Large-span roof fluctuating wind pressure spectrum prediction method based on frequency domain spectrum intrinsic orthogonal decomposition

Abstract

The invention discloses a large-span roof fluctuating wind pressure spectrum prediction method based on frequency domain spectrum intrinsic orthogonal decomposition. The method comprises the following steps: establishing a fluctuating wind pressure cross spectrum at any two spatial positions based on a fluctuating wind pressure spectrum; forming a fluctuating wind pressure cross spectrum matrix of all measuring points of the roof by the fluctuating wind pressure cross spectrum; solving a spectrum eigenvector matrix and a spectrum eigenvalue matrix of the fluctuating wind pressure cross-spectrum matrix; and reconstructing the fluctuating wind pressure spectrum matrix into a fluctuating wind pressure spectrum matrix with a finite order. According to the large-span roof fluctuating wind pressure spectrum prediction method based on the frequency domain spectrum eigen orthogonal decomposition, the frequency domain spectrum eigen orthogonal decomposition method based on the large-span roof surface fluctuating wind pressure cross-spectral density function can consider turbulence coherent structures in the frequency domain and the space range at the same time; the influence of characteristic turbulence on wind pressure characteristics and a wind pressure forming mechanism can be disclosed, and the method can be successfully applied to reconstruction of a fluctuating wind pressure spectrum on the roof surface and fluctuating wind pressure spectrum prediction of a sparse wind pressure matrix.

Description

Technical Field

[0001] The invention relates to a study on the coherent mechanism of wind pressure on a large-span roof, and in particular to a method for predicting pulsating wind pressure spectrum of a large-span roof based on intrinsic orthogonal decomposition of frequency domain spectrum. Background Art

[0002] In the field of wind resistance of building structures, large-span roofs are typical wind-sensitive structures. Under the action of wind loads, the incoming turbulence separates at the windward leading edge of the roof, forming characteristic turbulence such as columnar vortices or conical vortices, which affects the spatial distribution of wind pressure on the roof surface and the potential damage mechanism of the roof caused by the spatial correlation of wind pressure, thus attracting many scholars to study and analyze the temporal and spatial coherence mechanism of wind pressure on large-span roofs under the action of characteristic turbulence.

[0003] In order to gain a deeper understanding of the spatiotemporal evolution of the fluctuating pressure field of a large-span roof under the action of characteristic turbulence, the surface wind pressure field can be decomposed by the frequency domain spectrum intrinsic orthogonal decomposition method, so that the dominant subprocess after decomposition is related to the formation mechanism and specific physical phenomena of characteristic turbulence. The surface wind pressure field of a large-span roof has a spatiotemporal joint distribution characteristic, which is very important for describing turbulence-related and coherent structures. However, no existing technology has been found to accurately predict the fluctuating wind pressure spectrum of a large-span roof based on the frequency domain spectrum intrinsic orthogonal decomposition method.

[0004] Solving the above problems has become a top priority. Summary of the invention

[0005] In order to solve the technical problem that the current method based on the frequency domain spectrum intrinsic orthogonal decomposition cannot accurately predict the large-span roof fluctuating wind pressure spectrum, the present invention provides a large-span roof fluctuating wind pressure spectrum prediction method based on the frequency domain spectrum intrinsic orthogonal decomposition.

[0006] The technical solution is as follows:

[0007] A method for predicting fluctuating wind pressure spectrum of a large-span roof based on intrinsic orthogonal decomposition of frequency domain spectrum is mainly based on the following steps:

[0008] S1. Establish any two spatial positions υ based on the pulsating wind pressure spectrum p(v,f). i and j The cross spectrum of fluctuating wind pressure at

[0009] S2, from any two spatial positions υ i and j The cross spectrum of fluctuating wind pressure at The cross-spectrum matrix S of the fluctuating wind pressure of all measuring points on the roof p (υ,f);

[0010] S3. Solve the cross-spectrum matrix S of the fluctuating wind pressure at all measuring points on the roofp (υ,f) spectral eigenvector matrix ψ(υ,f) and spectral eigenvalue matrix Λ(f);

[0011] S4. Reconstruct the fluctuating wind pressure spectrum matrix p(υ,f) into a finite-order fluctuating wind pressure spectrum matrix using the finite-order spectrum eigenvector matrix ψ(υ,f) and the spectrum eigenvalue matrix Λ(f)

[0012] S5. Obtain the fluctuating wind pressure spectrum p at the set position on the roof surface based on the wind tunnel pressure test i (υ,f) and the distribution cloud diagram of the fluctuating wind pressure coefficient at each point on the roof surface;

[0013] S6. interpolating the spectral characteristic vector at any measuring point in the distribution cloud diagram of the fluctuating wind pressure coefficient at each point on the roof surface;

[0014] S7, the fluctuating wind pressure cross-spectrum matrix S of all measuring points on the roof in step S2 is p Substitute the spectral eigenvector matrix at the measuring point obtained by interpolation in step S6 into the fluctuating wind pressure spectrum matrix in step S4. The predicted value of the pulsating wind pressure spectrum at the measuring point is obtained.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] The large-span roof fluctuating wind pressure spectrum prediction method based on frequency domain spectrum intrinsic orthogonal decomposition using the above technical solution and the frequency domain spectrum intrinsic orthogonal decomposition method based on the cross-spectral density function of the fluctuating wind pressure on the surface of the large-span roof can simultaneously consider the turbulent coherent structure in the frequency domain and the spatial range, and can reveal the influence of characteristic turbulence on the wind pressure characteristics and the wind pressure formation mechanism, and can be successfully applied to the reconstruction of the fluctuating wind pressure spectrum on the roof surface and the prediction of the fluctuating wind pressure spectrum of the sparse wind pressure matrix. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The average and fluctuating wind pressure coefficient distribution of flat roofs in suburban terrain using wind tunnel pressure test;

[0018] Figure 2 The wind pressure spectrum of a typical measuring point of a flat roof pulsating wind pressure field reconstructed by the method of the present invention;

[0019] Figure 3 The wind pressure spectrum of typical measuring points of the pulsating wind pressure field of a flat roof predicted by the method of the present invention is shown in FIG. DETAILED DESCRIPTION

[0020] The present invention is further described below in conjunction with embodiments and drawings.

[0021] A method for predicting fluctuating wind pressure spectrum of a large-span roof based on intrinsic orthogonal decomposition of frequency domain spectrum is carried out in the following steps:

[0022] S1. Establish any two spatial positions υ based on the pulsating wind pressure spectrum p(v,f). i and j The cross spectrum of fluctuating wind pressure at

[0023] Specifically, the fluctuating wind pressure field on the roof surface is described in the frequency domain as a fluctuating wind pressure spectrum p(υ,f). Each subprocess represents the fluctuating wind pressure spectrum at a certain spatial position on the roof surface. Therefore, the fluctuating wind pressure spectrum p(υ,f) is expressed as: p(υ,f) = {p 1 (υ,f),p 2 (υ,f),…,p N (υ,f)}, where f is the frequency, N is the number of pressure measuring points on the roof surface, υ is the spatial coordinate of the wind pressure test position on the roof surface, and υ is expressed as: υ=(x,y,z). For a flat roof, υ is abbreviated as υ=(x,y).

[0024] S2, from any two spatial positions υ i and j The cross spectrum of fluctuating wind pressure at The cross-spectrum matrix S of the fluctuating wind pressure of all measuring points on the roof p (υ,f).

[0025] Specifically, any two spatial positions υ i and j The cross spectrum of fluctuating wind pressure at The expression is: in, Indicates i The transpose of the fluctuating wind pressure spectrum at p j ( j ,f) represents υ j Fluctuating wind pressure spectrum at , E[*] represents the expectation operator;

[0026] The cross-spectral matrix S of the fluctuating wind pressure at all measuring points on the roof p The expression of (υ,f) is:

[0027] S3. Solve the cross-spectrum matrix S of the fluctuating wind pressure at all measuring points on the roof p (υ,f) is the spectral eigenvector matrix ψ(υ,f) and the spectral eigenvalue matrix Λ(f).

[0028] Specifically, the cross-spectral matrix S of the fluctuating wind pressure at all measuring points on the roof is solved pThe expressions of the spectral eigenvector matrix ψ(υ,f) and spectral eigenvalue matrix Λ(f) of (υ,f) are:

[0029] S p (υ,f)ψ(υ,f)=Λ(f)ψ(υ,f) (1)

[0030] In formula (1), the spectral eigenvalue matrix Λ(f) is expanded into a subprocess: Λ(f) = diag(λ 1 (f),λ 2 (f),…,λ N (f)), and at the same time, the spectral eigenvector matrix ψ(υ,f) is expanded into a subprocess: ψ(υ,f) = {ψ 1 (υ,f),ψ 2 (υ,f),…,ψ N (υ,f)};

[0031] Then, the spectral principal coordinate matrix a(f) can be obtained from the spectral eigenvector matrix ψ(υ,f) and the fluctuating wind pressure spectrum matrix p(υ,f):

[0032] a(f)=ψ(v,f) T p(v,f) (2)

[0033] In formula (2), the spectrum principal coordinate matrix a(f) is expanded into a subprocess: a(f) = {a 1 (f),a 2 (f),…,a N (f)}.

[0034] S4. Reconstruct the fluctuating wind pressure spectrum matrix p(υ,f) into a finite-order fluctuating wind pressure spectrum matrix using the finite-order spectrum eigenvector matrix ψ(v,f) and the spectrum eigenvalue matrix Λ(f)

[0035] Specifically, the finite-order fluctuating wind pressure spectrum matrix It is expressed as:

[0036]

[0037] In formula (3), a i (f) represents the i-th spectrum principal coordinate, ψ i (υ,f) represents the i-th spectral eigenvector, From the kth to the The order spectrum principal coordinates and spectrum eigenvectors are reconstructed, where

[0038] S5, see Figure 1 , based on the wind tunnel pressure test, the fluctuating wind pressure spectrum p at the set position on the roof surface is obtained i(υ,f) and the distribution cloud diagram of the pulsating wind pressure coefficient at each point on the roof surface.

[0039] S6. Interpolate the spectral characteristic vector at any measuring point in the distribution cloud diagram of the fluctuating wind pressure coefficient at each point on the roof surface. It should be noted that the interpolation method preferably adopts the quadratic interpolation method.

[0040] S7, the fluctuating wind pressure cross-spectrum matrix S of all measuring points on the roof in step S2 is p Substitute the spectral eigenvector matrix at the measuring point obtained by interpolation in step S6 into the fluctuating wind pressure spectrum matrix in step S4. The predicted value of the pulsating wind pressure spectrum at the measuring point is obtained.

[0041] See also Figure 2 , Figure 2 The wind pressure spectrum of the typical measuring point shown in the sub-figure is reconstructed according to the order of steps S1-S7, and compared with the test wind pressure spectrum of the point. The results show that the wind pressure spectrum of the typical measuring point reconstructed only by the first-order spectrum principal coordinates and spectrum eigenvectors is almost completely consistent with the test wind pressure spectrum.

[0042] In order to test whether this method can be applied to predict the fluctuating wind pressure spectrum, see Figure 3 , assuming Figure 3 The fluctuating wind pressure spectrum of the measuring point shown in the sub-figure in is known, and the fluctuating wind pressure spectrum at the “+” measuring point needs to be predicted. In step S6, the spectrum feature vector ψ at the “+” measuring point is + (υ,f) is interpolated; in step S7, the predicted value of the fluctuating wind pressure spectrum at the "+" measuring point is obtained. The results show that the typical measuring point wind pressure spectrum predicted only by the first-order spectrum principal coordinates and spectrum eigenvectors is almost completely consistent with the test wind pressure spectrum, indicating that this method can be used to predict the fluctuating wind pressure spectrum and can achieve a high prediction accuracy.

[0043] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention, and such changes all fall within the scope of protection of the present invention.

Claims

1. A method for predicting fluctuating wind pressure spectrum of a large-span roof based on intrinsic orthogonal decomposition of frequency domain spectrum, characterized in that: Follow these steps: S1. Based on the pulsating wind pressure spectrum p(v,f), establish any two spatial positions v i and v j The cross spectrum of fluctuating wind pressure at S2, from any two spatial positions v i and v j The cross spectrum of fluctuating wind pressure at The cross-spectrum matrix S of the fluctuating wind pressure of all measuring points on the roof p (v,f); S3. Solve the cross-spectrum matrix S of the fluctuating wind pressure at all measuring points on the roof p The spectral eigenvector matrix ψ(v,f) and spectral eigenvalue matrix Λ(f) of (v,f); S4. Reconstruct the fluctuating wind pressure spectrum matrix p(v,f) into a finite-order fluctuating wind pressure spectrum matrix using the finite-order spectrum eigenvector matrix ψ(v,f) and the spectrum eigenvalue matrix Λ(f) S5. Obtain the fluctuating wind pressure spectrum p at the set position on the roof surface based on the wind tunnel pressure test i (v, f) and the distribution cloud diagram of the fluctuating wind pressure coefficient at each point on the roof surface; S6. interpolating the spectral characteristic vector at any measuring point in the distribution cloud diagram of the fluctuating wind pressure coefficient at each point on the roof surface; S7, the fluctuating wind pressure cross-spectrum matrix S of all measuring points on the roof in step S2 is p (v, f) and the spectral eigenvector matrix at the measuring point obtained by interpolation in step S6 are substituted into the fluctuating wind pressure spectrum matrix in step S4. The predicted value of the pulsating wind pressure spectrum at the measuring point is obtained.

2. The method for predicting fluctuating wind pressure spectrum of a large-span roof based on frequency domain spectrum intrinsic orthogonal decomposition according to claim 1 is characterized in that: In step S1, the fluctuating wind pressure field on the roof surface is described in the frequency domain as a fluctuating wind pressure spectrum p(v,f), which is expressed as: p(v,f)={p1(v,f),p2(v,f),…,p N (v,f)}, where f is the frequency, v is the spatial coordinate of the wind pressure test position on the roof surface, and N is the number of pressure measuring points on the roof surface.

3. The method for predicting fluctuating wind pressure spectrum of a large-span roof based on frequency domain spectrum intrinsic orthogonal decomposition according to claim 2 is characterized in that: In step S2, any two spatial positions v i and v j The cross spectrum of fluctuating wind pressure at The expression is: in, Indicates v i The transposition of the fluctuating wind pressure spectrum at p j (v j ,f) indicates v j Fluctuating wind pressure spectrum at , E[*] represents the expectation operator; The cross-spectral matrix S of the fluctuating wind pressure at all measuring points on the roof p The expression of (v,f) is:

4. The method for predicting fluctuating wind pressure spectrum of a large-span roof based on frequency domain spectrum intrinsic orthogonal decomposition according to claim 3 is characterized in that: In step S3, the cross-spectral matrix S of the fluctuating wind pressure at all measuring points on the roof is solved. p The expressions of the spectral eigenvector matrix ψ(v,f) and spectral eigenvalue matrix Λ(f) of (v,f) are: S p (v,f)ψ(v,f)=Λ(f)ψ(v,f)(1) In formula (1), the spectral eigenvalue matrix Λ(f) is expanded into subprocesses: Λ(f) = diag(λ1(f),λ2(f),…,λ N (f)), and at the same time, the spectral eigenvector matrix ψ(v,f) is expanded into subprocesses: ψ(v,f) = {ψ1(v,f), ψ2(v,f), …, ψ N (v,f)}; Then, the spectrum principal coordinate matrix a(f) can be obtained from the spectrum eigenvector matrix ψ(v,f) and the fluctuating wind pressure spectrum matrix p(v,f): a(f)=ψ(v,f) T p(v,f)(2) In formula (2), the spectrum principal coordinate matrix a(f) is expanded into subprocesses: a(f) = {a1(f), a2(f), …, a N (f)}.

5. The method for predicting fluctuating wind pressure spectrum of a large-span roof based on frequency domain spectrum intrinsic orthogonal decomposition according to claim 4 is characterized in that: In the step S4, Finite-order fluctuating wind pressure spectrum matrix It is expressed as: In formula (3), a i (f) represents the i-th spectrum principal coordinate, ψ i (v,f) represents the i-th spectral eigenvector, From the kth to the The order spectrum principal coordinates and spectrum eigenvectors are reconstructed, where

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