Method and system for calculating average temperature of cross section of main cable of suspension bridge

Abstract

The invention relates to a method for calculating the average temperature of the cross section of a main cable of a suspension bridge, and the method comprises the steps: carrying out the dimension reduction based on a two-dimensional plane heat transfer model, so as to obtain a one-dimensional radial heat transfer model; performing space and time discretization on the one-dimensional radial heat transfer model to discretize the radial continuous temperature field of the main cable into the temperature of space-time grid points; finite difference decomposition of the one-dimensional radial heat transfer model is obtained through difference, and a difference format is determined; gradually solving the temperature of each node in each time step to form a temperature field matrix; and calculating the area weighted average temperature to obtain the average temperature of the cross section of the main cable. According to the method, a two-dimensional plane heat transfer model is simplified into a one-dimensional radial heat transfer model based on a cross section heat energy change equivalence principle, a computational domain is reduced to a radius line from a whole main cable cross section, and consumption and requirements on computational resources are greatly reduced; and a differential equation is converted into a linear equation set based on a finite difference method, so that the calculation efficiency is greatly improved while the same precision is maintained, and the calculation speed is improved from an hour level to a sub-second level.

Description

Technical Field

[0001] This invention relates to the field of temperature field monitoring technology, specifically to a method and system for calculating the average temperature of the cross-section of the main cable of a suspension bridge. Background Technology

[0002] In recent years, with the continuous increase in the span of suspension bridges, the diameter of their main cables has also increased, with some suspension bridges having main cable diameters exceeding 1 meter. The rate of temperature change inside large-diameter main cables lags behind changes in ambient temperature, necessitating the calculation of the average temperature across the entire cross-section based on the temperature field distribution. The alignment of the main cable in long-span suspension bridges is highly sensitive to temperature changes, making accurate calculation of the average temperature of the main cable cross-section crucial for correcting temperature deformation. For example, after the main cable of a suspension bridge is erected, i.e., in an empty cable state, it is necessary to measure the actual cable alignment and tower top coordinates during construction. Based on the average temperature of the main cable at the time of measurement, the measured cable alignment is corrected to the design temperature state, and then compared with the designed cable alignment to obtain the construction error of the main cable alignment. This provides data support for subsequent cable clamp position layout and suspender length correction.

[0003] The cross-section of the main cable of a suspension bridge consists of steel wires and pores, with a porosity typically around 20%. Due to the influence of air within the pores, the thermal diffusivity of the main cable across its cross-section is much lower than that of the steel wires, resulting in a highly uneven temperature distribution within the cross-section.

[0004] Because it is difficult to place temperature sensors inside the main cable, the internal temperature field distribution cannot be directly obtained. The current common practice is to calculate the temperature field distribution of the main cable cross-section using the finite element method based on the measured temperature on the main cable surface, and then take the area-weighted average of the temperatures of each element in the cross-section as the cross-sectional average temperature.

[0005] In related technologies, calculating the transient temperature field of the main cable cross-section using the finite element method requires finely meshed elements. Assuming the main cable cross-section has a diameter of 1m, meshing at 2.5cm intervals results in approximately 3000 elements and 1600 nodes. Using ANSYS finite element software for calculation not only places high demands on the CPU and memory of the computing equipment, but more importantly, it results in long solution times and low computational efficiency. Calculating 5000 time steps takes nearly an hour, making it difficult to meet the needs of real-time online monitoring or parameter research. Summary of the Invention

[0006] This application provides a method and system for calculating the average temperature of the cross section of the main cable of a suspension bridge, solving the technical problems of long solution time and low calculation efficiency when calculating the transient temperature field of the main cable cross section based on the finite element method in related technologies.

[0007] This application provides a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge, which includes the following steps: The dimensionality of the two-dimensional planar heat transfer model is reduced to obtain a one-dimensional radial heat transfer model. The one-dimensional radial heat transfer model is discretized in space and time to obtain a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points ; in, T This indicates the temperature at a radial point within the cross-section of the main cable. t Indicates time; r The polar radius represents the distance from a point on a plane to the origin; the cross-sectional radius of the main cable is divided into... n Each unit, and the nodes between units form n +1 spatial grid point, subscript i The spatial grid point number is represented; the time domain is divided into multiple time steps. superscript p Indicates the time grid point number; The finite difference decomposition of the one-dimensional radial heat transfer model is obtained through finite difference, and the finite difference scheme is determined. The temperature at each node at each time step is solved step by step according to the difference scheme to form a temperature field matrix; The area-weighted average temperature is calculated based on the temperature field matrix to obtain the average temperature of the main cable cross section.

[0008] In one implementation, the dimensionality reduction based on the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model includes: A two-dimensional planar heat transfer model is established, represented as follows: ; Among them, the temperature at a certain radial point within the cross-section of the main cable T It's about time. t and spatial coordinates ( r, θ The function, r θ is the polar radius, representing the distance from a point on the plane to the origin; θ is the polar angle, representing the angle between the line connecting the point and the origin and the positive semi-axis. ρ , c , k These represent the equivalent density, equivalent specific heat capacity, and equivalent thermal conductivity of the main cable cross-section, taking into account both steel wire and pore air. Using the average temperature of the main cable's circumferential surface as the boundary temperature, a dimensionality reduction is performed to obtain the one-dimensional radial heat transfer model, which is expressed as: ; Where α represents the thermal diffusivity of the main cable cross section.

[0009] In one embodiment, a plurality of temperature sensors are arranged at equal intervals on the circumferential surface of the main cable to measure the average surface temperature of the main cable at various times, thereby obtaining a time series of the average surface temperature of the main cable. , which is the boundary temperature.

[0010] In one implementation, the one-dimensional radial heat transfer model is discretized spatially and temporally, resulting in a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points include: The one-dimensional radial heat transfer model is discretized in space and expressed as follows: , i =0,1,2,…, n , , R Indicates the cross-sectional radius of the main cable; Discretizing the one-dimensional radial heat transfer model over time, it is expressed as: , p =0,1,2,…, n t , n t This represents the total number of time steps required to solve the problem; Continuous temperature field in the radial direction of the main cable Temperature discretized into spatiotemporal grid points .

[0011] In one implementation, the finite difference decomposition of the one-dimensional radial heat transfer model is obtained through finite difference. When determining the finite difference scheme, any one of the forward Euler method, backward Euler method, or Crank-Nicolson method is used.

[0012] In one implementation, the temperature at each node at each time step is solved step by step according to the difference scheme to form a temperature field matrix. include: Set the initial temperature, to p At the initial moment when the value is 0, the average surface temperature of the main cable is the initial temperature of each node, i.e. ; A boundary temperature is set, and the average temperature at each moment is applied at the outer end of the main cable radius. , p =1,2,…, at the center of the main cable, the temperature gradient is 0, that is… ; since p Starting from the initial time when = 0, a system of linear equations is formed based on the initial temperature, boundary temperature, and difference scheme. The temperature at each node of each time step is solved step by step to form the temperature field matrix. .

[0013] In one implementation, when the difference scheme is the forward Euler method, the system of linear equations is expressed as: ; in, M for( n +1) order tridiagonal matrix, , These represent the temperatures of each node along the radius of the current time step and the previous time step, respectively.

[0014] In one embodiment, when the difference scheme is the backward Euler method or the Crank-Nicolson method, the system of linear equations is expressed as: ; in, M for( n +1) order tridiagonal matrix, , These represent the temperatures of each node along the radius of the current time step and the previous time step, respectively.

[0015] In one embodiment, when calculating the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable cross-section, The calculation formula is: .

[0016] This application also provides a system for calculating the average cross-sectional temperature of the main cable of a suspension bridge, using the method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in any of the above claims, which includes: The model creation module is configured to reduce the dimensionality of the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model. The discretization module is configured to: spatially and temporally discretize the one-dimensional radial heat transfer model, thereby ensuring a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points ; in, T This indicates the temperature at a radial point within the cross-section of the main cable. t Indicates time; r The polar radius represents the distance from a point on a plane to the origin; the cross-sectional radius of the main cable is divided into... n Each unit, and the nodes between units form n +1 spatial grid point, subscript i The spatial grid point number is represented; the time domain is divided into multiple time steps. superscript p Indicates the time grid point number; The difference calculation module is configured to: obtain the finite difference decomposition of the one-dimensional radial heat transfer model through difference, and determine the difference format; The first temperature calculation module is configured to: solve for the temperature of each node at each time step step by step according to the differential scheme to form a temperature field matrix; The second temperature calculation module is configured to calculate the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable cross section.

[0017] The beneficial effects of the technical solutions provided in this application include: This application provides a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge. Based on the equivalent principle of cross-sectional thermal energy change, the two-dimensional planar heat transfer model is simplified into a one-dimensional radial heat transfer model, eliminating the angular direction component and realizing model dimensionality reduction. The computational domain is reduced from the entire main cable cross-section to the radius line, avoiding the problem of needing to divide fine mesh in the traditional finite element method, and greatly reducing the consumption and requirements of computing resources. Furthermore, based on the finite difference method, the differential equation is transformed into a system of linear equations, which greatly improves the computational efficiency while maintaining the same accuracy, and the calculation speed is increased from "hours" to "sub-seconds". Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the steps of a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge in one embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the cross-section of the main cable and strands of a suspension bridge in one embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram of the spatial and temporal discretization of the temperature field at the surface temperature measurement point of the main cable and in the radial direction, according to an embodiment of the present invention.

[0022] Figure 4 This is a schematic diagram of the main cable circular cross-section radius node and unit number in one embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram of the finite difference scheme of a one-dimensional radial heat transfer model in one embodiment of the present invention.

[0024] Figure 6 This is a time history curve of the measured value and arithmetic mean of the surface temperature sensor of the main cable of a suspension bridge in one embodiment of the present invention.

[0025] Figure 7This is a mesh diagram of the main cable cross-section elements generated by a certain finite element software in one embodiment of the present invention.

[0026] Figure 8 This is a comparison diagram of the temperature field of the main cable section at step 5100 of a certain finite element software and the calculation method provided by the present invention in one embodiment of the present invention.

[0027] Figure 9 This is a comparison chart of the average temperature time history curves of the main cable cross section calculated by a certain finite element software and the calculation method provided by the present invention in one embodiment of the present invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0029] This application provides a method and system for calculating the average temperature of the cross-section of the main cable of a suspension bridge, which can solve the technical problems of long solution time and low calculation efficiency when calculating the transient temperature field of the main cable cross-section based on the finite element method in related technologies.

[0030] like Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge in one embodiment of the present invention.

[0031] This embodiment provides a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge, which includes the following steps: Step S1: Dimensionality reduction is performed based on the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model; Step S2: Discretize the one-dimensional radial heat transfer model in space and time to obtain a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points ; in, T This indicates the temperature at a radial point within the cross-section of the main cable. t Indicates time; r The polar radius represents the distance from a point on a plane to the origin; the cross-sectional radius of the main cable is divided into... n Each unit, and the nodes between units form n +1 spatial grid point, subscript i The spatial grid point number is represented; the time domain is divided into multiple time steps. superscriptp Indicates the time grid point number; Step S3: Obtain the finite difference decomposition of the one-dimensional radial heat transfer model through finite difference, and determine the finite difference scheme; Step S4: Solve for the temperature at each node at each time step step by step according to the difference scheme to form the temperature field matrix; Step S5: Calculate the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable section.

[0032] This embodiment provides a method for calculating the average temperature of the cross-section of the main cable of a suspension bridge. Based on the equivalent principle of cross-sectional thermal energy change, the two-dimensional planar heat transfer model is simplified into a one-dimensional radial heat transfer model, eliminating the angular direction component and realizing model dimensionality reduction. The computational domain is reduced from the entire main cable cross-section to the radius line, avoiding the problem of needing to divide fine mesh in the traditional finite element method, and greatly reducing the consumption and requirements of computing resources. Furthermore, based on the finite difference method, the differential equation is transformed into a system of linear equations, which greatly improves the computational efficiency while maintaining the same accuracy, and the calculation speed is increased from "hours" to "sub-seconds".

[0033] The following provides a detailed explanation of each step.

[0034] like Figure 2 As shown, Figure 2 This is a schematic diagram of the cross-section of the main cable and strands of a suspension bridge in one embodiment of the present invention.

[0035] Taking a suspension bridge as an example, the main cable cross-section is composed of 217 strands of 127 wires with a diameter of 5.6mm, the cross-sectional diameter is 1039.4mm, and the porosity of the cable clamp outer cross-section is 20%.

[0036] In one embodiment, step S1, reducing the dimensionality of the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model, includes: Step S11: Establish a two-dimensional planar heat transfer model, represented as: ; Among them, the temperature at a certain radial point within the cross-section of the main cable T It's about time. t and spatial coordinates ( r, θ The function, r θ is the polar radius, representing the distance from a point on the plane to the origin; θ is the polar angle, representing the angle between the line connecting the point and the origin and the positive semi-axis. ρ , c , k These represent the equivalent density, equivalent specific heat capacity, and equivalent thermal conductivity of the main cable cross-section, taking into account both steel wire and pore air.

[0037] Specifically, since the axial length of the main cable is much larger than the cross-sectional diameter, it can be regarded as an infinitely long cylinder heat transfer problem, and its differential equation in the polar coordinate system is expressed as the above two-dimensional planar heat transfer model.

[0038] Step S12: Using the average temperature of the circumferential surface of the main cable as the boundary temperature, the dimensions are reduced to obtain a one-dimensional radial heat transfer model.

[0039] Specifically, based on the principle of equivalent cross-sectional thermal energy change, the two-dimensional planar heat transfer model is simplified into a one-dimensional radial heat transfer model: Since the engineering focus is mainly on the average temperature of the main cable cross-section, i.e., the area-weighted average of the temperatures at each point, it is expressed as: ; in, R The radius of the main cable cross-section. A The cross-sectional area of ​​the main cable is πR 2 , T i , A i Discretize the main cable cross-section as follows: n The temperature and area of ​​each unit after the unit.

[0040] The amount of heat energy stored or released per unit thickness within the cross-section of the main cable at a certain moment is: ; Therefore, the change in the average temperature of the cross section can be expressed in the form of thermal energy: ; Note that the change in thermal energy within the main cable cross-section depends on the change in the average temperature of the main cable's circumferential surface. Therefore, the average temperature of the main cable's circumferential surface is used as the boundary temperature. That is, the average temperature of the main cable's surface is applied as the boundary on the circumference, thereby eliminating the angular component and achieving model dimensionality reduction.

[0041] The one-dimensional radial heat transfer model is expressed as: ; in, , which represents the thermal diffusivity of the main cable cross section.

[0042] The above scheme simplifies the two-dimensional planar heat transfer model into a one-dimensional radial heat transfer model, which greatly improves the calculation efficiency while ensuring the calculation accuracy.

[0043] In one embodiment, several temperature sensors are arranged at equal intervals on the circumferential surface of the main cable to measure the average surface temperature of the main cable at various times, thereby obtaining a time series of the average surface temperature of the main cable. , as the boundary temperature.

[0044] Temperature after dimensionality reduction TDepends only on radius r and time t The horizontal axis represents spatial coordinates, and the vertical axis represents time coordinates. The coordinates are discretized into several points in both the spatial and temporal dimensions.

[0045] like Figure 3 and Figure 4 As shown, where, Figure 3 This is a schematic diagram of the spatial and temporal discretization of the temperature field at the surface temperature measurement point of the main cable and in the radial direction, according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the main cable circular cross-section radius node and unit number in one embodiment of the present invention.

[0046] In one embodiment, step S2 involves discretizing the one-dimensional radial heat transfer model spatially and temporally, resulting in a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points include: Step S21: Discretize the one-dimensional radial heat transfer model in space, as follows: , i =0,1,2,…, n , , R Indicates the cross-sectional radius of the main cable; like Figure 3 and Figure 4 As shown, the continuous radial coordinates, i.e. the radius, are divided into a finite number of discrete points, called nodes or spatial grid points. The intersection of the discrete points in the spatial and temporal dimensions is the spatiotemporal grid point. i When =0, r 0=0 represents the center point, i.e., the center of the main cable. i = n hour, r n = R , representing the surface point, i.e., the outer end of the main cable radius; two adjacent nodes ( i=0~n , n A unit is formed by connecting lines to the radius (the number of equal divisions, i.e., the number of elements). Rotating these elements around the origin creates a ring. The temperature of each ring can be taken as the average of the temperatures of the two nodes. Δ r Indicates the unit length. Greater than 0. In the finite difference method, more attention is paid to the nodes themselves.

[0047] Step S22: Discretize the one-dimensional radial heat transfer model over time, as follows: , p =0,1,2,…, n t , n t This represents the total number of time steps required to solve the problem.

[0048] like Figure 3 As shown, continuous time t Divide into a finite number of time steps, i.e., time grid points, with a time step size of . , Greater than 0.

[0049] p =0 represents the initial time; p =1,2,… represents the subsequent calculation times.

[0050] Step S23, Continuous temperature field in the radial direction of the main cable Temperature discretized into spatiotemporal grid points .

[0051] That is to say, the first p At each time step, it is located at r i The node temperature.

[0052] The above scheme discretizes the continuous partial differential equation (one-dimensional radial unsteady heat transfer model) in two dimensions: space (radial direction) and time. This yields a set of temperature values ​​at discrete spatial grid points (nodes) and time grid points, transforming them into a solvable discrete form. This allows for an approximate simulation of the temperature change over time across the entire cross-section of the main cable.

[0053] In one embodiment, step S3 involves obtaining the finite difference decomposition of the one-dimensional radial heat transfer model through finite difference. When determining the finite difference scheme, any one of the forward Euler method, backward Euler method, or Crank-Nicolson method can be used.

[0054] like Figure 5 As shown, Figure 5 This is a schematic diagram of the finite difference scheme of a one-dimensional radial heat transfer model in one embodiment of the present invention.

[0055] The forward Euler method directly utilizes the definition of the derivative, i.e., the forward difference, and is an explicit method with high computational efficiency. The backward Euler method or the Crank-Nicolson method are both implicit methods. The backward Euler method utilizes the backward difference of the derivative, which has good stability. The Crank-Nicolson method uses the central difference at the midpoint of the interval and approximates the integral using the trapezoidal rule, which has high accuracy.

[0056] By using the above scheme, the difference scheme is determined, and the finite difference decomposition of each differential term of the first-order radial heat transfer differential equation is obtained, thereby transforming the continuous partial differential equation into a discrete system of algebraic equations.

[0057] In one embodiment, step S4, solving for the temperature at each node at each time step using a difference scheme to form a temperature field matrix, includes: Step S41: Set the initial temperature, so that... p At the initial moment when the initial temperature is 0, the average surface temperature of the main cable is the initial temperature of each node, i.e. .

[0058] According to heat transfer theory, the influence of the initial value on the subsequent results decays exponentially with time and becomes negligible within a finite time, thus setting the initial temperature.

[0059] Step S42: Set the boundary temperature by applying the average temperature at various times at the outer end of the main cable radius. , p =1,2,…, at the center of the main cable, the temperature gradient is 0, that is… .

[0060] The boundary temperature is obtained from the sensor's measured data and satisfies symmetry. The main cable's circular cross-section only has a temperature gradient in the radial direction, so it can be treated as a one-dimensional system, reducing the number of nodes and improving computational efficiency.

[0061] Step S43, Self p Starting from the initial time when =0, a system of linear equations is formed based on the initial temperature, boundary temperature, and difference scheme. The temperature at each node of each time step is solved step by step to form the temperature field matrix. .

[0062] In one embodiment, when the difference scheme is the forward Euler method, the system of linear equations is expressed as: ; in, M for( n +1) order tridiagonal matrix, , These represent the temperatures of each node along the radius of the current time step and the previous time step, respectively.

[0063] In one embodiment, when the difference scheme is the backward Euler method or the Crank-Nicolson method, the linear equation system is expressed as: ; in, M for( n +1) order tridiagonal matrix, , These represent the temperatures of each node along the radius of the current time step and the previous time step, respectively.

[0064] Using the above method, the matrix is ​​assembled according to the determined difference scheme. M Then, the solution is obtained step by step based on explicit or implicit methods.

[0065] In one embodiment, step S5, calculating the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable cross-section, includes: The calculation formula is: .

[0066] Specifically, the average temperature of the main cable cross-section at each time step is calculated, and the area-weighted average of the temperatures of each segment of the annulus along the radius is taken to obtain the average temperature of the main cable cross-section.

[0067] In the formula, e Indicates the unit number. i Indicates the node number. n Indicates the number of units.

[0068] This application also provides a system for calculating the average cross-sectional temperature of a suspension bridge main cable, which applies the above-mentioned method for calculating the average cross-sectional temperature of a suspension bridge main cable, and includes: The model creation module is configured to reduce the dimensionality of the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model. The discretization module is configured to spatially and temporally discretize the one-dimensional radial heat transfer model, thus ensuring a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points ; in, T This indicates the temperature at a radial point within the cross-section of the main cable. t Indicates time; r The polar radius represents the distance from a point on a plane to the origin; the cross-sectional radius of the main cable is divided into... n Each unit, and the nodes between units form n +1 spatial grid point, subscript i The spatial grid point number is represented; the time domain is divided into multiple time steps. superscript p Indicates the time grid point number; The differential calculation module is configured to: obtain the finite difference decomposition of the one-dimensional radial heat transfer model through differential calculation, and determine the differential scheme; The first temperature calculation module is configured to: solve for the temperature of each node at each time step step by step according to the difference scheme to form a temperature field matrix; The second temperature calculation module is configured to calculate the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable section.

[0069] The functions of each module correspond to the steps in the aforementioned calculation method, and will not be repeated here.

[0070] The following is a specific example for illustration.

[0071] based on Figure 2 For the suspension bridge shown, calculate the average temperature of the main cable cross section.

[0072] The main cable of the bridge is composed of 217 strands of 127 wires with a diameter of 5.6 mm, and the cross-sectional diameter is 1039.4 mm. The porosity of the cable clamp outer cross-section is 20%.

[0073] Step S1: Dimensionality reduction is performed based on the two-dimensional planar heat transfer model to obtain a one-dimensional radial heat transfer model.

[0074] Based on tests of the thermal properties of main cables of similar bridges, the equivalent thermal properties of the main cable cross-section considering the influence of pore air can be obtained as follows: thermal conductivity k =1.29W / (m·K), density ρ =6300 kg / m 3 Specific heat capacity c =508 J / (kg·K), therefore its thermal diffusivity is α=k / ρ / c =1.29 / 6300 / 508×3600×10000=14.51cm 2 / h.

[0075] like Figure 3 As shown in the left figure, in this embodiment, 16 temperature sensors are arranged at equal intervals along the surface of the main cable. The number of temperature sensors on the main cable surface can be adjusted appropriately according to the diameter of the main cable, such as 8, 16, or 32. Figure 6 As shown, the time series of the average surface temperature of the main cable is obtained based on the temperature sensor on the main cable surface. Total number of time steps in the analysis n t =5100, select an appropriate time step, time step Δ t =2min, meaning the total analysis time is 7 days and 2 hours.

[0076] Step S2: Discretize the one-dimensional radial heat transfer model in space and time to obtain a continuous temperature field in the radial direction of the main cable. Temperature discretized into spatiotemporal grid points .

[0077] like Figure 3 As shown in the right figure, the main cable radius R =519.7mm, take n =52, meaning there are 53 nodes on the radius, 52 elements, and the element length Δ r =10mm. The time step is consistent with the sensor sampling interval, i.e., Δ t =2min.

[0078] Step S3: Obtain the finite difference decomposition of the one-dimensional radial heat transfer model through finite difference. When determining the finite difference scheme, the backward Euler method is adopted.

[0079] Specifically, the one-dimensional radial heat transfer equation The difference format for each term is as follows: ; ; ; Thus, the finite difference scheme of the differential equation is obtained: .

[0080] Simplifying the above equation yields a system of linear equations. This system applies to internal space nodes, i.e. i =1,2,…, n -1 is represented as: ; in Let be a Fourier number, and be a dimensionless number.

[0081] Step S4: Solve for the temperature at each node at each time step using the difference scheme to form the temperature field matrix. .

[0082] Set the initial and boundary temperatures; assemble the matrix according to the determined difference scheme. M Based on the boundary temperature and the backward Euler difference scheme, the following system of linear equations is formed: ; in, M for( n +1) order tridiagonal matrix, calculated from thermal diffusivity, time step and radius node position subscripts; , Let represent the temperature vectors of each node along the radius direction at the current time step and the previous time step, respectively. The system of equations can be written in matrix form as follows: ,in: ; The solution is obtained step by step from the initial value to form the temperature field matrix. .

[0083] Step S5: Calculate the area-weighted average temperature based on the temperature field matrix to obtain the average temperature of the main cable cross-section, including: The calculation formula is: .

[0084] The above formula can be written in matrix form as follows: .

[0085] Among them, temperature field T for( p +1) row, ( n A matrix with +1) columns, where each row vector represents the temperature of each node at the radius of the corresponding time step. j for( n The area-weighted coefficient vector of row +1 is used to solve for the area-weighted average temperature.

[0086] Result comparison: against Figure 2 Radius shown R When calculating the transient average temperature of the 519.7mm main cable cross-section, the data was based on the measured values ​​of 16 temperature measuring points installed on the main cable surface (e.g., Figure 6 As shown), in Figure 7 In the finite element model shown, the temperature values ​​of each boundary node are calculated by linear interpolation based on the location of the main cable boundary nodes; in the differential model provided in this application embodiment, then as follows... Figure 3 The average temperature at 16 measuring points was directly applied to the right boundary. Table 1 shows a comparison of the model parameters with the calculation method provided in the embodiments of this application and the results of a certain finite element software.

[0087] The temperature field of the main cable section at step 5100, calculated by the finite element software and the embodiments of this application, is as follows: Figure 8 As shown, from Figure 8 As can be seen, although the spatial distribution of the temperature field calculated by the two methods is different, the cross-sectional area-weighted average temperature is consistent. From Figure 9 The comparison results show that the maximum deviation between the average temperature of the main cable section calculated by the method provided in this application and the result of the finite element reference model is 0.08℃, which proves the reliability of the calculation method provided in this application and is sufficient to maintain the same accuracy.

[0088] Table 1 shows the model parameters, the calculation methods provided in the embodiments of this application, and the results from a certain finite element software.

[0089] As shown in Table 1, the calculation method provided in this application embodiment takes only 0.18 seconds to calculate 5100 steps, which is much more efficient than the 64 minutes of the finite element method in related technologies. This greatly improves the calculation efficiency, and the calculation speed is increased from "hour level" to "sub-second level", making it possible to realize the real-time calculation of the average temperature of the main cable section or to carry out parameter analysis on embedded systems or ordinary computing devices.

[0090] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application 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 may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0091] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0092] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0093] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0094] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method of calculating the average temperature of a cross section of a main cable of a suspension bridge, characterized in that, It comprises the following steps: dimension reduction is performed based on a two-dimensional plane heat transfer model to obtain a one-dimensional radial heat transfer model; spatial and time discretization of the one-dimensional radial heat transfer model, such that the continuous temperature field in radial direction of the main cable is discretized into a grid of temperature values temperature values ; wherein, T represents the temperature of a certain point in the radial direction of the main cable cross section; t represents time; r represents the polar radius, i.e. the distance of a certain point on the plane to the origin; the radius of the main cable cross section is divided into n units, and the nodes between the units form n +1 spatial grid points, the subscript i represents the spatial grid point sequence number; the time domain is divided into multiple time steps, the superscript p represents the time grid point sequence number; finite difference solution of the one-dimensional radial heat transfer model is obtained through difference to determine a difference format; temperature of each node at each time step is solved step by step according to the difference format to form a temperature field matrix; area-weighted average temperature is calculated according to the temperature field matrix to obtain average temperature of the main cable cross section.

2. The method for calculating the average temperature of the cross-section of the main cable of a suspension bridge as described in claim 1, characterized in that, The dimension reduction based on the two-dimensional plane heat transfer model to obtain the one-dimensional radial heat transfer model comprises: a two-dimensional plane heat transfer model is established and expressed as: ； Wherein, the temperature of a certain point in the main cable cross section is T a function of time t and spatial coordinates r, θ , r is the polar radius, representing the distance from a certain point on the plane to the origin; θ is the polar angle, representing the angle between the line connecting the point and the origin and the positive half-axis; ρ , c , k respectively represent the equivalent density, equivalent specific heat capacity and equivalent thermal conductivity of the main cable cross section considering the steel wire and the pore air. dimension reduction is performed with average temperature of the circumferential surface of the main cable as a boundary temperature to obtain the one-dimensional radial heat transfer model, which is expressed as: ； wherein, α represents a heat diffusion coefficient of the main cable cross section.

3. The method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in claim 2, characterized in that, A plurality of temperature sensors are arranged equidistantly on the circumference surface of the main cable to measure the average temperature of the main cable surface at each time to obtain a time sequence of the average temperature of the main cable surface , as the boundary temperature.

4. The method for calculating the average temperature of the cross-section of the main cable of a suspension bridge as described in claim 1, characterized in that, The one-dimensional radial heat transfer model is discretized in space and time, so that the continuous temperature field in the radial direction of the main cable the temperature is discretized into space-time grid points comprises: The one-dimensional radial heat transfer model is discretized in space as follows: , i = 0, 1, 2,..., n , , R denotes the main cable cross-sectional radius; The one-dimensional radial heat transfer model is discretized in time as: , p = 0, 1, 2,..., n t , n t denotes the total number of time steps to be solved. Continuous temperature field in radial direction of main cable Temperature discretized into spatiotemporal grid points .

5. The method for calculating the average temperature of the cross-section of the main cable of a suspension bridge as described in claim 1, characterized in that, When the finite difference solution of the one-dimensional radial heat transfer model is obtained through difference to determine the difference format, any one of forward Euler method, backward Euler method or Crank-Nicolson method is adopted.

6. The method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in claim 5, characterized in that, Solving the temperature of each node at each time step according to the difference format, forming a temperature field matrix comprising: The initial temperature is set to be the average temperature of the main cable surface at the initial moment of t = 0, i.e. p =0, and the initial temperature of each node is the average temperature of the main cable surface at the initial moment of t = 0, i.e. ; Setting a boundary temperature, applying the average temperature at each time at the outer end of the main cable radius, i.e. , p =1,2,…, at the center of the main cable, the temperature gradient is 0, i.e. ; From p =0, based on the initial temperature, boundary temperature and difference format to form a system of linear equations, step by step to solve each time step each node temperature, forming a temperature field matrix .

7. The method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in claim 6, characterized in that, When the difference format is a forward Euler method, the system of linear equations is represented as: ; wherein, M is a (N+1) by (N+1) matrix, n +1) order tri-diagonal matrix, , Tn+1and Tn represent the temperature of each node in the current time step and the previous time step, respectively.

8. The method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in claim 6, characterized in that, When the difference format is the backward Euler method or the Crank-Nicolson method, the linear equation set is expressed as: ; wherein, M is a (N+1) by (N+1) matrix, n a (N+1) by (N+1) matrix, , Tn+1and Tnrepresent the temperature of each node in the current time step and the previous time step, respectively.

9. The method for calculating the average cross-sectional temperature of the main cable of a suspension bridge as described in claim 1, characterized in that, When the area-weighted average temperature is calculated according to the temperature field matrix to obtain the average temperature of the main cable cross section, The calculation formula is: .

10. A system for calculating the average temperature of a cross section of a main cable of a suspension bridge, characterized in that, application of the calculation method of the average temperature of the main cable cross section of the suspension bridge according to any one of claims 1 to 9 comprises: a model creation module configured to perform dimension reduction based on a two-dimensional plane heat transfer model to obtain a one-dimensional radial heat transfer model; a discrete module configured to discretize the one-dimensional radial heat transfer model in space and time such that the continuous temperature field in the radial direction of the main cable is discretized into a grid of temperature values in space and time temperature values at the grid points in space and time ; wherein, T denotes the temperature of a certain point in the radial direction of the main cable cross section; t denotes time; r denotes the polar radius, i.e. the distance of a certain point in the plane to the origin; the radius of the main cable cross section is divided equally into n units, the nodes between the units forming n +1 spatial grid points, the subscript i denotes the spatial grid point number; the time domain is divided into a plurality of time steps, the superscript p denotes the time grid point number; a difference calculation module configured to obtain finite difference solution of the one-dimensional radial heat transfer model through difference to determine a difference format; a first temperature calculation module configured to solve temperature of each node at each time step step by step according to the difference format to form a temperature field matrix; a second temperature calculation module configured to calculate area-weighted average temperature according to the temperature field matrix to obtain average temperature of the main cable cross section.

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