A method for estimating representative value of bridge temperature gradient based on long-term historical meteorological data

Abstract

A method for estimating the representative value of bridge temperature gradient based on long-term historical meteorological data, the steps are as follows: construct a localized training data sample set of 12 meteorological parameters and structural temperature gradient data based on a clustering method; establish a correlation model between structural temperature gradient monitoring indicators and meteorological parameters based on a neural network model; expand the temperature gradient data samples based on long-term historical meteorological data; estimate the representative value of the temperature gradient of the bridge structure based on the expanded structural gradient temperature data. This method effectively extends the data length of the structural temperature gradient, solves the problem of insufficient samples of structural temperature monitoring data and difficulty in reasonably calculating the representative value of the temperature effect with a return period of more than 50 years. This method makes full use of the existing monitoring data, so that various meteorological conditions can be effectively trained, and improves the accuracy of training, prediction and generalization. This method is suitable for estimating the representative value of the temperature gradient of various types of bridge structures in different regions, and has wide applicability and great engineering application potential.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge structure health monitoring, and in particular relates to a method for estimating a representative value of a bridge temperature gradient based on long-term historical meteorological data. Background Art

[0002] In the long-term service process, bridge structures, in addition to bearing dynamic and static loads, are also constantly affected by various factors such as periodic atmospheric temperature changes, solar radiation, day and night alternation, and sudden temperature drops. Due to the hysteresis of component size and material thermal conductivity, the structural temperature presents uneven and nonlinear distribution characteristics in space. This uneven temperature distribution itself will produce sufficiently large self-stress, and will also produce secondary stress when constrained. It is an important reason for the cracking or even destruction of bridge concrete structures. In severe cases, the effects caused by live and static loads are even equivalent, causing great harm to the durability and safe operation of bridge structures.

[0003] Although the current European Eurocode3, British BS5400, American AASHTO, and Chinese Highway Bridge and Culvert Design Code all provide temperature gradient models to consider the thermal effects of the structure itself, the proposed specifications are not sufficient to describe the temperature gradients in different climate zones. In addition, they are based on climate data accumulated in certain regions in the last few decades of the last century and may not be applicable to the current specific bridge locations and structural forms. Therefore, a reasonable analysis of the temperature gradient is of great significance to the life performance evaluation and maintenance of existing bridges as well as bridge design.

[0004] Extreme value analysis is one of the most successful methods for determining the characteristic value of temperature action within the expected return period. With the development of bridge health monitoring systems, more and more scholars have inferred long-term temperature gradient representative values ​​based on short-term monitoring data. Liu Yang et al. extrapolated extreme values ​​based on one-year temperature difference monitoring data of flat steel box girders, and Zhou Guangdong et al. evaluated the standard value of structural temperature difference based on one-year monitoring data. However, reasonable and accurate temperature gradient extreme value analysis requires at least 10 years of sufficient temperature difference data samples, but the current health monitoring system basically monitors for 1-2 years, and there is a large amount of data missing. Therefore, the existing methods are not sufficient to reasonably infer the representative value of the return period of temperature action for more than 50 years.

[0005] Compared with the temperature monitoring data of bridges, the meteorological data of the bridge site area is of sufficient length. In order to solve the double error that may be caused by predicting the temperature difference through the finite element method and the problem of insufficient monitoring data samples, the relationship between meteorological parameters and temperature gradients is directly established to estimate the temperature difference data of bridges for many years. This can effectively expand the structural temperature monitoring data set and is expected to solve the problem of insufficient length of structural temperature monitoring data. At present, there are also some studies on the relationship between environmental factors and structural temperature difference. Abid et al. established a linear relationship between meteorological temperature, wind speed and solar radiation and the maximum temperature difference of the structure. Liu Jiang et al. established a linear relationship with the structural temperature difference based on wind speed, meteorological temperature and daily maximum temperature difference. However, these studies have the following shortcomings in predicting long-term temperature differences: i) most of the studies are based on experimental data or finite element simulation data, the results may be too idealized, with poor practicality, and require long-term monitoring; ii) the studies only considered the relationship between the maximum temperature difference and the maximum air temperature, solar radiation and wind speed, but failed to fully consider other environmental factors that act together on the actual bridge structure, and the resulting linear regression relationship is not sufficient to meet the prediction accuracy required for bridge design; iii) these studies can only speculate on the relationship between environmental parameters and the maximum temperature difference of the cross-section, ignoring the correlation between temperature differences at different measuring points at different times, making it difficult to use them to establish a temperature gradient model. Summary of the invention

[0006] The purpose of the present invention is to provide a method for estimating a representative value of bridge temperature gradient based on long-term historical meteorological data.

[0007] The technical solution of the present invention:

[0008] A method for estimating a representative value of bridge temperature gradient based on long-term historical meteorological data, the steps are as follows:

[0009] Step 1. Construct a localized training data sample set of 12 meteorological parameters and structural temperature gradient data based on a two-stage clustering method

[0010] (1.1) Construction of meteorological parameter data samples; meteorological parameters include directly obtained parameters and derived parameters. Directly obtained parameters include: air temperature AT, air pressure AP, humidity AH, wind speed WS, cloud cover CF, daily total solar radiation SR and whether it rains Rain; derived parameters include: daily maximum temperature T dmax , daily minimum temperature T dmin 、Daily maximum temperature difference ATD d , the maximum temperature difference from the previous day ATD P and sunshine duration SD; the data accuracy is 1h, and the calculation formula for effective sunshine duration is as follows:

[0011]

[0012]

[0013]

[0014]

[0015] Where δ is the declination angle; is the latitude angle; ω is the solar hour angle; d is the dth day in a year; h SD is the effective sunshine duration; t is the local solar time, in hours; CF i is the cloud cover monitoring value of the ith hour, reflecting the degree to which the sky is covered by clouds, and its value is an integer from 0 to 10;

[0016] (1.2) Temperature gradient sample construction: When there are multiple monitoring points, the difference between adjacent monitoring points of the structure forms a temperature gradient vector. The structural temperature difference between two adjacent monitoring points is given by the following formula:

[0017] STD HI =T H -T I

[0018] Among them, STD HI is the temperature difference between the two monitoring points H and I; T H 、T I are the temperatures of measuring points H and I respectively;

[0019] (1.3) Construction of meteorological parameter localized training data samples based on two-stage clustering method; taking 12 types of meteorological parameters as input and temperature gradient vector as output, a relationship model between the above meteorological parameter input and temperature gradient output is established through a neural network;

[0020] According to the two-stage clustering method, the data set formed by 12 types of meteorological parameters and structural temperature gradient vectors is divided into training set and test set. dmax 、T dmin 、ATD d , daily total solar radiation, whether it rains or not are used as clustering indicators; the sample set formed by the above five meteorological parameters in N days is defined as X = {x1, x2, ..., x N}, where there are n1 continuous meteorological parameter variables and n2 categorical meteorological parameter variables in the data object x of each day; by clustering the above meteorological parameter sample set, a set consisting of j meteorological parameter clusters is formed, C j ={c1,c2,…c i ,…c j}; where any cluster c i and cluster c j The distance between is defined as:

[0021] D(c i ,c j )=λ i +λ j -λ {i,j}

[0022] Among them, {i,j} represents the meteorological parameter cluster c i and cluster c j The meteorological parameter sample set formed after merging; i Calculated using the following formula:

[0023]

[0024] Among them, N i is the meteorological parameter cluster c i The number of samples in ; It is the estimated variance of the kth continuous meteorological parameter variable estimated from all data points in the sample set X formed by meteorological parameters; is the estimated variance of the kth continuous meteorological parameter variable estimated based on the data points in meteorological parameter cluster i; L is the number of categories of the pth categorical meteorological parameter variable; N ipl is the meteorological parameter cluster c i The number of samples belonging to the lth category of the pth sub-type meteorological parameter variable;

[0025] In addition, λ i and λ {i,j} The calculation method of λ i same;

[0026] The method consists of two steps. The first step is to preliminarily determine the rough estimate of the number of meteorological parameter clusters based on the Bayesian Information Criterion, that is, when the decrease of BIC decreases significantly with the increase of the number of meteorological parameter clusters, the preliminary number of clusters is determined; cluster C j ={c1,c2,…c i ,…c j The calculation formula of BIC is:

[0027]

[0028] Where N is the total number of samples contained in the meteorological parameter cluster X;

[0029] In the second step, the pre-clustering result C obtained in the first step is used j ={c1,c2,…c i ,…c j} as the object, select the two clusters with the smallest distance to merge, and form a new cluster set C j-1 ; The calculation formula for the minimum distance is:

[0030] d min (C j )=min{D(c m ,c n ):m≠n,m∈1~j,n∈1~j}

[0031] Then, the ratio of the minimum distances of adjacent merges is used as an indicator to determine the final number of clusters. The formula for the ratio of the minimum distances of adjacent merges is:

[0032] And so on, the minimum distance ratio of the merged adjacent cluster sets is calculated in sequence;

[0033] When S =max{r s :s≥2}, determine the corresponding cluster number s as the optimal meteorological parameter cluster number; the second step is based on the fact that the largest ratio usually occurs when the last two meteorological data clusters are merged; use the change in the ratio of distances during each merger as the criterion to determine the optimal number of clusters; start by merging the roughly estimated meteorological data clusters obtained in the first step, and obtain a precise estimate of the number of meteorological parameter clusters when the distance ratio changes the most, thereby determining the meteorological parameter clustering data set;

[0034] After obtaining the meteorological parameter clustering data set according to the two-stage clustering method, 80% of the meteorological parameter and temperature gradient data are randomly selected from each meteorological parameter clustering data set as the training set, and 20% of the meteorological parameter and temperature gradient data are randomly selected as the test set for meteorological parameter and temperature gradient modeling;

[0035] Step 2. Establish a neural network-based structural temperature gradient monitoring index and meteorological parameter model

[0036] The 12 meteorological parameters of the monitoring time of the structural health monitoring system are used as input, and the temperature gradient data of the monitoring time is used as output. The training set and the test set divided in step (1.3) are modeled using a BP neural network; the neural network for modeling the relationship between meteorological parameters and temperature gradients is composed of multiple meteorological parameters as an input layer, one or more hidden layers and multiple temperature gradients as an output layer, and each layer contains a number of artificial neurons; the network training process based on the relationship between meteorological parameters and temperature gradients is to transmit the output value layer by layer through forward propagation, and adjust the weight and bias value backward through backward feedback, and iterate until the iteration condition is met;

[0037] Step 3. Temperature gradient data sample expansion based on long-term historical meteorological data

[0038] By obtaining the long-term historical meteorological data of AT, AP, AH, WS, CF, Rain, and SR in a certain area from the weather station, T dmax 、T dmin、ATD d 、ATD p , SD meteorological parameters; and then substitute the 12 meteorological parameters into the neural network-based structural temperature gradient monitoring index and meteorological parameter model established by the method in step 2 to obtain the predicted value of the temperature gradient data under the corresponding meteorological conditions, thereby effectively expanding the temperature gradient data sample set for subsequent calculation of the representative value of the temperature gradient of the bridge structure with a given return period;

[0039] Step 4. Estimation of the representative value of the temperature gradient of the bridge structure based on the expanded structural temperature gradient data

[0040] The super-threshold method is used to perform extreme value analysis on the expanded structural temperature gradient data to determine the representative value of the temperature gradient of the bridge structure; the POT method threshold is determined by the average excess function. When the threshold is set large enough, the super-threshold distribution will inevitably converge to the generalized Pareto distribution. The cumulative distribution function of the GP distribution is:

[0041]

[0042] Among them, μ is the threshold; σ is the scale parameter; ξ is the shape parameter;

[0043] The calculation method of the representative value of the temperature gradient of the bridge structure based on the expanded structural temperature gradient data is as follows:

[0044]

[0045]

[0046] Where R is the return period; p is the probability of exceeding the extreme value of the return period of a given R year; n is the number of STD extreme value samples used throughout the year, STD p It is the representative value of the STD for a given return period calculated from the GP distribution.

[0047] Beneficial effects of the present invention:

[0048] 1. The method of the present invention for determining the representative value of the recurrence period of the structural temperature gradient by establishing a correlation model between meteorological parameters and the structural temperature gradient can effectively extend the monitoring time of the structural temperature gradient and make the calculation result of the representative value of the recurrence period of the structural temperature gradient more accurate.

[0049] 2. The method for constructing a set of localized training samples of meteorological parameters and temperature gradients based on two-stage clustering of the present invention can consider the classification clustering index, and the divided training set and test set can ensure that all meteorological conditions of the monitoring time are effectively trained, thereby improving the prediction generalization accuracy of the model related to meteorological data and structural temperature gradient;

[0050] 3. The invented bridge temperature gradient representative value estimation method based on structural health monitoring and meteorological data correlation can be applied to bridges of different structural types in different regions and has high universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flow chart of the implementation adopted by the method of the present invention;

[0052] Figure 2 The two-stage clustering method used in the present invention is used to construct the localized training set samples for meteorological parameters and structural temperature gradient data;

[0053] Figure 3 The training and testing results of the temperature gradient and meteorological parameter correlation model established by the method of the present invention using the BP neural network;

[0054] Figure 4 The long-term structural temperature difference estimation result obtained by implementing the method of the present invention;

[0055] Figure 5 The super-threshold method structure temperature difference threshold selection diagram obtained by implementing the method of the present invention;

[0056] Figure 6 The structural temperature difference extreme value probability distribution and fitting diagram obtained by implementing the method of the present invention;

[0057] Figure 7 This is a structural temperature gradient model diagram obtained by implementing the method of the present invention. DETAILED DESCRIPTION

[0058] The present invention is further described in detail below with reference to the accompanying drawings and a specific example.

[0059] The bridge temperature gradient representative value estimation method based on the correlation between structural health monitoring and meteorological data of the present invention is divided into four steps: "constructing a localized training data sample set of 12 meteorological parameters and structural temperature gradient data based on a two-stage clustering method", "establishing a correlation model between structural temperature gradient monitoring indicators and meteorological parameters based on a neural network model", "expanding temperature gradient data samples based on long-term historical meteorological data" and "estimating the representative value of bridge structure temperature gradient based on expanded structural gradient temperature data". The specific implementation method has been given above, and the process is as follows. Figure 1 As shown, the usage and features of the invention are explained below with reference to specific examples.

[0060] In this specific numerical example, a two-stage clustering method is used to construct localized training set samples for meteorological parameters and structural temperature gradient data. The highest and lowest daily temperatures, the maximum daily temperature difference, the daily total solar radiation intensity, and whether it rains are selected as clustering indicators, and finally divided into three types of meteorological conditions. The clustering results are as follows: Figure 2As shown, they are rainy days, high temperature days and low temperature days respectively.

[0061] According to step (1.1), meteorological parameter samples are selected, and according to step (1.2), structural temperature gradient samples are selected, and the data interval is 1 hour. According to step 2, the BP neural network is used to establish the relevant model. The training results of the temperature difference between two points are as follows: Figure 3 The root mean square error of the test set of the traditional random data set division method is 1.41, and the correlation coefficient is 0.79. The error of the test set constructed by the clustering-based localized sample of the present invention is 0.94, and the correlation coefficient is 0.94, which shows the effectiveness of the present invention in training and generalization effects.

[0062] Based on the established meteorological parameter and structural temperature gradient correlation model, the long-term structural temperature gradient can be estimated by obtaining long-term historical meteorological data from the meteorological website, thereby effectively extending the duration of the structural temperature gradient data. The estimation results of the temperature difference between two points are shown as follows: Figure 4 shown.

[0063] According to the extended long-term structural temperature gradient data, the extreme value samples are selected by the super-threshold method. In order to ensure that there is no correlation between the samples taken, it is necessary to ensure that the extreme values ​​taken are not data from the same day. Therefore, the daily extreme values ​​of the long-term structural temperature data are first taken, and then the threshold values ​​of the daily extreme value samples are taken. The average excess function method is used for threshold selection, such as Figure 5 As shown in the figure, taking the temperature difference between two points as an example, the slope of the curve is close to 0 when the threshold is around 11.1℃, so the threshold is selected as 11.1℃. The probability distribution and fitting of the temperature difference extreme value of the structure taking the temperature difference between two points as an example are shown in the figure. Figure 6 As shown. According to the fitting parameters and the formula introduced in step 4, the representative value of the structural temperature difference for a given 100-year return period can be obtained as 17.16°C. The multi-point temperature difference is modeled, data expanded and extreme value analyzed to obtain the representative value of the structural temperature gradient. The comparison results of the established structural temperature gradient model with the traditional method and the measured maximum value are shown in Figure 7 shown.

[0064] In this implementation, the representative value of the temperature gradient calculated by the method of the present invention for the 100-year return period is greater than the actual short-term extreme value, which verifies the rationality of the result. The traditional method uses the short-term daily extreme value to estimate the representative value of the 10-year return period, and the result is 20.9℃, the representative value of the 100-year return period structure temperature is 23.71℃, and the extreme value of the estimated structure temperature difference in 10 years is only 15.74℃, which shows that the result of using short-term data to estimate the representative value is unreasonable. This shows the effectiveness and rationality of the bridge temperature gradient representative value estimation method based on the correlation between structural health monitoring and meteorological data of the present invention.

Claims

1. A method for estimating a representative value of bridge temperature gradient based on long-term historical meteorological data, characterized in that: Here are the steps: Step 1. Construct a localized training data sample set of 12 meteorological parameters and structural temperature gradient data based on a two-stage clustering method (1.1) Construction of meteorological parameter data samples; meteorological parameters include directly obtained parameters and derived parameters. Directly obtained parameters include: air temperature AT, air pressure AP, humidity AH, wind speed WS, cloud cover CF, daily total solar radiation SR and whether it rains Rain; derived parameters include: daily maximum temperature T dmax , daily minimum temperature T dmin 、Daily maximum temperature difference ATD d , the maximum temperature difference from the previous day ATD P and sunshine duration SD; the data accuracy is 1h, and the calculation formula for effective sunshine duration is as follows: Where δ is the declination angle; is the latitude angle; ω is the solar hour angle; d is the dth day in a year; h SD is the effective sunshine duration; t is the local solar time, in hours; CF i is the cloud cover monitoring value of the ith hour, reflecting the degree to which the sky is covered by clouds, and its value is an integer from 0 to 10; (1.2) Temperature gradient sample construction: When there are multiple monitoring points, the difference between adjacent monitoring points of the structure forms a temperature gradient vector. The structural temperature difference between two adjacent monitoring points is given by the following formula: STD HI =T H -T I Among them, STD HI is the temperature difference between the two monitoring points H and I; T H , T I are the temperatures of measuring points H and I respectively; (1.3) Construction of localized training data samples of meteorological parameters based on two-stage clustering method; taking 12 types of meteorological parameters as input and temperature gradient vector as output, a relationship model between the above meteorological parameter input and temperature gradient output is established through a neural network; According to the two-stage clustering method, the data set formed by 12 types of meteorological parameters and structural temperature gradient vectors is divided into training set and test set. dmax , T dmin 、ATD d , daily total solar radiation, whether it rains or not are used as clustering indicators; the sample set formed by the above five meteorological parameters in N days is defined as X = {x1, x2, ..., x N }, where there are n1 continuous meteorological parameter variables and n2 categorical meteorological parameter variables in the data object x of each day; by clustering the above meteorological parameter sample set, a set consisting of j meteorological parameter clusters is formed, C j ={c1,c2,…c i ,…c j }; where any cluster c i and cluster c j The distance between is defined as: D(c i ,c j )=λ i +λ j -l {i,j} Among them, {i,j} represents the meteorological parameter cluster c i and cluster c j The meteorological parameter sample set formed after merging; i Calculated using the following formula: Among them, N i is the meteorological parameter cluster c i The number of samples in ; It is the estimated variance of the kth continuous meteorological parameter variable estimated from all data points in the sample set X formed by meteorological parameters; is the estimated variance of the kth continuous meteorological parameter variable estimated based on the data points in meteorological parameter cluster i; L is the number of categories of the pth categorical meteorological parameter variable; N ipl is the meteorological parameter cluster c i The number of samples belonging to the lth category of the pth sub-type meteorological parameter variable; In addition, λ i and λ {i,j} The calculation method of λ i same; The method consists of two steps. The first step is to preliminarily determine the rough estimate of the number of meteorological parameter clusters based on the Bayesian Information Criterion, that is, when the decrease of BIC decreases significantly with the increase of the number of meteorological parameter clusters, the preliminary number of clusters is determined; cluster C j ={c1,c2,…c i ,…c j The calculation formula of BIC is: Where N is the total number of samples contained in the meteorological parameter cluster X; In the second step, the pre-clustering result C obtained in the first step is used j ={c1,c2,…c i ,…c j } as the object, select the two clusters with the smallest distance to merge, and form a new cluster set C j-1 ; The calculation formula for the minimum distance is: d min (C j )=min{D(c m ,c n ):m≠n,m∈1~j,n∈1~j} Then, the ratio of the minimum distances of adjacent merges is used as an indicator to determine the final number of clusters. The formula for the ratio of the minimum distances of adjacent merges is: And so on, the minimum distance ratio of the merged adjacent cluster sets is calculated in sequence; When S =max{r s :s≥2}, determine the corresponding cluster number s as the optimal meteorological parameter cluster number; the second step is based on the fact that the largest ratio usually occurs when the last two meteorological data clusters are merged; use the change in the ratio of distances during each merger as the criterion to determine the optimal number of clusters; start by merging the roughly estimated meteorological data clusters obtained in the first step, and obtain a precise estimate of the number of meteorological parameter clusters when the distance ratio changes the most, thereby determining the meteorological parameter clustering data set; After obtaining the meteorological parameter clustering data set according to the two-stage clustering method, 80% of the meteorological parameter and temperature gradient data are randomly selected from each meteorological parameter clustering data set as the training set, and 20% of the meteorological parameter and temperature gradient data are randomly selected as the test set for meteorological parameter and temperature gradient modeling; Step 2. Establish a neural network-based structural temperature gradient monitoring index and meteorological parameter model; Step 3. Temperature gradient data sample expansion based on long-term historical meteorological data; Step 4. Estimate the representative value of the temperature gradient of the bridge structure based on the expanded structural temperature gradient data.

2. A bridge temperature gradient representative value estimation method based on long-term historical meteorological data according to claim 1, characterized in that: Step 2 is as follows: The 12 meteorological parameters of the monitoring time of the structural health monitoring system are used as input, and the temperature gradient data of the monitoring time is used as output. The training set and the test set divided in step (1.3) are modeled using a BP neural network; the neural network for modeling the relationship between meteorological parameters and temperature gradients is composed of multiple meteorological parameters as an input layer, one or more hidden layers and multiple temperature gradients as an output layer, and each layer contains a number of artificial neurons; the network training process based on the relationship between meteorological parameters and temperature gradients is to transmit the output value layer by layer through forward propagation, and adjust the weight and bias value backward through backward feedback, and iterate until the iteration condition is met.

3. The method for estimating a representative value of bridge temperature gradient based on long-term historical meteorological data according to claim 1 is characterized in that: Step 3 is as follows: By obtaining the long-term historical meteorological data of AT, AP, AH, WS, CF, Rain, and SR in a certain area from the weather station, T dmax , T dmin 、ATD d 、ATD p , SD meteorological parameters; and then substitute the 12 meteorological parameters into the neural network-based structural temperature gradient monitoring index and meteorological parameter model established by the method in step 2 to obtain the predicted value of the temperature gradient data under the corresponding meteorological conditions, thereby effectively expanding the temperature gradient data sample set for the subsequent calculation of the representative value of the temperature gradient of the bridge structure with a given return period.

4. The method for estimating a representative value of a bridge temperature gradient based on long-term historical meteorological data according to claim 1, characterized in that: Step 4 is as follows: The super-threshold method is used to perform extreme value analysis on the expanded structural temperature gradient data to determine the representative value of the temperature gradient of the bridge structure; the POT method threshold is determined by the average excess function. When the threshold is set large enough, the super-threshold distribution will inevitably converge to the generalized Pareto distribution. The cumulative distribution function of the GP distribution is: Among them, μ is the threshold; σ is the scale parameter; ξ is the shape parameter; The calculation method of the representative value of the temperature gradient of the bridge structure based on the expanded structural temperature gradient data is as follows: Where R is the return period; p is the probability of exceeding the extreme value of the return period of a given R year; n is the number of STD extreme value samples used throughout the year, STD p It is the representative value of the STD for a given return period calculated from the GP distribution.

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