A random simulation method and device for the temperature field of a bridge

Abstract

The present invention provides a method and device for stochastic simulation of the temperature field of a bridge. The method of the present invention fully considers the variation characteristics of the actual temperature of the bridge structure over time and the statistical characteristics of temperature values, and realizes the simulation of the stochastic temperature field of the bridge. Based on the statistical characteristics and time-varying laws of the monitored temperature data, a practical method for statistical simulation of the long-term temperature field using the stochastic simulation method is established, making the temperature effect analysis more accurate and having broad engineering application prospects. In addition, the method provided by the present invention significantly reduces the calculation cost on the premise of ensuring no reduction in simulation accuracy by introducing the expression of a stochastic function.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge temperature field simulation, and particularly relates to a stochastic simulation method and device for bridge temperature field. Background Art

[0002] The existing bridge temperature field simulation method is realized by using finite element technology based on the basic assumptions of heat transfer theory. However, this process is highly dependent on thermal boundary conditions, and there are numerous climate parameters with strong randomness, making it difficult to comprehensively and fully consider them. In addition, the numerical simulation calculation workload of the long-term temperature field is also extremely large. It should be noted that the monitored temperature data has periodicity and time-variation, and thus the temperature field has statistical properties. Therefore, based on the statistical characteristics and time-varying laws of the monitored temperature data, it is of great significance to use a stochastic simulation method to statistically simulate the long-term temperature field.

[0003] CN 102393877 A discloses a simulation method for the stochastic temperature field of a steel box girder of a bridge structure, which considers the actual temperature change characteristics of the steel box girder of the bridge structure over time and the statistical characteristics of temperature values, and realizes the simulation of the stochastic temperature field of the steel box girder of the bridge structure by using numerical methods, providing an effective way to obtain the stochastic temperature field of the steel box girder. However, this method requires dividing the temperature interval and temperature difference interval into several sub-intervals, and also requires rearranging the simulation samples according to the daily and seasonal change laws of the steel box girder temperature, significantly increasing the workload of temperature field simulation.

[0004] The decomposition processes of the existing temperature field simulation methods are all relatively complex, and there is an urgent need to establish a simulation method that simplifies the calculation process without reducing the accuracy. Summary of the Invention

[0005] In order to improve the efficiency and accuracy of temperature simulation, the present invention provides a stochastic simulation method and device for bridge temperature field. The simulation method of the present invention utilizes the statistical characteristics and time-varying laws of the measured temperature data of the temperature field, obtains the simulation value according to the random temperature component separated from the measured temperature data, and adds it to the deterministic temperature component to obtain the simulated random temperature field.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] A stochastic simulation method for bridge temperature field, the method comprising:

[0008] Obtaining a deterministic temperature component and a random temperature component;

[0009] Adding the deterministic temperature component and the random temperature component to obtain the bridge temperature field.

[0010] Further, the obtaining of the deterministic temperature component includes:

[0011] Select a mathematical model according to the total temperature change of the measurement point, which is the deterministic temperature component.

[0012] The deterministic temperature component is T d = A sin(2π·w·t + θ) + B;

[0013] Wherein, T d is the deterministic temperature component, w is the angular frequency of the trigonometric function, determined by the sampling frequency of the measurement point, t is the time, and A, B, and θ are undetermined parameters;

[0014] The obtaining of the random temperature component includes: subtracting the deterministic temperature component from the total temperature change of the measurement point to obtain a data value, and performing random simulation on the data value to obtain the random temperature component.

[0015] Further, obtaining the random temperature component further includes:

[0016] Determine the first random variable and the second random variable, and the first random variable and the second random variable are orthogonal random variables with zero mean; simulate the random temperature component according to the first random variable and the second random variable;

[0017] The first random variable and the second random variable are respectively obtained by mapping through the first random variable function and the second random variable function.

[0018] Further, the first random variable function and the second random variable function are determined in the following manner:

[0019]

[0020]

[0021] Wherein, is the first random variable function, is the second random variable function; k = 1, 2,..., N; i = 1, 2,..., n, k represents the number of frequency truncation terms, i represents the variable dimension, and Θ1 and Θ2 are two basic random variables uniformly distributed and independent in the interval (0, 2π);

[0022] The first random variable function and the second random variable function are mapped to the first random variable R ik and the second random variable I ik .

[0023] Further, the random temperature component is determined according to the first random variable and the second random variable as,

[0024]

[0025] Among them, X(t) is the random temperature component; k = 1, 2, …, N; i = 1, 2, …, n; k represents the number of frequency truncation terms; i represents the variable dimension; Δω is the frequency step; ω k is the frequency with the number of frequency truncation terms being k, ω k = k × Δω; D(ω k ) is the auto-spectrum diagonal matrix at the frequency ω k ; t is the time; R ik is the first random variable, I ik is the second random variable; λ i (ω k ) is the eigenvalue of the proper orthogonal decomposition coherence function matrix at the frequency truncation term number ω k ; χ i (ω k ) and κ i (ω k ) are respectively the real part and the imaginary part of the eigenvector of the proper orthogonal decomposition coherence function matrix at the frequency truncation term number ω k .

[0026] Furthermore, the D(ω k ) is determined by the auto-spectrum diagonal matrix;

[0027] the auto-spectrum diagonal matrix is a matrix constructed according to the auto-power spectral density function. Specifically,

[0028]

[0029] where D(ω) is the auto-spectrum diagonal matrix, S 11 (ω), S 22 (ω) and S nn (ω)) are respectively the auto-power spectral density functions of the first measurement point, the second measurement point, and the nth measurement point; the auto-power spectral density function is determined by using the spectral analysis theory with the data value obtained by subtracting the deterministic temperature component from the total temperature change of a single measurement point;

[0030] Substitute the frequency ω k , and determine the D(ω k ).

[0031] Furthermore, the λ i (ω k ), χ i (ω k ) and κ i (ω k ) are determined by the proper orthogonal decomposition of the coherence function matrix. Specifically:

[0032] Coherence function matrix γ X (ω) is a non - negative definite Hermitian matrix:

[0033]

[0034] γ 12 γ(ω) and γ 21 γ(ω), is the coherence function between the first measurement point and the second measurement point; γ 1n γ(ω) and γ n1 γ(ω), is the coherence function between the first measurement point and the nth measurement point; γ 2n γ(ω) and γ n2 γ(ω), is the coherence function between the second measurement point and the nth measurement point; The coherence function is a function model constructed from data values obtained by subtracting the deterministic temperature component from the total temperature change at different measurement points;

[0035] Perform eigen - orthogonal decomposition on the coherence function matrix γ X γ(ω):

[0036]

[0037] where ω is the frequency, λ i γ(ω) and ψ i γ(ω)(i = 1, 2, …, n) are respectively the eigenvalues and eigenvectors of the eigen - orthogonal decomposition coherence function matrix, is the conjugate transpose vector of the eigenvector ψ i γ(ω), the eigenvector ψ i γ(ω)=χ i γ(ω)+iκ i γ(ω), χ i γ(ω) and κ i γ(ω) are respectively the real part and the imaginary part of the eigenvector ψ i γ(ω);

[0038] Substitute the frequency ω k , and determine the λ i γ(ω k ), χ i γ(ω k ) and κ i γ(ω k ).

[0039] On the other hand, the present invention provides a random simulation device for the bridge temperature field, and the device includes:

[0040] An acquisition unit, configured to acquire the deterministic temperature component and acquire the random temperature component;

[0041] A calculation unit for adding the deterministic temperature component and the stochastic temperature component to obtain a simulated stochastic temperature field;

[0042] The obtaining unit obtaining the deterministic temperature component includes:

[0043] Selecting a mathematical model through the total temperature change of the measurement points, which is the deterministic temperature component,

[0044] The deterministic temperature component is T d = A sin(2π·w·t + θ) + B;

[0045] Wherein, T d is the deterministic temperature component, w is the angular frequency of the trigonometric function, determined by the sampling frequency of the measurement points, t is the time, and A, B, and θ are undetermined parameters;

[0046] The obtaining unit obtaining the stochastic temperature component includes: subtracting the deterministic temperature component from the total temperature change of the measurement points to obtain a data value, performing stochastic simulation on the data value, and simulating the stochastic temperature component according to the first random variable and the second random variable.

[0047] Further, the determining unit determines the first random variable and the second random variable according to the following method:

[0048] Determining the first random variable function and the second random variable function;

[0049] Respectively mapping the first random variable function and the second random variable function to the first random variable and the second random variable, and the first random variable and the second random variable are orthogonal random variables with zero mean;

[0050] The determining the first random variable function and the second random variable function is determined by the following method:

[0051]

[0052]

[0053] Wherein, is the first random variable function, is the second random variable function k = 1, 2,..., N; i = 1, 2,..., n, k represents the number of frequency truncation terms, i represents the variable dimension; Θ1 and Θ2 are independent basic random variables uniformly distributed in the interval (0, 2π);

[0054] The first random variable function and the second random variable function are mapped to the first random variable R through the rand('state', 0) and temp = randperm(n×N) functions of MATLAB ikand the second random variable I ik .

[0055] Further, the determining unit simulates the random temperature component according to the first random variable and the second random variable:

[0056]

[0057] where X(t) is the random temperature component; k = 1, 2, …, N; i = 1, 2, …, n; k represents the number of frequency truncation terms; i represents the variable dimension; Δω is the frequency step; ω k is the frequency with the number of frequency truncation terms being k, ω k = k×Δω; D(ω k ) is the auto-spectrum diagonal matrix at the frequency ω k ; t is the time; R ik is the first random variable, I ik is the second random variable; λ i (ω k ) is the eigenvalue of the proper orthogonal decomposition coherence function matrix at the frequency truncation term number ω k ; χ i (ω k ) and κ i (ω k ) are respectively the real part and the imaginary part of the eigenvector of the proper orthogonal decomposition coherence function matrix at the frequency truncation term number ω k ;

[0058] The D(ω k ) is determined by the auto-spectrum diagonal matrix;

[0059] The auto-spectrum diagonal matrix is a matrix constructed according to the auto-power spectral density function. Specifically,

[0060]

[0061] where D(ω) is the auto-spectrum diagonal matrix, S 11 (ω), S 22 (ω) and S nn (ω) are respectively the auto-power spectral density functions of the first measurement point, the second measurement point and the nth measurement point; the auto-power spectral density function is determined by using the spectral analysis theory with the data value obtained by subtracting the deterministic temperature component from the total temperature change of a single measurement point to determine the auto-power spectral density function model;

[0062] Substitute the frequency ω k , and determine the D(ω k );

[0063] The λ i (ω k ), χi (ω k ) and κ i (ω k ) are determined according to the orthogonal decomposition of the coherence function matrix, specifically:

[0064] The coherence function matrix γ X (ω) is a non - negative definite Hermitian matrix:

[0065]

[0066] γ 12 (ω) and γ 21 (ω) are the coherence functions between the first measurement point and the second measurement point; γ 1n (ω) and γ n1 (ω) are the coherence functions between the first measurement point and the nth measurement point; γ 2n (ω) and γ n2 (ω) are the coherence functions between the second measurement point and the nth measurement point; The coherence function is a function model constructed from the data values obtained by subtracting the deterministic temperature component from the total temperature change of the measurement point;

[0067] Perform orthogonal decomposition on the coherence function matrix γ X (ω):

[0068]

[0069] where ω is the frequency, λ i (ω) and ψ i (ω) (i = 1, 2, …, n) are the eigenvalues and eigenvectors of the coherence function matrix of the proper orthogonal decomposition respectively, is the conjugate transpose vector of the eigenvector ψ i (ω), and the eigenvector ψ i (ω) = χ i (ω) + iκ i (ω), χ i (ω) and κ i (ω) are the real part and the imaginary part of the eigenvector ψ i (ω) respectively;

[0070] Substitute the frequency ω k , and determine the λ i (ω k ), χ i (ω k ) and κ i (ω k ).

[0071] Compared with the prior art, the present invention has achieved the following beneficial effects:

[0072] Based on the statistical characteristics and time-varying laws of the monitored temperature data, the present invention establishes a practical method for statistically simulating the long-term temperature field by using the random simulation method, making the temperature effect analysis more accurate and having broad engineering application prospects. In addition, by introducing the random function expression, the calculation cost is significantly reduced on the premise of ensuring that the simulation accuracy is not reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flowchart of the random simulation method for the bridge temperature field in the specific embodiment of the present invention;

[0074] Figure 2 It is a schematic diagram of the random simulation device for the bridge temperature field in the specific embodiment of the present invention;

[0075] Figure 3 It is an elevation view of the bridge in the embodiment of the present invention;

[0076] Figure 4 It is a layout diagram of the measuring points in the embodiment of the present invention;

[0077] Figure 5 It is a curve of the total temperature, deterministic temperature component and difference (the difference between the total temperature and the deterministic temperature component) of the measuring point T1 in the embodiment of the present invention;

[0078] Figure 6 It is a comparison between the average value of the auto-power spectral density function (measured average) of the difference between the total temperature and the deterministic temperature component of 3 typical measuring points in the embodiment of the present invention, and the average value of the power spectral density function model of 3 typical measuring points (fitted);

[0079] Figure 7 It is a comparison between the measured coherence function and the fitted coherence function of the typical measuring points T1 and T3 in the embodiment of the present invention;

[0080] Figure 8 It is a comparison between the measured coherence function and the fitted coherence function of the typical measuring points T1 and T10 in the embodiment of the present invention;

[0081] Figure 9 It is a comparison between the measured coherence function and the fitted coherence function of the typical measuring points T3 and T10 in the embodiment of the present invention;

[0082] Figure 10 It is the random temperature component of 3 typical measuring points simulated in the embodiment of the present invention;

[0083] Figure 11 It is a comparison between the mean value of all samples of the random temperature component of 3 typical measuring points simulated in the embodiment of the present invention and the target value;

[0084] Figure 12Comparison between the standard deviation of the random temperature components at three typical measuring points simulated in the embodiments of the present invention and the target values;

[0085] Figure 13 Measured values of the temperatures at three typical measuring points in the embodiments of the present invention;

[0086] Figure 14 Random temperature fields at three typical measuring points in the embodiments of the present invention. Detailed implementation manners

[0087] Next, in combination with the specific embodiments of the present invention and the accompanying drawings of the specification, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0088] In the specific implementation manners of the present invention, a flowchart of a random simulation method for a bridge temperature field is provided, as shown in Figure 1 and includes the following steps:

[0089] Select a mathematical model according to the annual temperature change of the measuring points to obtain the deterministic temperature component,

[0090] Subtract the deterministic temperature component from the total temperature change of the measuring points to obtain data values, and simulate the data values to obtain the random temperature component;

[0091] The process of simulating the data values includes: obtaining the power spectrum function model of the measuring points and the coherence function model of the measuring points; performing proper orthogonal decomposition and introducing a random function expression to obtain the random temperature component;

[0092] Add the random temperature component and the deterministic temperature component to obtain the random temperature field.

[0093] In the specific implementation manners of the present invention, a schematic diagram of a random simulation device for a bridge temperature field is also provided, as shown in Figure 2 and the device includes:

[0094] An acquisition unit for acquiring the deterministic temperature component and acquiring the random temperature component;

[0095] A calculation unit for adding the deterministic temperature component and the random temperature component to obtain the simulated random temperature field;

[0096] The acquisition unit is connected to the calculation unit.

[0097] Embodiment

[0098] Taking an overpass in Wuhan as an example, this paper illustrates how to simulate the bridge temperature field by the random simulation method based on the specific implementation mode of the present invention.

[0099] The bridge in the engineering example involved in this embodiment is located at the intersection of the southern section of the Third Ring Road in Wuhan and the Wuhuang Expressway. The analysis object is the steel structure variable cross-section continuous curved box girder of the sixth continuous section (35m + 45m + 35m) of Ramp B. There are pavement sensors on the bridge deck and structure sensors are set under the bridge, such as Figure 3 shown. Existing research shows that the temperature distribution along the bridge direction is basically the same, and the effect of the vertical temperature gradient of the box girder under the sunlight on the bridge structure is the largest. Therefore, temperature sensors are only arranged at the mid-span section of the side span (section 1-1) of the above engineering example for real-time monitoring. The actual detected bridge is as Figure 4 shown. The width of the top plate of the box girder is 10m, the width of the bottom plate is 5m, the cantilever length is 2.5m, the height is 0.15m - 0.4m, the lower edge of the bottom plate changes in a broken line, and a total of 11 temperature sensors (T1 - T11) are arranged on the beam body, and 1 temperature sensor IT1 is arranged on the bridge deck. The time period for temperature data acquisition is 1 hour, and the monitoring data of the bridge measuring points throughout the year 2019 is selected for analysis. It should be noted that due to partial loss of the detection data of the sensors, there are missing data in some time periods of the annual temperature, but the statistical data values still have statistical significance.

[0100] Here, the measuring point T1 on the top plate (measuring point 1), the measuring point T3 on the web (measuring point 3), and the measuring point T10 on the bottom plate (measuring point 10) are selected as typical measuring points, and the simulation is carried out with these 3 typical measuring points as examples. The specific simulation method is as follows:

[0101] Step (1): Using the least square method to fit the annual temperature change data of the total temperature of the typical measuring points to obtain the mathematical model of the annual temperature change of the measuring points and time, and obtain the deterministic temperature component:

[0102]

[0103] T d That is, the deterministic temperature component, t is time, and A, B, and θ are the fitting parameters of the deterministic temperature component;

[0104] The results of the fitting parameters of the deterministic temperature component are shown in Table 1:

[0105] Table 1 Fitting parameters of the deterministic temperature component of the typical measuring points

[0106]

[0107] Subtracting the random temperature component T d from the total temperature T to obtain the difference;

[0108] Figure 5Curves of the total temperature, deterministic temperature component, and difference (total temperature minus deterministic temperature component) at measuring point T1. The discontinuities are caused by missing monitoring data. From Figure 5 it can be seen that the deterministic temperature component can well describe the annual temperature change trend, which further verifies the rationality of the mathematical model of the deterministic temperature component. In addition, the mean value of the difference is zero, and the difference can be regarded as a zero-mean random process. Therefore, a stochastic simulation method can be used to simulate it.

[0109] Step (2): Consider the differences between the total temperatures and the deterministic temperature components of the 3 typical measuring points as a 1D-3V vector random process, and use spectral analysis theory to obtain the curve of its auto-power spectral density function. It is found that the curves of the 3 measuring points are very close. Here, take the average of the three, and the fitted auto-power spectral density function model is as follows:

[0110]

[0111] In the formula, ω is the frequency, a, b, and c are undetermined parameters, and Δln S0(ω) is the following piecewise function:

[0112]

[0113] In the formula, d, f, g, h, v, and p are all undetermined parameters; ω1 and ω2 are the boundary frequencies of the first peak of the auto-power spectral density function frequency from small to large; ω3 and ω4 are the boundary frequencies of the second peak of the auto-power spectral density function frequency from small to large;

[0114] Determine the undetermined parameters using the principle of best square approximation, and their values are shown in Table 2.

[0115] Table 2 Values of undetermined parameters of the auto-power spectral model

[0116]

[0117] The average of the auto-power spectral density functions of the differences between the total temperatures and the deterministic temperature components of the 3 typical measuring points is compared with the average of the power spectral density function models of the 3 typical measuring points as Figure 6 shown. In Figure 6, the average of the measured auto-power spectral density functions of the daily temperature changes of the 3 typical measuring points is represented as measured average; the average of the power spectral density function models of the 3 typical measuring points is represented as fitted. It can be seen that the model established by the present invention has a good fitting result, and the fitting result is very close to the measured value, which indicates that the established theoretical model of the power spectral density function is reasonable and effective.

[0118] Furthermore, represent the auto-spectrum diagonal matrix D(ω) as:

[0119]

[0120] Wherein, S 11 (ω), S 22 (ω) and S 33 (ω) are the auto-power spectral density functions obtained by fitting the difference between the total temperature and the deterministic temperature component at measuring point 1, measuring point 2 and measuring point 3 respectively. It should be noted that since the fitting results of the auto-power spectral density functions of the 3 typical measuring points are very close, here S 11 (ω), S 22 (ω) and S 33 (ω) are the same, and are all the average values of the auto-power spectral density functions of the 3 typical measuring points.

[0121] Step (3): Establish a coherence function model γ(ω) between typical measuring points according to the difference between the total temperature and the deterministic temperature component of two typical measuring points;

[0122]

[0123] Wherein, m, r, k, n, u, l are undetermined parameters.

[0124] Determine the undetermined parameters by using the principle of best square approximation, and the values are shown in Table 3.

[0125] Table 3 Results of Undetermined Parameters of Coherence Function Model

[0126]

[0127] The comparison results of the coherence function (expressed as the measured coherence function) of the difference between the total temperature and the deterministic temperature component between typical measuring points T1 and T3 and the established model (expressed as the fitted coherence function) are respectively as Figure 7 shown; the comparison of the measured coherence function and the fitted coherence function of typical measuring points T1 and T10 is as Figure 8 shown; the comparison of the measured coherence function and the fitted coherence function of typical measuring points T3 and T10 is as Figure 9 shown.

[0128] From Figure 7 , 8 and 9, it can be seen that the coherence function model established by the present invention is close to the actual measurement value and can be used for data simulation of two measuring points;

[0129] Furthermore, the coherence function matrix γ(ω) can be obtained as,

[0130]

[0131] Wherein, γ 12 (ω) and γ 21 (ω) are the coherence functions of measuring point T1 and measuring point T3; γ 13 (ω) and γ31 γ(ω) is the coherence function between measurement point T1 and measurement point T10; γ 23 γ(ω) and γ 32 γ(ω) is the coherence function between measurement point T3 and measurement point T10;

[0132] The eigen - orthogonal decomposition method is used to perform eigen - decomposition on the coherence function matrix γ(ω), and the coherence function matrix γ X (ω) of the eigen - orthogonal decomposition is obtained.

[0133]

[0134] where ω is the frequency, λ i λ(ω) and ψ i ψ(ω) (i = 1, 2, …, n) are respectively the eigenvalues and eigenvectors of the coherence function matrix of the eigen - orthogonal decomposition. is the conjugate transpose vector of the eigenvector ψ i (ω), χ i χ(ω) and κ i κ(ω) are respectively the real part and the imaginary part of ψ i (ω);

[0135] Step (4): The first random variable R ik and the second random variable I ik are obtained by mapping according to the first random variable function and the second random variable function.

[0136] The first random variable function and the second random variable function are determined in the following way:

[0137]

[0138]

[0139] where, is the first random variable function, is the second random variable function; k = 1, 2, …, N; i = 1, 2, …, n, N is the number of frequency truncation terms, n is the variable dimension; Θ1 and Θ2 are two basic random variables uniformly distributed in the interval (0, 2π) and independent of each other; the mapping process is implemented by the rand('state', 0) and temp = randperm(n×N) functions in MATLAB;

[0140] Step (5): Combine D(ω), λ i (ω), χ i (ω) and κ i (ω), R ik and I ikSubstitute into the above simulation formula to obtain the random temperature component:

[0141]

[0142] where X(t) is the random temperature component, k = 1, 2, …, N; i = 1, 2, …, n, k represents the number of frequency truncation terms, i represents the variable dimension, Δω is the frequency step, ω k is the frequency of the k-th frequency truncation term, ω k = k×Δm, D(ω k ) is the auto-spectrum diagonal matrix at the frequency ω k , R ik is the first random variable, I ik is the second random variable, λ i (ω k ) is the eigenvalue of the proper orthogonal decomposition coherence function matrix at the frequency ω k , χ i (ω k ) and κ i (ω k ) are respectively the real part and the imaginary part of the eigenvector of the proper orthogonal decomposition coherence function matrix at the frequency ω k ;

[0143] Add the random temperature component X(t) obtained in step (5) to the deterministic temperature component obtained in step (1) to obtain the simulated random temperature field.

[0144] Figure 10 are the random temperature components of 3 typical measurement points in the simulation. It can be seen from them that the change trend is basically the same as Figure 5 the change trend of the difference between the total temperature and the deterministic temperature component obtained in

[0145] To further verify the accuracy of the simulation results, compare the sample mean and standard deviation of the random temperature components of the typical measurement points simulated in the embodiments of the present invention with their target values respectively. Among them, the sample mean and standard deviation are calculated from their definitions, the target value of the mean is 0; the target value of the standard deviation is: Calculated to be 4.046.

[0146] The comparison of all sample means of the random temperature sample components of 3 typical measurement points with the target value is as Figure 11 shown, where the simulated value is the simulated random temperature component, and the target value is the data value obtained by subtracting the deterministic temperature component from the total temperature. From Figure 11 it can be seen that the relative error between the simulated value and the standard value is within 10 -14 , which indicates that the random temperature component simulated in the embodiments of the present invention is close to the actual target value with a mean of zero. Figure 12Comparison of the simulated values and the target values of the standard deviations of the random temperature components at 3 typical measuring points. As can be seen from Figure 12 it, the target values and the simulated values are very close. These results indicate that the random temperature components calculated by the random simulation method constructed in the present invention are reasonable and effective.

[0147] The measured values of the total temperature at 3 typical measuring points are as shown in Figure 13 . The random temperature field is obtained by adding the simulated random temperature components and the deterministic temperature components. The random temperature fields at 3 typical measuring points are as shown in Figure 14 . By comparing Figure 13 and Figure 14 , it can be seen that the random temperature field simulated in the present invention has good consistency with the measured values and can correctly reflect the change trend of the temperature. In addition, the simulated random temperature field also makes up for the missing part of the measured value data.

[0148] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A random simulation method for the temperature field of a bridge, characterized in that, The method includes: Obtaining a deterministic temperature component and a stochastic temperature component; Adding the deterministic temperature component and the stochastic temperature component to obtain a bridge temperature field; Among them, obtaining the deterministic temperature component includes: selecting a mathematical model according to the total temperature change of the measurement point, which is the deterministic temperature component, and the deterministic temperature component is ; among them, is the deterministic temperature component, is the angular frequency of the trigonometric function, which is determined by the sampling frequency of the measurement point, t is the time, , , are undetermined parameters; Obtaining the stochastic temperature component includes: subtracting the deterministic temperature component from the total temperature change of the measuring point to obtain a data value, and performing random simulation on the data value to obtain the stochastic temperature component; Obtaining the stochastic temperature component includes: determining a first random variable and a second random variable, where the first random variable and the second random variable are orthogonal random variables with zero mean; simulating the stochastic temperature component according to the first random variable and the second random variable; the first random variable and the second random variable are respectively obtained by mapping through a first random variable function and a second random variable function; The first random variable function and the second random variable function are determined in the following manner: Among them, is the first random variable function, is the second random variable function; , k represents the number of frequency truncation terms, i represents the variable dimension, Θ 1 and Θ 2 are two basic random variables uniformly distributed and independent within the interval (0, 2π); The first random variable function and the second random variable function are mapped to a first random variable and a second random variable through the MATLAB functions rand('state', 0) and temp = randperm(n×N). and a second random variable ; Determining the stochastic temperature component according to the first random variable and the second random variable as, Among them, X ( t ) is the random temperature component; ; k represents the number of frequency truncation terms; i represents the variable dimension; is the frequency step; ω k is the frequency when the number of frequency truncation terms is k ; ; D ( ω k ) is the auto-spectrum diagonal matrix when the frequency is ω k ; t is the time; is the first random variable, is the second random variable; λ i ( ω k ) is the eigenvalue of the coherent function matrix of the proper orthogonal decomposition when the number of frequency truncation terms is ω k ; and are respectively the real part and the imaginary part of the eigenvector of the coherent function matrix of the proper orthogonal decomposition when the number of frequency truncation terms is ω k .

2. The method according to claim 1, wherein The said D ( ω k ) is determined by the auto-spectrum diagonal matrix; The auto-spectrum diagonal matrix is a matrix constructed according to the auto-power spectral density function, specifically, Among them, is the auto-spectrum diagonal matrix, , and are the auto-power spectral density functions of the first measurement point, the second measurement point and the n measurement point respectively; the auto-power spectral density function is determined by using the spectral analysis theory with the data value obtained by subtracting the deterministic temperature component from the total temperature change of a single measurement point to determine the auto-power spectral density function model; Substitute the frequency , and determine the D ( ω k ).

3. The method according to claim 1, characterized in that, The said , and are determined according to the eigen-orthogonal decomposition of the coherence function matrix, specifically as follows: Coherence function matrix is a non - negative definite Hermitian matrix: Among them, γ 12 ( ω ) and γ 21 ( ω ) is the coherence function between the first measurement point and the second measurement point; γ 1n ( ω ) and γ n1 ( ω ) is the coherence function between the first measurement point and the n th measurement point; γ 2n ( ω ) and γ n2 ( ω ) is the coherence function between the second measurement point and the n th measurement point; The coherence function is a function model constructed based on the data values obtained by subtracting the deterministic temperature component from the total temperature of different measurement points; Coherence function matrix γ X (ω) Proper orthogonal decomposition: Among them, is the frequency, and are the eigenvalue and eigenvector of the proper orthogonal decomposition coherence function matrix respectively, is the conjugate transpose vector of the eigenvector , and the eigenvector = +i . and are the real part and imaginary part of the eigenvector respectively; Substitute the frequency , and determine the , and .

4. A random simulation device for the temperature field of a bridge, characterized in that The device includes: An acquisition unit for acquiring a deterministic temperature component and acquiring a stochastic temperature component; A calculation unit for adding the deterministic temperature component and the stochastic temperature component to obtain a simulated random temperature field; The obtaining unit obtains the deterministic temperature component, including: selecting a mathematical model based on the annual temperature variation of the measuring point, which is the deterministic temperature component, and the deterministic temperature component is ; Among them, is the deterministic temperature component, is the angular frequency of the trigonometric function, which is determined by the sampling frequency of the measurement point, t is the time, 、 、 are parameters to be determined; The acquisition unit acquires the stochastic temperature component by: subtracting the deterministic temperature component from the total temperature of the measuring point to obtain a data value, performing random simulation on the data value, and simulating the stochastic temperature component according to a first random variable and a second random variable; The acquisition unit determines the first random variable and the second random variable in the following manner: Determining a first random variable function and a second random variable function; Mapping the first random variable function and the second random variable function to the first random variable and the second random variable respectively, where the first random variable and the second random variable are orthogonal random variables with zero mean; The determination of the first random variable function and the second random variable function is determined in the following manner: Among them, is the first random variable function, is the second random variable function, , k represents the number of frequency truncation terms, i represents the variable dimension; Θ 1 and Θ 2 are basic random variables uniformly distributed and independent in the interval (0, 2π); The first random variable function and the second random variable function are mapped to a first random variable and a second random variable through the MATLAB functions rand('state', 0) and temp = randperm(n×N). and a second random variable ; The acquisition unit simulates the stochastic temperature component according to the first random variable and the second random variable: Among them, X ( t ) is the random temperature component; ; k represents the number of frequency truncation terms; i represents the variable dimension; is the frequency step; ω k is the frequency when the number of frequency truncation terms is k ; ; D ( ω k ) is the auto-spectrum diagonal matrix when the frequency is ω k ; t is the time; is the first random variable, is the second random variable; λ i ( ω k ) is the eigenvalue of the proper orthogonal decomposition coherence function matrix when the number of frequency truncation terms is ω k ; and are the real and imaginary parts of the eigenvector of the proper orthogonal decomposition coherence function matrix when the number of frequency truncation terms is ω k respectively.

5. The device according to claim 4, wherein The said is determined by the self-spectrum diagonal matrix; The auto-spectrum diagonal matrix is a matrix constructed according to the auto-power spectral density function, specifically, Among them, D ( ω ) is the auto-spectrum diagonal matrix, , and are the auto-power spectral density functions of the first measurement point, the second measurement point and the n measurement point respectively; the auto-power spectral density function is determined by using the spectral analysis theory for the data value obtained by subtracting the deterministic temperature component from the total temperature change of a single measurement point to determine the auto-power spectral density function model; Substitute the frequency to determine the ; The said , and are determined according to the eigen-orthogonal decomposition of the coherence function matrix, specifically as follows: Coherence function matrix γ X ( ω ) is a non - negative definite Hermitian matrix: and is the coherence function between the first measurement point and the second measurement point; and is the coherence function between the first measurement point and the n th measurement point; and is the coherence function between the second measurement point and the n th measurement point; the coherence function is a function model constructed from data values obtained by subtracting the deterministic temperature component from the total temperature change at different measurement points; Coherence function matrix γ X ( ω ) Proper orthogonal decomposition: Among them, is the frequency, and are the eigenvalue and eigenvector of the coherence function matrix of the proper orthogonal decomposition respectively, is the eigenvector ψ i ( ω ) is the conjugate transpose vector of = +i . and are the real part and the imaginary part of the eigenvector ψ i ( ω ) respectively; Substitute the frequency ω k , and determine the λ i ( ω k ), and .

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