Method for determining non-Gaussian characteristic areas on roof surfaces

Abstract

The present invention relates to the field of architectural design. To facilitate the determination of non-Gaussian characteristic areas on a roof surface, a method for determining non-Gaussian characteristic areas on a roof surface is provided, comprising: 1. modeling and conducting wind tunnel tests; 2. calculating the average wind pressure coefficient and the fluctuating wind pressure coefficient on the roof surface; 3. calculating the skewness and kurtosis of the fluctuating wind pressure; 4. determining the vortex distribution and non-Gaussian characteristic areas above the roof; 5. selecting measurement points within the non-Gaussian characteristic areas, analyzing the difference between the probability density function of the fluctuating wind pressure and the Gaussian distribution, and deriving the flow field conditions above the corresponding positions on the roof; 6. establishing a numerical model of the roof, setting boundary conditions according to wind tunnel test parameters, and obtaining numerical simulation data; 7. obtaining a wind pressure cloud map and a flow field streamline map on the roof; 8. further determining the non-Gaussian characteristic areas and their causes; and 9. dividing the non-Gaussian areas. The above steps facilitate the determination of non-Gaussian characteristic areas on the roof surface.

Description

Technical Field

[0001] The present invention relates to the field of architectural design, and in particular to a method for determining a non-Gaussian characteristic area on a roof surface. Background Art

[0002] Long-span roof structures offer advantages such as high flexibility, low damping, and low mass. However, due to their sensitivity to wind loads, wind disasters are the most damaging of all natural disasters. The strong suction caused by wind loads, along with the resulting pulsation and wind vibration, often damages long-span roof structures.

[0003] When designing existing large-span roof structures for wind resistance, the fluctuating wind pressure on the roof surface is generally assumed to follow a Gaussian distribution, and a uniform peak factor is used to calculate the extreme wind pressure. However, research by domestic and international scholars has shown that flow separation in areas such as the windward leading edge and roof corners can lead to asymmetric wind pressure distributions, resulting in non-Gaussian wind pressure histories characterized by large-amplitude wind pressure pulses. Using the peak factor used for Gaussian surfaces in these areas will underestimate the extreme wind pressure, making structures in these areas more susceptible to wind damage. Summary of the Invention

[0004] In order to facilitate the determination of non-Gaussian characteristic areas on a roof surface, the present application provides a method for determining non-Gaussian characteristic areas on a roof surface.

[0005] The technical solution adopted by the present invention to solve the above problems is:

[0006] The method for determining the non-Gaussian characteristic area on the roof surface includes:

[0007] Step 1: Establish a roof model and conduct a wind tunnel test to obtain wind pressure parameters and wind tunnel test parameters on the roof surface;

[0008] Step 2: Calculate the average wind pressure coefficient and pulsating wind pressure coefficient on the roof surface according to the wind pressure parameters;

[0009] Step 3: Calculate the skewness and kurtosis of the fluctuating wind pressure based on the average wind pressure coefficient;

[0010] Step 4: Determine the vortex distribution and non-Gaussian characteristic area above the roof based on the fluctuating wind pressure coefficient;

[0011] Step 5: Select a measuring point in the non-Gaussian characteristic area, analyze the difference between the probability density function of the fluctuating wind pressure and the Gaussian distribution, and deduce the flow field above the corresponding position of the roof;

[0012] Step 6: Establish a numerical model of the roof, set boundary conditions according to the wind tunnel test parameters, and obtain numerical simulation data;

[0013] Step 7: Obtain the wind pressure cloud map and flow field streamline map on the roof based on the numerical simulation data;

[0014] Step 8: If the skewness and kurtosis of the fluctuating wind pressure deviate from the Gaussian distribution curve, and there is a large-scale vortex at the corresponding position on the roof, it is considered that the probability density distribution of the fluctuating wind at this location on the roof exhibits non-Gaussian characteristics. Based on this, the cause of the non-Gaussian phenomenon is analyzed by combining the skewness, kurtosis, and flow field streamline diagram; the correlation of the measuring points in the large-scale vortex is greater than or equal to the threshold;

[0015] Step 9: Divide the non-Gaussian area based on the causes of the non-Gaussian phenomenon.

[0016] Furthermore, the calculation formula of the average wind pressure coefficient is: The calculation formula for the pulsating wind pressure coefficient is: V H is the average wind speed at the maximum height, p H is the reference static pressure at that height, is the pressure at each measuring point of the model, ρ is the air density, and N is the number of test samples of wind pressure at the measuring point.

[0017] Furthermore, Where γ3 and γ4 represent the skewness and kurtosis of the pulsating wind pressure at the measuring point, respectively; θ is the wind pressure coefficient at the measuring point; μ is the average wind pressure coefficient at the measuring point; σ is the root mean square value of the wind pressure coefficient at the measuring point; and N is the number of test samples of the wind pressure at the measuring point.

[0018] Furthermore, the method further includes step 10 of calculating the non-Gaussian peak factor of a typical measurement point.

[0019] Furthermore, in step 4, the specific steps of determining the vortex distribution above the roof based on the fluctuating wind pressure coefficient are as follows:

[0020] Step 411: Select one or more measuring points on the roof in the downwind direction or the crosswind direction;

[0021] Step 412: Process the pulsating wind pressure coefficient using Matlab programming software to obtain the correlation of the pulsating wind pressure at the measuring point;

[0022] Step 413: Set a correlation threshold and classify vortices according to the threshold: measuring points with correlation greater than or equal to the threshold are considered to be in the same large-scale vortex, and measuring points with correlation less than the threshold are considered to be in another vortex.

[0023] Furthermore, in step 4, the specific steps of determining the non-Gaussian characteristic area based on the fluctuating wind pressure coefficient are as follows:

[0024] Step 421: Select one or more measuring points on the roof in the downwind direction or the crosswind direction;

[0025] Step 422: Process the pulsating wind pressure coefficient by programming with the Matlab software to obtain the pulsating wind pressure time history coefficient;

[0026] Step 423: Determine the data burr situation at each measuring point based on the fluctuating wind pressure time history coefficient. If the variance of the fluctuating wind pressure time history coefficient exceeds 20% of the average variance of all measuring points, it is inferred that the corresponding roof area has non-Gaussian characteristics.

[0027] Furthermore, the wind tunnel test parameters include wind profile, reference point wind speed, wind field type and turbulence.

[0028] Compared with the prior art, the present invention has the following advantages: the method for determining non-Gaussian characteristic regions provided in the present application is clear and unambiguous, quantifiable and calculable, and combines experiments with numerical simulations to make the results more realistic and reliable, thus achieving a logical closed loop. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Flowchart of the method for determining non-Gaussian characteristic areas on roof surfaces;

[0030] Figure 2 is a schematic diagram of the average wind speed profile;

[0031] Figure 3 is a schematic diagram of the turbulence profile;

[0032] Figure 4 is the power spectrum of the fluctuating wind along the wind direction;

[0033] Figure 5 This is the numerical simulation model diagram;

[0034] Figure 6 This is the calculation domain diagram for numerical simulation;

[0035] Figure 7 Comparison chart of wind tunnel test and numerical simulation data. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0037] like Figure 1 As shown in FIG, the method for determining the non-Gaussian characteristic area on the roof surface includes:

[0038] Step 1: Establish a roof model and conduct a wind tunnel test to obtain wind pressure parameters and wind tunnel test parameters on the roof surface. The wind tunnel test parameters include wind profile, reference point wind speed, wind field type, and turbulence.

[0039] Step 2: Calculate the average wind pressure coefficient and pulsating wind pressure coefficient on the roof surface according to the wind pressure parameters;

[0040] Step 3: Calculate the skewness and kurtosis of the fluctuating wind pressure based on the average wind pressure coefficient;

[0041] Step 4: Determine the vortex distribution and non-Gaussian characteristic area above the roof based on the fluctuating wind pressure coefficient;

[0042] Step 5: Select a measuring point in the non-Gaussian characteristic area, analyze the difference between the probability density function of the fluctuating wind pressure and the Gaussian distribution, and deduce the flow field above the corresponding position of the roof;

[0043] Step 6: Establish a numerical model of the roof, set boundary conditions according to the wind tunnel test parameters, and obtain numerical simulation data;

[0044] Step 7: Obtain the wind pressure cloud map and flow field streamline map on the roof based on the numerical simulation data;

[0045] Step 8: If the skewness and kurtosis of the fluctuating wind pressure deviate from the Gaussian distribution curve, and there is a large-scale vortex at the corresponding position on the roof, it is considered that the probability density distribution of the fluctuating wind at this location on the roof exhibits non-Gaussian characteristics. Based on this, the cause of the non-Gaussian phenomenon is analyzed by combining the skewness, kurtosis, and flow field streamline diagram; the correlation of the measuring points in the large-scale vortex is greater than or equal to the threshold;

[0046] Step 9: Divide the non-Gaussian area based on the causes of the non-Gaussian phenomenon.

[0047] Specifically, the calculation formula of the average wind pressure coefficient is: The calculation formula for the pulsating wind pressure coefficient is: V H is the average wind speed at the maximum height, p H is the reference static pressure at that height, is the pressure at each measuring point of the model, ρ is the air density, and N is the number of test samples of wind pressure at the measuring point.

[0048] Where γ3 and γ4 They represent the skewness and kurtosis of the pulsating wind pressure at the measuring point respectively; θ is the wind pressure coefficient of the measuring point; μ is the average wind pressure coefficient of the measuring point; σ is the root mean square value of the wind pressure coefficient of the measuring point; and N is the number of test samples of the wind pressure at the measuring point.

[0049] In step 4, the specific steps of determining the vortex distribution above the roof based on the fluctuating wind pressure coefficient are as follows:

[0050] Step 411: Select one or more measuring points on the roof in the downwind direction or the crosswind direction;

[0051] Step 412: Process the pulsating wind pressure coefficient using Matlab programming software to obtain the correlation of the pulsating wind pressure at the measuring point;

[0052] Step 413: Set a correlation threshold and classify vortices according to the threshold: measuring points with correlation greater than or equal to the threshold are considered to be in the same large-scale vortex, and measuring points with correlation less than the threshold are considered to be in another vortex.

[0053] In step 4, the specific steps of determining the non-Gaussian characteristic area based on the fluctuating wind pressure coefficient are as follows:

[0054] Step 421: Select one or more measuring points on the roof in the downwind direction or the crosswind direction;

[0055] Step 422: Process the pulsating wind pressure coefficient by programming with the Matlab software to obtain the pulsating wind pressure time history coefficient;

[0056] Step 423: Determine the data burr situation at each measuring point based on the fluctuating wind pressure time history coefficient. If the variance of the fluctuating wind pressure time history coefficient exceeds 20% of the average variance of all measuring points, it is inferred that the corresponding roof area has non-Gaussian characteristics.

[0057] Furthermore, the method further includes step 10 of calculating the non-Gaussian peak factor g of a typical measurement point:

[0058] Where: v0 is the zero crossing rate, m i is the i-th order spectral moment, S iy (n) is the unilateral power spectral density, n is the frequency, T is the time interval, γ = 0.5772 is the Euler constant; h3, h4, and κ are the parameters of the Hermite series method: The skewness and kurtosis values ​​of the wind pressure time series are represented by symbols λ3 and λ4 respectively.

[0059] Example

[0060] In this embodiment, the roof structure is designed as a rigid model according to a geometric scale ratio of 1:100, and the corresponding test blockage ratio is less than 5%. The model is made of organic glass and ABS plastic to meet the model stiffness and appearance requirements. In order to accurately obtain the surface wind load, hundreds of pressure measuring points are arranged on the roof surface. At the same time, in view of the significant flow separation at the edge of the roof and the top of the curved surface and the complex wind load characteristics, the measuring points in the above-mentioned areas are encrypted. In terms of the test condition setting, tests are carried out and data is collected every 10° within the wind direction angle range of 0° to 360°. The pressure measurement and data acquisition system is a Scanvalve electronic scanning valve with a sampling frequency of 256Hz and a sampling time of 60s, which meets the test similarity ratio requirements.

[0061] The simulated atmospheric boundary layer turbulence field was a Class B turbulence field as specified in GB50009-2012, "Code for Loads on Building Structures." The experimental turbulence field was simulated in a wind tunnel using a wedge and roughness element setup. Wind speed in the turbulent field was measured using a TFI Cobra 3D pulsating anemometer (Cobra Probe), with a sampling frequency of 256 Hz and a sampling duration of 60 seconds. Figure 2 is a schematic diagram of the average wind speed profile; Figure 3 is a schematic diagram of the turbulence profile; Figure 4 is the power spectrum of the fluctuating wind in the downwind direction; where Z is the height, ZG is the height of the model reference point, U is the average wind speed, UG is the wind speed at the model reference point, and Iu is the longitudinal turbulence intensity. The test results show that the turbulent flow field simulated in the test meets the requirements of the specification.

[0062] The pressure values ​​of each pressure measuring point obtained in the wind tunnel test are processed by programming to calculate the average wind pressure coefficient of each pressure measuring point. The calculation formula is: V H is the average wind speed at the maximum height, p H is the reference static pressure at that height, is the pressure at each measuring point of the model, and ρ is the air density. The pressure values ​​of each pressure measuring point obtained in the wind tunnel test are processed by programming to calculate the pulsating wind pressure coefficient of each pressure measuring point. The calculation formula is: N is the number of test samples of wind pressure at the measuring point.

[0063] One or more measuring points along the roof or across the wind at a wind direction of 0° were selected, and the pulsating wind pressure coefficient time history of each measuring point was calculated using Matlab. The pulsating wind pressure coefficient time history of the measuring points fluctuated violently, and the wind pressure time history was no longer symmetrical about the mean. The wind pressure signal showed instantaneous and intermittent downward pulses. These glitches at the measuring points often lead to non-Gaussian characteristics of the wind pressure. Therefore, it is necessary to analyze the non-Gaussian characteristics of the wind pressure.

[0064] The skewness γ3 and kurtosis γ4 of the fluctuating wind pressure at a measuring point can be expressed as follows: θ is the wind pressure coefficient at the measuring point; μ is the average wind pressure coefficient at the measuring point; σ is the root mean square value of the wind pressure coefficient at the measuring point; and N is the number of wind pressure test samples at the measuring point. For a Gaussian distribution, the skewness of the fluctuating wind pressure is λ3 = 0, and the kurtosis is λ4 = 3. Therefore, whether the skewness and kurtosis are 0 and 3, respectively, can be used as criteria for judging whether the fluctuating wind pressure at a measuring point follows a Gaussian distribution. When the skewness is less than 0, the probability distribution of the fluctuating wind pressure tends to be negative. When the skewness is greater than 0, the probability distribution of the fluctuating wind pressure tends to be positive compared to the Gaussian distribution. When the kurtosis is greater than 3, the distribution curve is more tapered than the Gaussian distribution curve, while when the kurtosis is less than 3, the curve is relatively flat.

[0065] The distribution characteristics of the fluctuating wind pressure on the roof surface are directly determined by the flow field structure around the roof. When the measuring point is located in a small-scale vortex area, the fluctuating wind pressure shows a weak correlation, thus showing Gaussian characteristics; when the measuring point is located in a large-scale vortex area, the fluctuating wind pressure shows a strong correlation, thus showing non-Gaussian characteristics. Therefore, by calculating the spatial correlation between measuring points, the Gaussian distribution and non-Gaussian distribution characteristics of the fluctuating wind pressure at the measuring point can be displayed. The calculation results of the spatial correlation between measuring points can show whether the fluctuating wind pressure at the measuring point has obvious non-Gaussian characteristics. The relevant expressions are as follows: Cpi and Cpj represent the standard deviation of the wind pressure time series at the two measuring points, respectively. If the calculated correlation coefficient value exceeds 0.5, it can be understood that there is a strong correlation characteristic between the measuring points. If the calculated correlation coefficient is lower than 0.2 at this time, it should be a weak correlation characteristic. Previous studies have shown that non-Gaussian areas of pulsating wind loads often appear in large-scale vortices after airflow diversion, and there is a close logical connection between the vortex structure and the spatial correlation of wind pressure. In order to explore the spatial correlation of wind pressure, the correlation between each measuring point in the crosswind and alongwind measuring point strips and the first measuring point in the strip is calculated, and the non-Gaussian characteristics of the vortex structure and wind load are inferred based on this.

[0066] After trial calculations, it was found that although the RNGk-ε model corrected the viscosity of the flow field, the simulation effect of turbulence in the numerical simulation of this model was not ideal. In comparison, after the Realizablek-ε model corrected the viscosity of the flow field, the flow field conditions had a better fit with the flow field conditions in the wind tunnel test. Therefore, the Realizablek-ε model was selected as the turbulence model to be solved.

[0067] When setting the inlet and outlet conditions of the computational domain in Fluent software, the outlet of the computational domain is set to an unobstructed fully developed outlet. In Fluent, the wind velocity boundary layer at the airflow inlet of the computational domain is set by importing a pre-compiled udf file. The flow field wind profile properties generated in the CFD numerical simulation are determined according to the average wind profile properties in the wind tunnel test. Because the wind tunnel test simulates a Class B boundary layer, α is set to 0.15 in the setting. The turbulent kinetic energy k and turbulent dissipation rate ε can be determined by the following formula: k(z)=1.2[I(z)×V z ] 2 , Where I(z) is the turbulence intensity, which can be calculated according to the specification Obtain, I 10 The nominal turbulence at a height of 10m. u It is often set to a constant of 0.09 during calculations. L is the characteristic scale of the calculation domain when it is imported. The value here refers to the Japanese standard.

[0068] The two sides and the top of the computational domain are set to symmetry conditions, and the model surface needs to be set to wall. To use the single precision separation method to complete the solver calculation, it is necessary to use the SIMPLE algorithm to express the velocity-pressure coupling method, select the second-order upwind method, and set the parameter to 0.5. The accuracy of the calculated residual should be 1×10 -4 Select a smooth point on the roof surface close to the windward side as the reference point. When the calculation accuracy reaches the set accuracy, the software automatically completes the calculation and waits for data storage and analysis. The numerical simulation model diagram and numerical simulation calculation domain diagram are as follows: Figure 5 Figure 6 shown.

[0069] The average wind pressure coefficient converted from the data measured by the wind tunnel test is compared with the numerical simulation results to verify the accuracy of the wind tunnel test. The comparison results are as follows: Figure 7 The causes of the non-Gaussian phenomenon on the roof are analyzed by combining the skewness and kurtosis values ​​measured in the wind tunnel test with the flow field streamline diagram in the numerical simulation.

[0070] The non-Gaussian region of the roof is divided in a reasonable manner. The following methods are used: Gioffre et al. used the absolute value of skewness greater than 0.5 and the kurtosis greater than 3.5 as the criteria for the non-Gaussian region of a cylindrical high-rise building. Sun Ying et al. used the absolute value of skewness greater than 0.2 and the kurtosis greater than 3.7 as the criteria for the non-Gaussian region of a flat roof. Li Yuxue et al. used the critical value of skewness and kurtosis when the cumulative probability distribution of the skewness and kurtosis of the wind pressure signal reached 80% as the criteria for the non-Gaussian region of a cylindrical roof.

[0071] Furthermore, based on the kurtosis and skewness values ​​in the wind pressure process, the non-Gaussian process is transformed into a Hermite series, and the peak factor is represented by the symbol g: Where: v0 is the zero crossing rate, m i is the i-th order spectral moment, S iy (n) is the unilateral power spectral density, n is the frequency, T is the time interval, γ = 0.5772 is the Euler constant; h3, h4, and κ are the parameters of the Hermite series method: The skewness and kurtosis of the wind pressure time history are represented by the symbols λ3 and λ4, respectively. The obtained peak factor is compared with the standard value (0.25), providing a valuable reference for practical engineering applications.

Claims

1. A method for determining non-Gaussian characteristic areas on a roof surface, characterized in that: include: Step 1: Establish a roof model and conduct a wind tunnel test to obtain wind pressure parameters and wind tunnel test parameters on the roof surface; Step 2: Calculate the average wind pressure coefficient and pulsating wind pressure coefficient on the roof surface according to the wind pressure parameters; Step 3: Calculate the skewness and kurtosis of the fluctuating wind pressure based on the average wind pressure coefficient; Step 4: Determine the vortex distribution and non-Gaussian characteristic area above the roof based on the fluctuating wind pressure coefficient; Step 5: Select a measuring point in the non-Gaussian characteristic area, analyze the difference between the probability density function of the fluctuating wind pressure and the Gaussian distribution, and deduce the flow field above the corresponding position of the roof; Step 6: Establish a numerical model of the roof, set boundary conditions according to the wind tunnel test parameters, and obtain numerical simulation data; Step 7: Obtain the wind pressure cloud map and flow field streamline map on the roof based on the numerical simulation data; Step 8: If the skewness and kurtosis of the fluctuating wind pressure deviate from the Gaussian distribution curve, and there is a large-scale vortex at the corresponding position on the roof, it is considered that the probability density distribution of the fluctuating wind at this location on the roof exhibits non-Gaussian characteristics. Based on this, the cause of the non-Gaussian phenomenon is analyzed by combining the skewness, kurtosis, and flow field streamline diagram; the correlation of the measuring points in the large-scale vortex is greater than or equal to the threshold; Step 9: Divide the non-Gaussian area based on the causes of the non-Gaussian phenomenon; In step 4, the specific steps of determining the non-Gaussian characteristic area based on the fluctuating wind pressure coefficient are as follows: Step 421: Select one or more measuring points on the roof in the downwind direction or the crosswind direction; Step 422: Process the pulsating wind pressure coefficient by programming with the Matlab software to obtain the pulsating wind pressure time history coefficient; Step 423: Determine the data burr situation at each measuring point based on the fluctuating wind pressure time history coefficient. If the variance of the fluctuating wind pressure time history coefficient exceeds 20% of the average variance of all measuring points, it is inferred that the corresponding roof area has non-Gaussian characteristics.

2. The method for determining non-Gaussian characteristic areas on a roof surface according to claim 1, characterized in that: The calculation formula of the average wind pressure coefficient is: , the calculation formula of the pulsating wind pressure coefficient is: ; is the average wind speed at the maximum height, is the reference static pressure at that height, is the pressure at each measuring point of the model, ρ is the air density, and N is the number of test samples of wind pressure at the measuring point.

3. The method for determining non-Gaussian characteristic areas on a roof surface according to claim 1, wherein: , , where r3 and r4 represent the skewness and kurtosis of the pulsating wind pressure at the measuring point respectively; is the wind pressure coefficient of the measuring point; is the average wind pressure coefficient at the measuring point; is the root mean square value of the wind pressure coefficient at the measuring point; N is the number of test samples of the wind pressure at the measuring point.

4. The method for determining non-Gaussian characteristic areas on a roof surface according to claim 1, wherein: The method further includes step 10 of calculating the non-Gaussian peak factor of a typical measuring point.

5. The method for determining non-Gaussian characteristic areas on a roof surface according to claim 1, characterized in that: In step 4, the specific steps of determining the vortex distribution above the roof based on the fluctuating wind pressure coefficient are as follows: Step 411: Select one or more measuring points on the roof in the downwind direction or the crosswind direction; Step 412: Process the pulsating wind pressure coefficient using Matlab programming software to obtain the correlation of the pulsating wind pressure at the measuring point; Step 413: Set a correlation threshold and classify vortices according to the threshold: measuring points with correlation greater than or equal to the threshold are considered to be in the same large-scale vortex, and measuring points with correlation less than the threshold are considered to be in another vortex.

6. The method for determining non-Gaussian characteristic areas on a roof surface according to any one of claims 1 to 5, characterized in that: The wind tunnel test parameters include wind profile, reference point wind speed, wind field type and turbulence.

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