Load spectrum construction method for large-span roof fatigue analysis

Abstract

The invention relates to a load spectrum construction method for large-span roof fatigue analysis, and belongs to the field of fatigue analysis methods.According to the method, a wind speed and wind direction joint distribution model is constructed by adopting a Copula function based on historical wind field data, the model precision is optimized through edge distribution, a wind load distribution template is generated and corrected by utilizing finite element simulation and monitoring data, and the wind load distribution model is constructed by adopting the Copula function. Mapping wind field data to a template to construct a cyclic load spectrum; the construction of the wind speed and wind direction joint distribution model comprises the following specific steps: constructing the wind speed and wind direction joint distribution model; using GEV distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find most appropriate edge distribution for the wind direction and the wind speed; a joint probability density distribution relation of two variables is described through a binary Archimedes Copula function, and a joint distribution model of wind speed and wind direction is established. The whole roof is covered through gridding, simulation data and sensor data fusion correction are combined, a time-space multi-dimensional cyclic load spectrum is constructed, and the analysis precision and practicability are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the field of fatigue analysis methods, and in particular relates to a load spectrum construction method for fatigue analysis of a large-span roof. Background Art

[0002] As an important structural form of modern buildings, the fatigue problem of long-span roofs under wind loads is directly related to the safety and durability of the structure. Since long-span roofs usually cover a large area and have a complex configuration, their structures are subjected to cyclic loads caused by wind for a long time. Fatigue damage is easy to accumulate in high stress concentration areas, which may lead to local failure or even overall destruction. Therefore, accurately evaluating the fatigue life of long-span roofs has important engineering significance, which can not only extend the service life of the structure, but also improve the safety and operational efficiency of the building.

[0003] In this field, traditional methods usually perform fatigue analysis based on single-point monitoring data or wind load distribution at a specific location. These methods mainly rely on single sensor data or wind load spectra in local areas, combined with the material's SN curve and cumulative damage theory to estimate fatigue life. However, this single-point or local analysis method cannot fully reflect the wind load distribution characteristics of the entire roof, especially when the wind field changes complexly, the analysis results are prone to deviations. In addition, the existing technology usually directly relies on simulation data or a single data source in the construction of cyclic load spectra. This approach fails to fully combine actual monitoring data for correction, resulting in deviations between the load spectrum and the actual situation, reducing the reliability and accuracy of fatigue analysis. At the same time, these methods are mostly limited to two-dimensional plane analysis, and it is difficult to fully capture the fatigue distribution characteristics of the roof in the spatial dimension, and it is impossible to effectively identify high-risk areas and vulnerable points.

[0004] Based on the above research background, this patent proposes a load spectrum construction method for fatigue analysis of large-span roofs. Summary of the invention

[0005] The purpose of the present invention is to provide a load spectrum construction method for large-span roof fatigue analysis, thereby improving the accuracy and practicability of large-span roof fatigue analysis.

[0006] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0007] A load spectrum construction method for fatigue analysis of a large-span roof, the method uses a Copula function to construct a joint distribution model of wind speed and wind direction based on historical wind field data, optimizes the model accuracy through edge distribution, generates and corrects a wind load distribution template using finite element simulation and monitoring data, and constructs a cyclic load spectrum by mapping wind field data to the template;

[0008] The specific steps of constructing the joint distribution model of wind speed and wind direction include:

[0009] Use GEV distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find the most appropriate marginal distribution for wind direction and wind speed;

[0010] The binary Archimedean Copula function is used to describe the joint probability density distribution relationship between two variables, and a joint distribution model of wind speed and wind direction is established.

[0011] In one aspect, a load spectrum construction system for fatigue analysis of a large-span roof is provided, the system comprising:

[0012] The joint distribution modeling module uses the Copula function to build a joint distribution model of wind speed and wind direction based on historical wind field data, and uses GEV distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find the most suitable marginal distribution for wind direction and wind speed; the binary Archimedean Copula function is used to describe the joint probability density distribution relationship of the two variables, and the joint distribution model of wind speed and wind direction is established;

[0013] A wind load distribution generation module is used to generate a preliminary wind load distribution template through finite element simulation and monitoring data, and to calibrate the template using actual sensor data;

[0014] Load spectrum construction module, used to map wind field data to templates and construct cyclic load spectra for large-span roofs.

[0015] Beneficial effects:

[0016] This paper proposes a load spectrum construction method for fatigue analysis of large-span roofs. By covering the entire roof with gridding and combining simulation data with sensor data fusion correction, a time-space multi-dimensional cyclic load spectrum is constructed, which significantly improves the accuracy and practicality of the analysis.

[0017] The present disclosure overcomes the defects of the prior art that single-point or local sensor data cannot fully reflect the wind load characteristics of the roof, and the defects that the prior analysis is mostly limited to a two-dimensional plane and is difficult to capture the spatial fatigue distribution of the roof.

[0018] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0020] Figure 1 is a flow chart of the disclosed method;

[0021] Figure 2 This is a schematic diagram of the northwest corner of Daxing Airport;

[0022] Figure 3 This is the wind pressure distribution template under 40 wind field conditions disclosed in this disclosure;

[0023] Figure 4 The wind direction and speed data disclosed in this disclosure are summarized into 40 wind farm templates;

[0024] Figure 5 is a cyclic load spectrum at a certain node of the present disclosure;

[0025] Figure 6 Fitting the marginal distribution of wind direction disclosed in the present invention;

[0026] Figure 7 Fitting the marginal distribution of wind speed disclosed in the present invention;

[0027] Figure 8 This is the fatigue life distribution diagram of the northwest corner roof of this disclosure. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] The present invention discloses a load spectrum construction method for fatigue analysis of large-span roofs. The method uses a Copula function to construct a joint distribution model of wind speed and wind direction based on historical wind field data, and optimizes the model accuracy through edge distribution; then, a wind load distribution template is generated and corrected using finite element simulation and monitoring data; then, a cyclic load spectrum is constructed by mapping the wind field data to the template; finally, based on the cyclic load spectrum and the cumulative damage criterion, the fatigue damage of the roof nodes is calculated and a fatigue characteristic distribution diagram is drawn, so as to solve the problems of inaccurate wind load modeling, complex cyclic load spectrum construction and incomplete fatigue life assessment in traditional roof fatigue analysis.

[0030] like Figure 1 As shown in the figure, the load spectrum construction method for fatigue analysis of large-span roofs includes the following steps:

[0031] S1: Construct a joint distribution model of wind direction and speed;

[0032] The airflow separation caused by the roof configuration will have a great impact on the distribution of the roof wind load. Under different wind direction conditions, the wind load distribution of the entire roof will be quite different. In order to study the fatigue characteristics of the entire roof, it is necessary to comprehensively consider the two conditions of wind speed and wind direction to construct the cyclic wind load spectrum of the roof. In order to accurately describe the cyclic wind load spectrum affected by wind speed and wind direction, the present invention uses a probabilistic joint distribution model to construct a wind field model, and uses the Copula function as a probabilistic joint distribution function. It is a practical function that can connect multiple random variables and is widely used in various fields.

[0033] Before using the Copula function to construct the joint probability distribution of wind direction and wind speed, it is necessary to determine the marginal distribution of wind speed and wind direction respectively. Use GEV (Generalized Extreme Value) distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find the most suitable marginal distribution for wind direction and wind speed. The probability density formulas of these marginal distribution models are as follows:

[0034] GEV Distribution:

[0035]

[0036] Where μ, σ, and k are the location, scale, and shape parameters of the GEV distribution, respectively. Depending on the value of k, there are three types of GEV distribution: when k = 0, it is a Gumbel distribution (extreme type I); when k>0, it is a Fréchet distribution (extreme type II); and when k<0, it is an inverse three-parameter Weibull distribution (extreme type III).

[0037] Rayleigh distribution:

[0038]

[0039] In the above formula, b is the scale parameter of the Rayleigh distribution.

[0040] Weibull distribution:

[0041]

[0042] Where a and b are the scale and shape parameters of the Weibull distribution, respectively. The Weibull distribution has two forms: two-parameter and three-parameter. The two-parameter form is used here, which has the advantage of better fitting of the tail data.

[0043] Logistic Distribution:

[0044]

[0045] Where μ and σ are the location and scale parameters of the Logistic distribution, respectively.

[0046] In order to determine whether the sample conforms to the fitted distribution model, this patent uses the Kolmogorov-Smirnov (KS) test to perform a fitting test on the distribution model. Assume that the theoretical probability distribution function of the random variable X is F(x), and the empirical probability distribution function of the sample is S n (x), then the maximum deviation between the two constructs the test statistic D n It can be expressed as:

[0047] D n =max|S n (x)-F(x)| (5)

[0048] The significance level is α = 0.05, and the KS test will compare the statistic D n With critical value For comparison, the critical value under the significance level α Defined as:

[0049]

[0050] If the observed value D n Less than critical value Then the assumed theoretical probability distribution is valid under the specified significance level α, that is, the sample is considered to satisfy the distribution.

[0051] After establishing the marginal distribution of wind direction and wind speed, the commonly used binary Archimedean Copula function is selected to describe the joint probability density distribution relationship of the two variables. Archimedean Copula functions include Gumbel, Clayton and Frank functions. The Frank function is not very sensitive to tail dependence, while the Gumbel and Clayton functions are sensitive to tail dependence. Their probability distribution and density functions are as follows:

[0052] Gumbel Copula:

[0053] C θ (u,v)=exp(-[(-lnu) θ +(-lnv) θ ] 1 / θ ) (7)

[0054]

[0055] Clayton Copula:

[0056] C θ (u,v)=(u -θ +v-θ -1) -1 / θ (9)

[0057]

[0058] Frank Copula:

[0059]

[0060] In the above formula, θ is the parameter value of the Copula function, and this scheme uses the maximum likelihood method for estimation; u and v represent the marginal distributions of two random variables respectively; C θ represents the joint cumulative probability distribution function; c θ is the joint probability density distribution function.

[0061] Different marginal distribution functions and various Copula functions will construct various forms of joint distribution. In order to make the constructed joint distribution model closer to reality, it is necessary to ensure that the marginal distribution can describe the distribution characteristics of random variables, and the relevant parameters θ can accurately describe the correlation between variables. This patent uses the following goodness of fit indicators to comprehensively evaluate the constructed joint sub-model, including the root mean square error method (RMSE), the AIC information criterion method, and the Nash efficiency coefficient NSE method.

[0062] Root mean square error (RMSE):

[0063]

[0064] AIC Information Criteria Method:

[0065]

[0066] Nash efficiency coefficient NSE method:

[0067]

[0068] In the above formula, n is the sample size; p0 is the empirical value of the empirical distribution; p s is the theoretical value of the fitted distribution; is the average value of p0; k is the number of joint distribution parameters. The smaller the value of the evaluation index RMSE is, the closer the value of NSE is to 1, the smaller the residual of the model distribution and the empirical distribution is, and the better the fitting effect of the Copula function is. The smaller the value of AIC is, the better the fitting effect of the Copula function is. The AIC information criterion method takes into account both the complexity of the model and the minimization of the residual. When the statistical sample of the random variable is large, the AIC criterion still has high credibility and computational efficiency.

[0069] At this point, the wind direction and wind speed data for a whole year are divided into four quarters for probability density fitting, and the joint probability distribution model of wind direction and wind speed in the four quarters can be obtained.

[0070] S2: Divide the wind load distribution template

[0071] By analyzing and fitting the actual data, the joint probability distribution model of wind speed and direction can be obtained. However, to calculate the fatigue distribution of the entire roof, it is also necessary to map the joint probability distribution model of wind field conditions to the wind load distribution of the entire roof.

[0072] Taking the northwest corner of Daxing Airport as an example, in order to study the fatigue condition of the roof at the northwest corner of the terminal building of Daxing Airport, Figure 2 As shown. In order to solve the wind load response of the roof, it is necessary to traverse the wind speed and wind direction. The wind field conditions are subdivided into 8 wind directions and 5 wind speeds, a total of 40 groups of wind field conditions. The finite element software is used to calculate the finite element wind load distribution under each wind field condition as the initial template. In order to more accurately reflect the actual wind load conditions, the least squares method is used to modify the initial template using the actual sensor data, and the following is obtained: Figure 3 The resulting wind load distribution is shown as the final template.

[0073] S3: Constructing cyclic load spectrum

[0074] After obtaining the joint probability density distribution model of wind speed and direction, as well as the roof wind load distribution templates under forty typical wind field conditions. First, a series of wind direction and wind speed data are generated through the joint probability density distribution model, and then these data are summarized into the forty set wind field templates according to the proximity principle, such as Figure 4 As shown, the cyclic wind load spectrum of each node in the entire roof area can be obtained, such as Figure 5 shown.

[0075] S4: Perform fatigue analysis of roof nodes;

[0076] On the basis of the cyclic wind load spectrum, the roof is meshed according to the size of the metal roof panel to obtain the cyclic wind load spectrum of each grid point. The fatigue SN curve of the roof panel and the linear damage accumulation criterion can be used to obtain the fatigue condition of the entire roof.

[0077] S5: output roof fatigue distribution map;

[0078] The node fatigue damage value is used as the attribute value and annotated in the 3D model in a pseudo-color map. The fatigue distribution map uses red to represent high damage risk areas and blue to represent low damage areas, so as to intuitively show the fatigue characteristics distribution of the roof.

[0079] The method combines multi-source data and can construct a cyclic load spectrum for fatigue analysis covering the entire roof area, thereby improving the accuracy and practicality of fatigue analysis of large-span roofs.

[0080] Furthermore, the disclosed method is verified by the following method, taking the roof fatigue analysis at the northwest corner of Daxing Airport as an example.

[0081] First, for the wind speed and marginal distribution fitting, taking the spring wind field as an example, the wind speed and wind direction data of the roof of Daxing Airport for three months from January 1, 2024 to March 31, 2024 were selected, the mean was calculated according to the ten-minute time interval, and different marginal distribution functions were used to fit it.

[0082] Figure 6 Different marginal distribution functions of the average wind direction in the first quarter of 2024 are given. CDF represents the cumulative probability. It can be seen that the wind direction with the highest probability of occurring in the first quarter is near 120° and 220°. The GEV distribution of the average wind direction in the first quarter has the best fitting effect, and its R square is closest to 1. The AIC index and the root mean square error are the smallest. Therefore, the GEV distribution is adopted as the distribution type of the average wind direction in the first quarter.

[0083] Figure 7 Different marginal distribution functions of the average wind speed in the first quarter of 2024 are given. CDF represents the cumulative probability. The Rayleigh distribution of the average wind speed in the first quarter has the best fitting effect, its R square is closest to 1, and the AIC index and the root mean square error are the smallest. Therefore, Rayleigh distribution is adopted as the distribution type of the average wind speed in the first quarter.

[0084] Then, three Copula functions are used to fit the wind speed and direction data for the first quarter of 2024, and the fitting results are shown in Table 1. The fitting model Frank and Clayton Copula function is insufficient in describing larger wind directions and longer periods, so the joint probability model obtained by the Gumbel Copula function will be used to describe the correlation between wind direction and wind speed distribution in the first quarter.

[0085] Table 1 Parameter fitting of wind speed and wind direction joint distribution

[0086]

[0087] On the basis of the cyclic wind load spectrum, the roof is meshed according to the size of the metal roof panel to obtain the cyclic wind load spectrum of each grid point. The fatigue SN curve of the roof panel and the linear damage accumulation criterion can be used to obtain the fatigue condition of the entire roof.

[0088] The northwest corner roof of Daxing Airport was taken as the research object, and the fatigue distribution of the roof was studied. A cyclic wind load spectrum was applied to it, and the load was stopped when a node on the roof reached the fatigue limit. The distribution of roof fatigue is as follows Figure 8 As shown, it can be seen from the figure that in the lowest corner of the northwest corner of the roof, the edge of the skylight has the lowest lifespan and is most likely to be damaged. This provides a reference for the key maintenance areas of the roof for roof health monitoring and management.

[0089] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0090] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A load spectrum construction method for fatigue analysis of large-span roofs, characterized in that: The method uses Copula function to construct a joint distribution model of wind speed and wind direction based on historical wind field data, optimizes the model accuracy through edge distribution, generates and corrects wind load distribution templates using finite element simulation and monitoring data, and constructs a cyclic load spectrum by mapping wind field data to the template; The specific steps of constructing the joint distribution model of wind speed and wind direction include: Use GEV distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find the most appropriate marginal distribution for wind direction and wind speed; The binary Archimedean Copula function is used to describe the joint probability density distribution relationship between two variables, and a joint distribution model of wind speed and wind direction is established.

2. The load spectrum construction method for fatigue analysis of a large-span roof according to claim 1 is characterized in that: The method uses Kolmogorov-Smirnov (KS) to determine whether the marginal distribution probability of the sample wind direction and wind speed is established.

3. The load spectrum construction method for large-span roof fatigue analysis according to claim 1 is characterized in that: The method adopts AIC information criterion method and Nash efficiency coefficient NSE method to evaluate the model fitting effect.

4. The load spectrum construction method for fatigue analysis of a large-span roof according to claim 1 is characterized in that: The steps of generating the wind load distribution template are as follows: setting multiple groups of wind field templates to traverse the wind speed and wind direction, and using finite element software to calculate the finite element wind load distribution under each wind field condition as the initial template; The initial template is modified using the actual sensor data using the least squares method.

5. The load spectrum construction method for fatigue analysis of a large-span roof according to claim 1 is characterized in that: The step of constructing the cyclic load spectrum includes generating a series of wind direction and wind speed data through a joint probability density distribution model, and then summarizing these data into multiple groups of wind field templates according to the proximity principle to obtain the cyclic wind load spectrum of each node.

6. The load spectrum construction method for large-span roof fatigue analysis according to claim 5 is characterized in that: The fatigue analysis of the roof nodes includes, based on the cyclic wind load spectrum, meshing the roof according to the size of the metal roof panel to obtain the cyclic wind load spectrum of each grid point, and using the fatigue SN curve of the roof panel and the linear damage accumulation criterion to obtain the fatigue condition of the entire roof.

7. The load spectrum construction method for fatigue analysis of a large-span roof according to claim 5 is characterized in that: The method comprises calculating fatigue damage of roof nodes based on cyclic load spectrum and cumulative damage criterion and drawing a fatigue characteristic distribution diagram; The fatigue characteristic distribution diagram uses the node fatigue damage value as the attribute value and is marked in the three-dimensional model in a pseudo-color diagram manner.

8. The load spectrum construction method for large-span roof fatigue analysis according to claim 7 is characterized in that: The fatigue property distribution map uses red to represent high damage risk areas and blue to represent low damage areas.

9. A load spectrum construction system for large-span roof fatigue analysis, characterized in that: The system comprises: The joint distribution modeling module uses the Copula function to build a joint distribution model of wind speed and wind direction based on historical wind field data, and uses GEV distribution, Rayleigh distribution, Weibull distribution and Logistic distribution to find the most suitable marginal distribution for wind direction and wind speed; the binary Archimedean Copula function is used to describe the joint probability density distribution relationship of the two variables, and the joint distribution model of wind speed and wind direction is established; A wind load distribution generation module is used to generate a preliminary wind load distribution template through finite element simulation and monitoring data, and to calibrate the template using actual sensor data; Load spectrum construction module, used to map wind field data to templates and construct cyclic load spectra for large-span roofs.

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