the target total displacement, the damper section displacement at the previous moment, the preset target step, the preset damping coefficient, the preset reference speed, and the preset spring stiffness;
[0056] Exemplarily, in the embodiment of the present application, a simple and accurate bridge model can be quickly established by Midas Civil software first; then, the model parameters can be exported to a data analysis platform through the built-in function of Midas Civil software. The data analysis platform can be Matlab software or Python, etc., and this data analysis platform is used as a real-time hybrid test platform to complete the modeling. It should be noted that the hybrid experiment platform divides the complete test object into a numerical substructure and a physical substructure. Among them, the numerical substructure mainly refers to the linear and known-law structures in the bridge, and this part is modeled by a computer; the physical substructure mainly refers to the nonlinear and unknown-law dampers in the bridge, and this part is physically loaded by a loading system.
[0057] It can be understood that the specific steps of modeling are as follows:
[0058] Step M1: Use the Midas Civil software to establish a bridge visualization model and quickly obtain an accurate bridge numerical model. Establishing the bridge visualization model specifically includes the following steps: material definition, section definition, boundary condition establishment, load case definition, construction stage definition, etc.
[0059] Step M2: Use the built-in function of the Midas Civil software to quickly export some parameters of the bridge model. The exported parameters mainly include its mass matrix M, mode shape matrix Φ = [Φ1, Φ2, Φ 2n , and the frequency vectors ω = [ω1, ω2, ω 2n T .
[0060] Step M3: Substitute the mass matrix M and the mode shape matrix Φ into the following formula to calculate the modal mass of each order The calculation formula is:
[0061]
[0062] Among them, M * is the modal mass, and is obtained from the formula The modal stiffness K can be calculated * , and its expression is as follows:
[0063]
[0064] From the formula the modal damping C can be calculated * , and its expression is as follows:
[0065]
[0066] It should be noted that the bridge part parameters in this application also include bridge dampers. The dampers in this embodiment are viscous dampers. Referring to Figure 2 shown, the damping model can preferably be the Maxwell model, where F d is the damping force of the viscous pot section, F b is the damping force of the spring section, c d is the damping coefficient of the viscous pot section, d d is the displacement of the viscous pot section, d b is the displacement of the spring section, k b is the spring stiffness.
[0067] Specifically, after constructing the bridge model, target parameters such as the target total displacement of the target bridge damper, the damping section displacement at the previous moment, the preset damping coefficient, the preset reference speed, the preset target step length, and the preset spring stiffness are obtained. It should be noted that the preset lower bound of the spring displacement, the preset damping coefficient, the preset target step length, the preset reference speed, and the preset spring stiffness can be determined according to actual needs and are not limited here. Among them, the lower bound of the spring displacement is preferably taken as -0.01 m; according to the target total displacement, the damping section displacement at the previous moment, the step length, and the lower bound of the spring displacement, the lower bound of the damping section speed is determined, and then according to the lower bound of the damping section speed, the lower bound of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness, the first function value is determined.
[0068] Step S20: Determine the second function value based on the target parameters and the preset upper bound of the spring displacement;
[0069] Exemplarily, in the embodiment of this application, the preset upper bound of the spring displacement can be determined according to actual needs and is not limited here. Among them, the upper bound of the spring displacement is preferably taken as +0.01 m; specifically, the upper bound of the damping section speed can be determined according to the target total displacement, the step length, the damping section displacement at the previous moment, and the upper bound of the spring displacement; then according to the upper bound of the damping section speed, the upper bound of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness, the second function value is determined.
[0070] Step S30: Determine the spring displacement based on the bisection method, the target parameter, the first function value, and the second function value, and determine the nonlinear damping force based on the spring displacement and the spring stiffness;
[0071] Exemplarily, in the embodiments of the present application, the upper bound and the lower bound of the spring displacement are continuously updated through the bisection method, and judgments and adjustments are made according to the relationship between the first function value and the second function value, and then the true value of the spring displacement is gradually approximated to obtain the spring displacement; the range of the spring displacement can be reduced by half through iteration by the bisection method, reducing the number of iterations and improving the solution efficiency; then the spring displacement and the spring stiffness are multiplied to obtain the nonlinear damping force.
[0072] Step S40: Construct a balance equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset node parameters of the target bridge damper, and the nonlinear damping force, where the preset node parameters include node acceleration, node velocity, and node displacement;
[0073] Exemplarily, in the embodiments of the present application, the preset mass matrix, the preset proportional damping matrix, the preset stiffness matrix, and the preset node parameters can be determined according to actual needs and are not limited herein; the explicit nonlinear mode superposition method (ENMS) is used to consider the local nonlinear elements existing in the numerical model of the bridge structure. Specifically, the mass matrix, the proportional damping matrix, the stiffness matrix, the node acceleration, the node velocity, the node displacement, and the nonlinear damping force are substituted into the following formula to construct the balance equation, and the balance equation is:
[0074]
[0075] In the formula, M is the mass matrix, C is the proportional damping matrix, is the stiffness matrix, is the node acceleration, is the node velocity, u(t) is the node displacement, is the nonlinear damping force.
[0076] Step S50: Perform mode decomposition on the balance equation to obtain the modal equations of each order of the target bridge damper, and solve each order of the modal equations based on the explicit integration method to obtain the modal displacements of each order of the target bridge damper.
[0077] Exemplarily, in the embodiments of the present application, the mode decomposition of the balance equation obtains the decoupled modal equations as follows:
[0078]
[0079] In the formula, is the modal acceleration, is the modal velocity, Y(t) is the modal displacement, and F * (t) is the modal effective external load, all of which are N×N order matrices.
[0080] It should be noted that each row of the matrix is a mode. There are a total of zn modes, where zn is the number of structural degrees of freedom. The specific steps for solving each order of the modal equation are as follows:
[0081]
[0082] Specifically, substituting the expressions of the modal mass M * , the modal stiffness K * , the modal damping C * , and the modal effective external load F * (t) into the modal equation can obtain each order of the modal equation. Taking the nth row of the above system of equations, the nth order modal equation can be obtained, and its expression is as follows:
[0083]
[0084] In the formula: is the modal acceleration of the nth order, is the modal velocity of the nth order, y(t) n is the modal displacement of the nth order, ζ n is the damping coefficient of the nth order, ω n is the structural frequency of the nth order, f(t) n is the modal force of the nth order, m n is the modal mass of the nth order.
[0085] The explicit integration method is used to solve each order of the modal equation. Taking the nth order as an example, the modal displacement of the current integration step is obtained by solving the modal displacements of the previous two integration steps, the modal displacement of the previous integration step, and the modal effective external load. The formula is as follows:
[0086]
[0087] In the formula, y i-1,n is the modal displacement of the previous two integration steps, y i,n is the modal displacement of the previous integration step, f i+1,n is the discretized modal effective external load, and y i+1,n is the modal displacement of the current integration step.
[0088] Repeat the above steps until the modal displacements of each order of the target bridge damper are calculated.
[0089] It should be noted that with reference to Figure 3As shown, in the embodiment of the present application, a bridge model is quickly and accurately established through Midas Civil software, and by exporting and adjusting the model parameters, a numerical model of a real-time hybrid test platform is constructed in Matlab, solving the problem that it is difficult to efficiently establish a numerical model for real-time hybrid tests by traditional methods; at the same time, by using the explicit nonlinear mode superposition method for dynamic analysis of the bridge structure and constructing an equilibrium equation to solve the modal displacements of each order of the equilibrium equation, the local nonlinear characteristics of the bridge model are accurately considered, greatly improving the solution speed and accuracy of the test model; in addition, to meet the real-time requirements of real-time hybrid tests, the present application adopts a multi-threaded parallel computing technology of CPU and GPU, significantly improving the solution efficiency of the numerical model.
[0090] In the present application, the first function value and the second function value are respectively determined through the target parameter, the preset lower bound of the spring displacement, and the preset upper bound of the spring displacement, and then the spring displacement is determined according to the bisection method, the first function value, and the second function value. The calculation by the bisection method reduces the number of iterations; the nonlinear damping force is determined according to the spring displacement and the spring stiffness, and an equilibrium equation is constructed based on the preset mass matrix, the preset proportional damping matrix, the preset stiffness matrix, the preset node parameters, and the nonlinear damping force, and then the equilibrium equation is solved according to the explicit integration method, breaking through the limitations of traditional methods on the load term and the step size to a certain extent, thereby improving the solution efficiency of the bridge model.
[0091] Further, in one embodiment, referring to Figure 4 As shown, determining the first function value based on the target parameter of the target bridge damper and the preset lower bound of the spring displacement includes:
[0092] Step S101: Determine the lower bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the lower bound of the spring displacement;
[0093] Step S102: Determine the first function value based on the lower bound of the damping section velocity, the lower bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness.
[0094] Exemplarily, in the embodiment of the present application, the target total displacement, the damping section displacement at the previous moment, the step size, and the lower bound of the spring displacement are substituted into the following calculation formula to obtain the lower bound of the damping section velocity, and the calculation formula is:
[0095]
[0096] In the formula, d is the target total displacement, d d,i-1 is the damping section displacement at the previous moment, d sa is the lower bound of the spring displacement, Δt is the step size, and v da is the lower bound of the damping section velocity.
[0097] Substitute the lower bound of the damping section velocity, the lower bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness into the following calculation formula to obtain the first function value. The calculation formula is:
[0098]
[0099] In the formula, v da is the lower bound of the damping section velocity, d sa is the lower bound of the spring displacement, c d is the damping coefficient, v0 is the reference velocity, k s is the spring stiffness, g a is the first function value.
[0100] Furthermore, in one embodiment, determining the second function value based on the target parameter and the preset upper bound of the spring displacement includes:
[0101] Determine the upper bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the upper bound of the spring displacement;
[0102] Determine the second function value based on the upper bound of the damping section velocity, the upper bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness.
[0103] Exemplarily, in the embodiments of the present application, substitute the target total displacement, the damping section displacement at the previous moment, the step size, and the upper bound of the spring displacement into the following calculation formula to obtain the upper bound of the damping section velocity. The calculation formula is:
[0104]
[0105] In the formula, d is the target total displacement, d d,i-1 is the damping section displacement at the previous moment, d sb is the upper bound of the spring displacement, Δt is the step size, v db is the upper bound of the damping section velocity.
[0106] Substitute the upper bound of the damping section velocity, the upper bound of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness into the following calculation formula to obtain the second function value. The calculation formula is:
[0107]
[0108] In the formula, v db is the upper bound of the damping section velocity, d sb is the upper bound of the spring displacement, c d is the damping coefficient, v0 is the reference velocity, k s is the spring stiffness, g b is the second function value.
[0109] Further, in one embodiment, before the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value, the following steps are further included:
[0110] Judge whether the first function value and the second function value have different signs;
[0111] If so, execute the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value;
[0112] If not, update the upper bound and the lower bound of the spring displacement to make the first function value and the second function value have different signs, and execute the step of determining the spring displacement based on the first function value and the second function value.
[0113] Exemplarily, in the embodiment of the present application, judge whether the first function value and the second function value have different signs; if the first function value and the second function value have different signs, it means that the spring displacement exists between the lower bound and the upper bound of the spring displacement, then execute the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value; if the first function value and the second function value have the same sign, it means that the spring displacement does not exist between the lower bound and the upper bound of the spring displacement, then update the upper bound and the lower bound of the spring displacement, and then determine the updated first function value based on the new lower bound of the spring displacement and the target parameter, and determine the updated second function value based on the new upper bound of the spring displacement and the target parameter, until the first function value and the second function value have different signs, and then execute the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value.
[0114] Further, in one embodiment, the step of determining the spring displacement based on the first function value and the second function value includes:
[0115] Determine the spring displacement midpoint based on the dichotomy method, the upper bound and the lower bound of the spring displacement;
[0116] Determine the damping section speed midpoint based on the spring displacement midpoint, the target total displacement, the target step length, and the damping section displacement at the previous moment;
[0117] Determine the third function value based on the damping section speed midpoint, the spring displacement midpoint, the damping coefficient, the reference speed, and the spring stiffness;
[0118] Determine the spring displacement based on the first function value, the second function value, the third function value, and the spring displacement midpoint.
[0119] Exemplarily, in an embodiment of the present application, the midpoint of the upper bound and the lower bound of the spring displacement is obtained by the bisection method, and the upper bound and the lower bound of the spring displacement are substituted into the following formula to obtain the midpoint of the spring displacement. The calculation formula is as follows:
[0120]
[0121] In the formula, d sa is the lower bound of the spring displacement, d sb is the upper bound of the spring displacement, and d st is the midpoint of the spring displacement.
[0122] The midpoint of the damping section velocity is obtained by substituting the midpoint of the spring displacement, the target total displacement, the step size, and the damping section displacement at the previous moment into the following calculation formula. The calculation formula is as follows:
[0123]
[0124] In the formula, d is the target total displacement, d d,i-1 is the damping section displacement at the previous moment, d st is the midpoint of the spring displacement, Δt is the step size, and v dt is the midpoint of the damping section velocity.
[0125] The third function value is obtained by substituting the midpoint of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness into the following calculation formula. The calculation formula is as follows:
[0126]
[0127] In the formula, v dt is the midpoint of the damping section velocity, d st is the midpoint of the spring displacement, c d is the damping coefficient, v0 is the reference velocity, k s is the spring stiffness, and g b is the third function value.
[0128] Further, in an embodiment, determining the spring displacement based on the first function value, the second function value, the third function value, and the midpoint of the spring displacement includes:
[0129] If the first function value and the third function value have different signs, a fourth function value is determined based on the upper bound of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness;
[0130] When the absolute value of the difference between the fourth function value and the first function value is less than a preset difference threshold, the midpoint of the spring displacement is used as the spring displacement;
[0131] If the second function value and the third function value have different signs, a fifth function value is determined based on the lower bound of the damping section speed, the midpoint of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness;
[0132] When the absolute value of the difference between the fifth function value and the second function value is less than a preset difference threshold, the midpoint of the spring displacement is taken as the spring displacement.
[0133] Exemplarily, in the embodiment of the present application, since the first function value and the second function value have different signs, it indicates that the first function value is negative, the second function value is positive, and the third function value is between the first function value and the second function value. Then the third function value can be positive or negative; when the third function value is positive, it indicates that the first function value and the third function value have different signs, and the second function value and the third function value have the same sign. Therefore, the spring displacement exists between the first function value and the third function value. Then, the upper bound of the damping section speed, the midpoint of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness are substituted into the following formula to obtain the fourth function value. The calculation formula is:
[0134]
[0135] In the formula, v db is the upper bound of the damping section speed, d st is the midpoint of the spring displacement, c d is the damping coefficient, v0 is the reference speed, k s is the spring stiffness, g e is the fourth function value.
[0136] It should be noted that the preset difference threshold can be determined according to actual needs and is not limited here. Preferably, it is taken as 0.0000001. When the absolute value of the difference between the fourth function value and the first function value is less than the difference threshold, the midpoint of the spring displacement is taken as the spring displacement; if the absolute value of the difference between the fourth function value and the first function value is not less than the difference threshold, the upper bound and the lower bound of the spring displacement are continuously updated until the absolute value of the difference between the fourth function value and the first function value is less than the difference threshold, and then the midpoint of the spring displacement is taken as the spring displacement.
[0137] Among them, when the third function value is negative, it indicates that the second function value and the third function value have different signs, and the first function value and the third function value have the same sign. Therefore, the spring displacement exists between the second function value and the third function value. Then, the lower bound of the damping section speed, the midpoint of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness are substituted into the following formula to obtain the fifth function value. The calculation formula is:
[0138]
[0139] In the formula, v dais the upper bound of the damping section speed, d st is the midpoint of the spring displacement, c d is the damping coefficient, v0 is the reference speed, k s is the spring stiffness, g f is the value of the fourth function.
[0140] It can be understood that when the absolute value of the difference between the fifth function value and the second function value is less than the difference threshold, the midpoint of the spring displacement is taken as the spring displacement; if the absolute value of the difference between the fifth function value and the second function value is not less than the difference threshold, the upper bound and the lower bound of the spring displacement are continuously updated until the absolute value of the difference between the fifth function value and the second function value is less than the difference threshold, and then the midpoint of the spring displacement is taken as the spring displacement.
[0141] In the embodiments of the present application, since the number of degrees of freedom of the bridge model is often large, simplifying the model will lose the accuracy of the results. Therefore, a CPU combined with GPU calculation idea is provided. Referring to Figure 5 as shown, the calculation efficiency is further improved to meet the requirements of the calculation time of the real-time hybrid test, which mainly includes the following steps:
[0142] Step P1: The CPU is mainly responsible for calculating the load terms of the typical equation, including using the bisection method to iteratively solve the nonlinear damping force, solving the effective elastic force, accumulating the damping force, the effective elastic force, the external load and other parameters. The advantage of "the CPU emphasizes program execution efficiency" can be fully utilized to improve the calculation efficiency of data.
[0143] Step P2: The GPU is mainly responsible for parallel computing the solutions of the typical equation. The GPU of the computer is called through the Parallel Computing Toolbox in Matlab; through GPU parallel computing, the advantage of "the GPU has high parallel numerical computing capabilities for graphics or non-graphics" can be fully utilized to significantly improve the calculation speed of the numerical model.
[0144] Step P3: By combining the CPU and the GPU, the fast solution of the modal equation is realized, thereby greatly improving the calculation speed of the numerical model and meeting the requirements of the real-time hybrid test.
[0145] In the second aspect, the embodiments of the present application also provide a bridge model solving system.
[0146] In one embodiment, referring to Figure 6 , Figure 6 is the schematic diagram of the functional modules of the embodiment of the bridge model solving system of the present application. As Figure 6 shown, the bridge model solving system includes:
[0147] The first processing module is configured to determine a first function value based on the target parameters of the target bridge damper and a preset lower bound of the spring displacement, where the target parameters include the target total displacement, the damping section displacement at the previous moment, a preset target step size, a preset damping coefficient, a preset reference speed, and a preset spring stiffness;
[0148] The second processing module is configured to determine a second function value based on the target parameters and a preset upper bound of the spring displacement;
[0149] The third processing module is configured to determine the spring displacement based on the bisection method, the target parameters, the first function value, and the second function value, and determine the non-linear damping force based on the spring displacement and the spring stiffness;
[0150] The fourth processing module is configured to construct an equilibrium equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset node parameters of the target bridge damper, and the non-linear damping force, where the preset node parameters include node acceleration, node velocity, and node displacement;
[0151] The fifth processing module is configured to perform mode decomposition on the equilibrium equation to obtain modal equations of each order of the target bridge damper, and solve the modal equations of each order based on the explicit integration method to obtain modal displacements of each order of the target bridge damper.
[0152] Further, in an embodiment, the first processing module is specifically configured to:
[0153] Determine a lower bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the lower bound of the spring displacement;
[0154] Determine the first function value based on the lower bound of the damping section velocity, the lower bound of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness.
[0155] Further, in an embodiment, the second processing module is specifically configured to:
[0156] Determine an upper bound of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step size, and the upper bound of the spring displacement;
[0157] Determine the second function value based on the upper bound of the damping section velocity, the upper bound of the spring displacement, the damping coefficient, the reference speed, and the spring stiffness.
[0158] Further, in an embodiment, the third processing module is specifically configured to:
[0159] Judge whether the first function value and the second function value have different signs;
[0160] If so, perform the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value, and the second function value;
[0161] If not, update the upper bound and the lower bound of the spring displacement to make the first function value and the second function value have different signs, and perform the step of determining the spring displacement based on the first function value and the second function value.
[0162] Further, in an embodiment, the third processing module is further specifically configured to:
[0163] Determine the midpoint of the spring displacement based on the dichotomy method, the upper bound of the spring displacement, and the lower bound of the spring displacement;
[0164] Determine the midpoint of the damping section velocity based on the midpoint of the spring displacement, the target total displacement, the target step size, and the damping section displacement at the previous moment;
[0165] Determine the third function value based on the midpoint of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness;
[0166] Determine the spring displacement based on the first function value, the second function value, the third function value, and the midpoint of the spring displacement.
[0167] Further, in an embodiment, the third processing module is further specifically configured to:
[0168] If the first function value and the third function value have different signs, determine the fourth function value based on the upper bound of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness;
[0169] When the absolute value of the difference between the fourth function value and the first function value is less than a preset difference threshold, use the midpoint of the spring displacement as the spring displacement;
[0170] If the second function value and the third function value have different signs, determine the fifth function value based on the lower bound of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness;
[0171] When the absolute value of the difference between the fifth function value and the second function value is less than a preset difference threshold, use the midpoint of the spring displacement as the spring displacement.
[0172] In this application, the first function value and the second function value are respectively determined by the target parameter, the preset lower bound of the spring displacement, and the preset upper bound of the spring displacement. Then, the spring displacement is determined according to the bisection method, the first function value, and the second function value. The calculation using the bisection method reduces the number of iterations. The nonlinear damping force is determined based on the spring displacement and the spring stiffness. An equilibrium equation is constructed based on the preset mass matrix, the preset proportional damping matrix, the preset stiffness matrix, the preset nodal parameters, and the nonlinear damping force. Then, the equilibrium equation is solved according to the explicit integration method, which breaks through the limitations of the traditional method on the load term and the step size to a certain extent, thereby improving the solution efficiency of the bridge model.
[0173] Among them, the functional implementation of each module in the above bridge model solution system corresponds to each step in the above bridge model solution method embodiment, and its functions and implementation processes will not be elaborated here one by one.
[0174] In a third aspect, an embodiment of this application provides a bridge model solution device. The bridge model solution device can be a device with data processing functions such as a personal computer (PC), a laptop computer, or a server.
[0175] Refer to Figure 7 , Figure 7 which is a schematic diagram of the hardware structure of the bridge model solution device involved in the embodiment of this application. In the embodiment of this application, the bridge model solution device may include a processor, a memory, a communication interface, and a communication bus.
[0176] Among them, the communication bus can be of any type and is used to interconnect the processor, the memory, and the communication interface.
[0177] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces, etc., which are used to implement the interconnection of internal components of the bridge model solution device, as well as interfaces for interconnecting the bridge model solution device with other devices (such as other computing devices or user devices). The physical interface can be an Ethernet interface, a fiber optic interface, an ATM interface, etc.; the user device can be a display screen (Display), a keyboard (Keyboard), etc.
[0178] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical memory, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.
[0179] The processor can be a general-purpose processor, which can call the bridge model solving program stored in the memory and execute the bridge model solving method provided by the embodiments of the present application. For example, the general-purpose processor can be a central processing unit (CPU). Among them, the method executed when the bridge model solving program is called can refer to the various embodiments of the bridge model solving method of the present application, which will not be elaborated here.
[0180] Those skilled in the art can understand that Figure 7 the hardware structure shown in
[0181] In a fourth aspect, the embodiments of the present application further provide a readable storage medium.
[0182] The bridge model solving program is stored on the readable storage medium of the present application. When the bridge model solving program is executed by a processor, the steps of the bridge model solving method as described above are implemented.
[0183] Among them, the method implemented when the bridge model solving program is executed can refer to the various embodiments of the bridge model solving method of the present application, which will not be elaborated here.
[0184] The terms "including" and "having" and any variations thereof in the specification and claims of the present application and the above-mentioned drawings are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products or devices. The descriptions of the terms "first", "second", "third", etc. are used to distinguish different objects, etc., which do not represent a sequence, nor do they limit that "first", "second", and "third" are different types.
[0185] In the description of the embodiments of the present application, terms such as "exemplary", "for example", or "for instance" are used to represent examples, illustrations, or explanations. Any embodiment or design solution described as "exemplary", "for example", or "for instance" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of terms such as "exemplary", "for example", or "for instance" is intended to present related concepts in a specific manner.
[0186] In the description of the embodiments of the present application, unless otherwise specified, " / " means "or". For example, A / B may represent A or B. The "and / or" in the text is merely a description of the association relationship between associated objects, indicating that there can be three relationships. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of the present application, "a plurality of" means two or more than two.
[0187] In some processes described in the embodiments of the present application, there are multiple operations or steps that appear in a specific order. However, it should be understood that these operations or steps may not be executed in the order in which they appear in the embodiments of the present application or may be executed in parallel. The serial numbers of the operations are only used to distinguish different operations, and the serial numbers themselves do not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed in order or in parallel, and these operations or steps may be combined.
[0188] It should be noted that the serial numbers of the above embodiments of the present application are only for description and do not represent the superiority or inferiority of the embodiments.
[0189] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases, the former is a better implementation method. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disc) as described above and includes several instructions for causing a terminal device to execute the methods described in the various embodiments of the present application.
[0190] The above are only the preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structural or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present application.
Claims
1. A bridge model solution method, characterized in that: The bridge model solving method comprises: Determining a first function value based on target parameters of a target bridge damper and a preset lower bound of a spring displacement, wherein the target parameters include a target total displacement, a damping section displacement at a previous moment, a preset target step length, a preset damping coefficient, a preset reference speed, and a preset spring stiffness; Determining a second function value based on the target parameter and a preset upper bound of the spring displacement; determining a spring displacement based on a dichotomy method, the target parameter, the first function value, and the second function value, and determining a nonlinear damping force based on the spring displacement and the spring stiffness; Constructing a balance equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset node parameters of a target bridge damper, and the nonlinear damping force, wherein the preset node parameters include node acceleration, node velocity, and node displacement; Decomposing the equilibrium equation by vibration mode to obtain each order modal equation of the target bridge damper, solving each order modal equation based on explicit integration method to obtain each order modal displacement of the target bridge damper; Wherein, before the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value and the second function value, the method further includes: Determine whether the first function value and the second function value have different signs; If yes, then executing the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value and the second function value; If not, updating the upper bound of the spring displacement and the lower bound of the spring displacement so that the first function value and the second function value have different signs, and performing the step of determining the spring displacement based on the dichotomy, the target parameter, the first function value and the second function value; The step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value and the second function value comprises: Determine the midpoint of the spring displacement based on the dichotomy method, the upper bound of the spring displacement, and the lower bound of the spring displacement; Determine the damping section velocity midpoint based on the spring displacement midpoint, the target total displacement, the target step length, and the damping section displacement at the previous moment; Determining a third function value based on the damping section velocity midpoint, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness; Determining the spring displacement based on the first function value, the second function value, the third function value, and the midpoint of the spring displacement; determining the spring displacement based on the first function value, the second function value, the third function value, and the midpoint of the spring displacement comprises: If the first function value and the third function value have different signs, a fourth function value is determined based on the upper limit of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness; When the absolute value of the difference between the fourth function value and the first function value is less than a preset difference threshold, the midpoint of the spring displacement is used as the spring displacement; If the second function value and the third function value have different signs, a fifth function value is determined based on the damping section velocity lower bound, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness; When the absolute value of the difference between the fifth function value and the second function value is less than a preset difference threshold, the midpoint of the spring displacement is used as the spring displacement.
2. The bridge model solving method according to claim 1, characterized in that: The step of determining the first function value based on the target parameter of the target bridge damper and the preset lower bound of the spring displacement includes: Determining a damping section velocity lower bound based on the target total displacement, the damping section displacement at the previous moment, the target step length, and the spring displacement lower bound; A first function value is determined based on the damping section velocity lower bound, the spring displacement lower bound, the damping coefficient, the reference velocity, and the spring stiffness.
3. The bridge model solving method according to claim 1, characterized in that: Determining the second function value based on the target parameter and a preset upper limit of the spring displacement includes: Determine the upper limit of the damping section velocity based on the target total displacement, the damping section displacement at the previous moment, the target step length, and the upper limit of the spring displacement; A second function value is determined based on the damping section velocity upper limit, the spring displacement upper limit, the damping coefficient, the reference velocity, and the spring stiffness.
4. A bridge model solving system, characterized in that: The bridge model solving system comprises: A first processing module, which is used to determine a first function value based on target parameters of a target bridge damper and a preset lower bound of a spring displacement, wherein the target parameters include a target total displacement, a damping section displacement at a previous moment, a preset target step length, a preset damping coefficient, a preset reference speed, and a preset spring stiffness; A second processing module, which is used to determine a second function value based on the target parameter and a preset upper limit of the spring displacement; a third processing module, configured to determine a spring displacement based on a dichotomy method, the target parameter, the first function value, and the second function value, and to determine a nonlinear damping force based on the spring displacement and the spring stiffness; A fourth processing module, which is used to construct an equilibrium equation based on a preset mass matrix, a preset proportional damping matrix, a preset stiffness matrix, preset node parameters of the target bridge damper and the nonlinear damping force, wherein the preset node parameters include node acceleration, node velocity, and node displacement; A fifth processing module, which is used to perform vibration mode decomposition on the equilibrium equation to obtain each order modal equation of the target bridge damper, and solve each order modal equation based on an explicit integration method to obtain each order modal displacement of the target bridge damper; Wherein, the third processing module is specifically used for: Determine whether the first function value and the second function value have different signs; If yes, then executing the step of determining the spring displacement based on the dichotomy method, the target parameter, the first function value and the second function value; If not, updating the upper bound of the spring displacement and the lower bound of the spring displacement so that the first function value and the second function value have different signs, and performing the step of determining the spring displacement based on the dichotomy, the target parameter, the first function value and the second function value; The third processing module is further specifically used for: Determine the midpoint of the spring displacement based on the dichotomy method, the upper bound of the spring displacement, and the lower bound of the spring displacement; Determine the damping section velocity midpoint based on the spring displacement midpoint, the target total displacement, the target step length, and the damping section displacement at the previous moment; Determining a third function value based on the damping section velocity midpoint, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness; Determine the spring displacement based on the first function value, the second function value, the third function value and the midpoint of the spring displacement; the third processing module is further configured to: If the first function value and the third function value have different signs, a fourth function value is determined based on the upper limit of the damping section velocity, the midpoint of the spring displacement, the damping coefficient, the reference velocity, and the spring stiffness; When the absolute value of the difference between the fourth function value and the first function value is less than a preset difference threshold, the midpoint of the spring displacement is used as the spring displacement; If the second function value and the third function value have different signs, a fifth function value is determined based on the damping section velocity lower bound, the spring displacement midpoint, the damping coefficient, the reference velocity, and the spring stiffness; When the absolute value of the difference between the fifth function value and the second function value is less than a preset difference threshold, the midpoint of the spring displacement is used as the spring displacement.
5. The bridge model solving system according to claim 4, characterized in that: The first processing module is specifically used for: Determining a damping section velocity lower bound based on the target total displacement, the damping section displacement at the previous moment, the target step length, and the spring displacement lower bound; A first function value is determined based on the damping section velocity lower bound, the spring displacement lower bound, the damping coefficient, the reference velocity, and the spring stiffness.
6. A bridge model solving device, characterized in that: The bridge model solving device comprises a processor, a memory, and a bridge model solving program stored in the memory and executable by the processor, wherein when the bridge model solving program is executed by the processor, the steps of the bridge model solving method according to any one of claims 1 to 3 are implemented.
7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a bridge model solving program, wherein when the bridge model solving program is executed by a processor, the steps of the bridge model solving method according to any one of claims 1 to 3 are implemented.