Method and device for identifying equivalent physical stiffness and damping matrix of super high-rise building

Abstract

The application discloses a method and device for identifying equivalent physical stiffness and damping matrix of super high-rise building. First, the design parameters of the target super high-rise building are obtained, the static condensation method is used to condense the degrees of freedom of the target super high-rise building to obtain a corresponding low-degree equivalent system, and an equivalent mass matrix is obtained. Then, the physical time history signal measured at the condensation position is decoupled by using the complex second-order blind identification method to obtain a modal signal and a complex mode shape, and the improved Bayesian spectral density method is used to identify the modal parameters of the modal signal to obtain a frequency and a damping ratio. Finally, the equivalent physical stiffness and damping matrix are obtained by combining the obtained complex modal parameters with the equivalent mass matrix. The application adopts the degree of freedom condensation strategy, simplifies the system with high degree of freedom into an equivalent reduced model with less degree of freedom according to the actual measurement conditions and the structural response characteristics, and then evaluates the equivalent physical stiffness and damping matrix of the building based on the incomplete complex modal parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of building structure system identification, and particularly relates to a method and device for identifying equivalent physical stiffness and damping matrix of super high-rise buildings. BACKGROUND

[0002] The self-excited aerodynamic force generated by the interaction of wind and structure is the cause of the aeroelastic effect of super high-rise buildings. The self-excited aerodynamic force can be simplified as an aerodynamic stiffness term, an aerodynamic damping term and an aerodynamic mass term, which are related to the displacement, velocity and acceleration of the structure motion respectively. Since the air density is much smaller than the building density, the aerodynamic mass term is generally considered negligible.

[0003] The most direct manifestation of the aeroelastic effect of super high-rise buildings is the change of modal frequency and damping ratio of the structure. Wind engineering researchers have carried out a series of wind tunnel test studies on the aeroelastic effect of super high-rise buildings through single degree of freedom aeroelastic model, multi-degree of freedom aeroelastic model and forced vibration, and the research content mainly focuses on the change of modal frequency and damping ratio with the scaled wind speed.

[0004] The content of the existing wind tunnel test study on the aeroelastic effect of super high-rise buildings only involves the change of modal frequency and damping ratio, and the physical stiffness and damping matrix which can truly represent the change of the physical stiffness and damping of the building has not been studied. Obviously, the content of the existing wind tunnel test study on the aeroelastic effect of super high-rise buildings is not accurate and comprehensive enough. SUMMARY

[0005] Based on this, the embodiments of the present application provide a method and device for identifying equivalent physical stiffness and damping matrix of super high-rise buildings, which can use the degree of freedom condensation strategy to simplify the system with high degree of freedom into an equivalent reduced model with less degree of freedom according to the actual measurement conditions and the structure response characteristics, and then establish a method for evaluating the equivalent physical stiffness and damping matrix of the building based on incomplete complex modal parameters according to the signal separation and modal parameter identification based on complex modal.

[0006] In a first aspect, a method for identifying equivalent physical stiffness and damping matrix of super high-rise buildings is provided, which comprises:

[0007] Obtaining design parameters of the target super high-rise building based on a finite element model, wherein the design parameters at least include the mass, the moment of inertia, the translational stiffness and the torsional stiffness of each layer;

[0008] Performing degree of freedom condensation on the target super high-rise building by using a static condensation method to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtaining an equivalent mass matrix;

[0009] The physical time history signals measured at the condensation position of the target super high-rise building are decoupled by the complex second-order blind identification method to obtain modal signals and complex modes; the number of physical time history signals, the number of modal signals, and the number of complex modes are consistent with the number of degrees of freedom of the equivalent system.

[0010] The modal parameters are identified by the improved Bayesian spectral density method to obtain the frequency and damping ratio; the number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system.

[0011] Based on the complex modal basic theory, the equivalent physical stiffness and damping matrix are obtained by the obtained complex modal parameters and the equivalent mass matrix.

[0012] Optionally, the degrees of freedom of the super high-rise building are condensed, the physical signals are decoupled, the modal signals are modal parameter identified, and then the equivalent physical stiffness and damping matrix are obtained by combining the equivalent mass matrix, comprising:

[0013] The low-degree-of-freedom equivalent system is obtained based on the design parameters of the target building by using the static condensation method, and the equivalent mass matrix is obtained.

[0014] The physical time history signals are decoupled by the complex second-order blind identification method to obtain modal signals and complex modes.

[0015] The modal parameters are identified by the improved Bayesian spectral density method to obtain the modal frequency and damping ratio.

[0016] Based on the frequency and damping ratio, the eigenvalue is obtained, the complex eigenvector is obtained based on the eigenvalue and the complex mode, and then the target matrix is solved by the eigenvalue matrix and the complex eigenvector matrix to obtain the equivalent physical stiffness and damping matrix.

[0017] Optionally, the physical time history signals measured at the condensation position of the target super high-rise building are decoupled by the complex second-order blind identification method, which includes that when each modal signal obtained by decoupling contains only one modal frequency, it indicates that the physical signal has been successfully decoupled.

[0018] Optionally, when the damping is non-proportional damping, the decoupling is performed by the complex modal method.

[0019] In the second aspect, an identification device for the equivalent physical stiffness and damping matrix of a super high-rise building is provided, and the device comprises:

[0020] An acquisition module acquires the design parameters of the target super high-rise building based on a finite element model, wherein the design parameters at least include the mass, the moment of inertia, the translational stiffness, and the torsional stiffness of each layer.

[0021] The degree of freedom condensation module adopts a static force condensation method to condense degrees of freedom of the target super high-rise building to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtain an equivalent mass matrix.

[0022] The decoupling module decouples physical time history signals measured at the condensed position of the target super high-rise building by using a complex second-order blind identification method to obtain modal signals and complex modes; the number of physical time history signals, the number of modal signals, and the number of complex modes are consistent with the number of degrees of freedom of the equivalent system.

[0023] The identification module is configured to identify modal parameters of the modal signals by using an improved Bayesian spectral density method to obtain frequencies and damping ratios; the number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system.

[0024] The determination module is configured to obtain equivalent physical stiffness and damping matrices based on the obtained complex modal parameters and the equivalent mass matrix according to a complex modal basic theory.

[0025] Optionally, the device further comprises:

[0026] The degree of freedom condensation module adopts a static force condensation method to obtain a low degree of freedom equivalent system based on design parameters of the target building, and obtain an equivalent mass matrix.

[0027] The decoupling module decouples physical time history signals by using a complex second-order blind identification method to obtain modal signals and complex modes.

[0028] The identification module identifies modal parameters of the modal signals by using an improved Bayesian spectral density method to obtain modal frequencies and damping ratios.

[0029] The determination module obtains eigenvalues based on the frequencies and the damping ratios, obtains a complex eigenvector based on the eigenvalues and the complex modes, and then obtains a target matrix by solving an eigenvalue matrix and a complex eigenvector matrix, and obtains equivalent physical stiffness and damping matrices by combining the target matrix with the equivalent mass matrix.

[0030] Optionally, the decoupling module decouples physical time history signals measured at the condensed position of the target super high-rise building by using a complex second-order blind identification method, which includes that when each modal signal obtained by decoupling contains only one modal frequency, it indicates that the physical signal has been successfully decoupled.

[0031] Optionally, when the damping is a non-proportional damping, the decoupling is performed by using a complex modal method.

[0032] The technical scheme provided by the embodiment of the application first acquires the design parameters of a target super high-rise building, adopts a static force condensation method to perform degree of freedom condensation processing on the target super high-rise building to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtains an equivalent mass matrix; then decouples a physical time history signal measured at the condensation position of the target super high-rise building by using a complex second-order blind identification method to obtain a modal signal and a complex mode shape, and adopts an improved Bayesian spectral density method to perform modal parameter identification on the modal signal to obtain a frequency and a damping ratio; finally, based on a complex modal basic theory, the equivalent physical stiffness and damping matrix are obtained by using the obtained complex modal parameters (the frequency, the damping ratio and the complex mode shape) and combining the equivalent mass matrix. It can be seen that the beneficial effects of the application are as follows: the degree of freedom condensation strategy can be adopted to simplify a system with a very high degree of freedom into an equivalent reduced model with a smaller degree of freedom according to actual measurement conditions and structural response characteristics, and then a method for evaluating the equivalent physical stiffness and damping matrix of a building based on incomplete complex modal parameters is established based on signal separation and modal parameter identification based on complex modes. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the application or the technical schemes in the prior art, the drawings needed to be used in the following embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are only exemplary, and other drawings can be derived from the provided drawings without creative labor for those skilled in the art.

[0034] Figure 1 A flowchart of a method for identifying an equivalent physical stiffness and damping matrix of a super high-rise building provided by the embodiment of the application;

[0035] Figure 2 A schematic diagram of three direction time history curves and power spectral densities in a physical coordinate provided by the embodiment of the application;

[0036] Figure 3 A signal in a modal coordinate obtained by decoupling a physical signal by using a complex second-order blind identification method provided by the embodiment of the application;

[0037] Figure 4 A flowchart of a method for identifying an equivalent physical stiffness and damping matrix of a super high-rise building provided by the embodiment of the application;

[0038] Figure 5 A schematic diagram of a system after condensation of a target building provided by the embodiment of the application. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not intended to limit the present application.

[0040] In the description of the present application, the meaning of "a plurality of" is two or more, unless otherwise specified. The terms "first", "second", "third", "fourth" and the like (if any) in the description of the present application and claims and the above-mentioned drawings are intended to distinguish the objects referred to. For the scheme with time sequence flow, such a term expression manner is not necessarily understood as describing a specific order or sequence, and for the scheme of device structure, there is no distinction of importance, positional relationship, etc.

[0041] In addition, the terms "include", "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units does not have to be limited to only those steps or units explicitly listed, but can also include other steps or units inherent to the process, method, product or device, or steps or units added based on further optimization of the inventive concept.

[0042] Step 101, obtaining the design parameters of the target super high-rise building based on the finite element model, wherein the design parameters at least include the mass of each layer, the moment of inertia, the translational stiffness and the torsional stiffness.

[0043] In the present application, the design parameters of the target super high-rise building are obtained by finite element model or other data acquisition means, including the complete mass matrix and stiffness matrix of the building.

[0044] Step 102, using the static condensation method to condense the degrees of freedom of the target super high-rise building to obtain the low degree of freedom equivalent system corresponding to the target super high-rise building, and obtain the equivalent mass matrix.

[0045] Because the air density is much smaller than the building density, it is generally believed that the mass of the super high-rise building will not change under the interaction of wind and structure, and the condensed equivalent mass matrix can be obtained based on the design parameters. Based on the physical parameters in the design stage, the building (model) system with more degrees of freedom is condensed into an equivalent system with fewer degrees of freedom, and the mass matrix condensation formula is as follows:

[0046]

[0047] Wherein, where [M] is the condensed mass matrix, [K] is the condensed stiffness matrix, a is the number of retained degrees of freedom, and b is the number of other degrees of freedom. The number of condensed degrees of freedom should be less than or equal to the number of modes to be identified.

[0048] The number of degrees of freedom of a multi-degree-of-freedom aeroelastic model in a super high-rise building or a wind tunnel test is usually high (usually more than 12 degrees of freedom), and the wind-induced response of the building is usually dominated by the fundamental mode (usually 2 lateral displacements and 1 torsion). Therefore, the original system is usually condensed into a 3-degree-of-freedom system.

[0049] In the alternative embodiments of the present application, when the damping in the structural system is non-proportional damping, the damping matrix cannot be diagonalized by the real mode shape, and the complex mode method must be used for decoupling.

[0050] For a non-proportional damping system, an identity equation is added to the system motion equation to obtain

[0051]

[0052]

[0053] where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, f is the external load vector, and x are the acceleration, velocity and displacement vectors, respectively. Combining the two equations, the equation

[0054]

[0055] where Let the homogeneous solution of the above equation be Substituting the homogeneous equation of equation (4) can obtain

[0056]

[0057] Let D = A- B, then the above equation can be converted to

[0058]

[0059] That is, the problem is transformed into solving the eigenvalues and eigenvectors of matrix D. Solving the above equation, n pairs of complex eigenvalues λ r 、 and n pairs of complex eigenvectors where n is the number of degrees of freedom of the system, r ranges from 1 to n, and * represents conjugate. For an under-damped system

[0060]

[0061]

[0062]

[0063]

[0064] Where, ζ r Let ω be the modal damping ratio. r Let ψ be the modal angular frequency, i be the imaginary unit, and ψ be the complex mode shape. Substituting n pairs of eigenvalues ​​and eigenvectors into the equation and transforming it, we can obtain...

[0065]

[0066] Therefore, based on the complex modal parameters (frequency, damping ratio, and complex vibration mode), a matrix D consisting of mass, stiffness, and damping elements can be derived. Combined with the equivalent mass matrix, the equivalent physical stiffness and damping matrices can then be obtained. The key is obtaining accurate modal parameters, especially the complex vibration mode.

[0067] Step 103: Decouple the physical time history signal measured at the condensation location of the target super high-rise building using the complex second-order blind identification method to obtain the modal signal and complex vibration mode.

[0068] Among them, the number of physical time history signals, the number of modal signals, the number of complex vibration modes are consistent with the number of degrees of freedom of the equivalent system.

[0069] This application employs a complex second-order blind identification method to decouple physical time-history signals to obtain modal signals and complex vibration modes. As can be seen from the basic theory of complex modes, regardless of whether the stiffness and damping matrices are symmetric, the equations of motion can be decoupled using certain methods to obtain independent modal signals. Furthermore, the basic principle of the complex second-order blind identification method shows that as long as the modal signals of each order are independent, this method can be used for modal decoupling. Therefore, the complex second-order blind identification method is applicable to both proportional and non-proportional damping when the stiffness and damping matrices are symmetric, and also to proportional and non-proportional damping when the stiffness and damping matrices are asymmetric.

[0070] The following example, using the free decay motion of a 3-DOF system, verifies the applicability of the complex second-order blind identification method to the most special system where the stiffness and damping matrices are asymmetric and the damping is non-proportional. Assume the system's mass matrix, stiffness matrix, and damping matrix are...

[0071]

[0072] With an initial velocity of 0 and initial displacements of 2, 10, and 30 in the three directions, the time history curves and power spectral densities in the three directions in physical coordinates are obtained as follows: Figure 2The physical signals in different directions all contain multi-order modal signals. In addition, the first two order modal frequencies of the system are close to each other, and the third order modal frequency is far away from the first two order modal frequencies, which is similar to the distribution rule of the first three order modal frequencies of a general super high-rise building.

[0073] The modal signals in the modal coordinates are obtained by decoupling the physical signals by using the complex second-order blind identification method as shown in the following table. Figure 3 It can be seen that each order modal signal obtained by decoupling only contains one modal frequency, which indicates that the physical signal has been successfully decoupled, and the effectiveness of the complex second-order blind identification method is verified.

[0074] In step 104, the modal parameter identification is performed on the above modal signals by using the improved Bayesian spectral density method to obtain the frequency and damping ratio.

[0075] The number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system.

[0076] The improved Bayesian spectral density method is used in the present application for modal parameter identification. The improved Bayesian spectral density method can be applied to colored noise with certain characteristics, and has the advantage of being able to obtain the error of the parameter identification result.

[0077] In step 105, based on the complex modal basic theory, the equivalent physical stiffness and damping matrix are obtained by combining the obtained complex modal parameters (frequency, damping ratio and complex mode shape) and the equivalent mass matrix.

[0078] Based on the modal frequency and damping ratio obtained in step 102, the eigenvalues are obtained according to formula and. Based on the eigenvalues and the complex mode shape obtained in step 102, the complex eigenvectors are obtained according to formula and. Then, the matrix D is solved by the eigenvalue matrix and the complex eigenvector matrix according to formula. The matrix D is composed of equivalent mass, stiffness and damping elements. For the condensed 3-DOF system, the equivalent mass, stiffness and damping matrix is assumed as follows

[0079]

[0080] According to the complex modal basic theory, D=A\-B, Therefore, the specific composition of the matrix D can be obtained as follows

[0081]

[0082] The equivalent physical stiffness and damping matrix can be obtained by combining the condensed equivalent mass matrix with formula. The complete identification process of the equivalent physical stiffness and damping matrix identification method proposed in the present application is shown in the following table. Figure 4

[0083] In another optional embodiment of the present application:

[0084] ​A multi-degree-of-freedom (MDOF) aeroelastic model of a super high-rise building with significant aeroelastic effect and modal coupling was designed and wind tunnel test was conducted. The prototype building is about 200 m high, with a cross section of approximately rectangular shape, 33.6 m in length and 26 m in width.

[0085] The wind tunnel test was conducted in a laboratory, with a test section of 5.4 m in width, 3 m in height and 24 m in length. The wind field around the building was simulated by using the B type of landform specified in the Load Code for the Design of Building Structures (GB50009-2012), with a gradient wind height of 350 m and a ground roughness coefficient of 0.12. A rectangular light plate was installed on the model skeleton, and the single model test was conducted under the above wind field.

[0086] Before the test, three uniaxial acceleration sensors were installed on the 2nd, 3rd, 4th and 6th floors of the model skeleton, respectively, two of which were along the y direction and i is the number of model floors), and one along the x direction The vertical distance between the y direction acceleration sensor and the model center of gravity was 0.023 m, and the torsional angular acceleration could be calculated by the following formula

[0087]

[0088] The test was conducted at two wind direction angles of 0° and 90° (narrow side windward and wide side windward, respectively), and the wind speed was gradually increased from 5.8 m / s to 13.9 m / s at certain intervals under each wind direction angle.

[0089] Before the physical stiffness and damping matrix identification, based on the physical parameters in the design stage, the static condensation method of the formula was used to condense the 18 degrees of freedom of the aeroelastic model into 3 degrees of freedom at the top floor, and the condensed system is shown in Figure 5 .

[0090] The equivalent mass matrix after condensation is as follows (in international units)

[0091]

[0092] The first three modes of the model were obtained by decoupling the measured time history signals of the top floor of the model (x, y and θ three directions) through the complex second-order blind identification method. The first three frequencies and damping ratios of the model were obtained by identifying the decoupled modal signals through the improved Bayesian spectral density method. Combined with the equivalent mass matrix after condensation, the equivalent physical stiffness and damping matrix of the model can be obtained by back calculation, which is shown in the following formula

[0093]

[0094]

[0095] Where, k xx k xy and k xθ These represent the forces generated in the x-translational direction by the unit displacement in the x-translational direction, the unit displacement in the y-translational direction, and the unit torsional angle in the α-torsional direction, respectively; k yx k yy and k yθ These represent the forces generated in the y-translational direction by the unit displacement in the x-translational direction, the unit displacement in the y-translational direction, and the unit torsional angle in the θ-torsional direction, respectively; k θx k θy and k θθ c represents the torque generated by a unit displacement in the x-direction, a unit displacement in the y-direction, and a unit torsional angle in the θ-direction, respectively. xx c xy and c xθ c represents the force generated in the x-direction by the unit linear velocity in the x-direction, the unit linear velocity in the y-direction, and the unit torsional angular velocity in the θ-direction, respectively; yx c yy and c yθ c represents the force generated in the y-translational direction by the unit linear velocity in the x-translational direction, the unit linear velocity in the y-translational direction, and the unit torsional angular velocity in the θ-torsional direction, respectively; θx c θy and c θθ These represent the torques generated in the torsional direction by the unit linear velocity in the x-direction, the unit linear velocity in the y-direction, and the unit torsional angular velocity in the θ-direction, respectively.

[0096] Because the scaling ratios of mass and moment of inertia differ, the scaling ratios of each element in the equivalent mass matrix of the model also differ. Similarly, the scaling ratios of translational displacement (linear velocity) and torsional angle (angular velocity) differ, as do the scaling ratios of force and torque. Therefore, the scaling ratios of each element in the equivalent stiffness and damping matrices of the model are also not identical. Based on the model's scaling parameters, the scaling ratios of each element in the equivalent physical mass, stiffness, and damping matrices of the model can be determined as follows:

[0097]

[0098]

[0099]

[0100] The calculated model equivalent physical stiffness and damping matrix divided by the corresponding scale ratio can obtain the prototype building equivalent physical stiffness and damping matrix, the results of which are consistent with the results of first dividing the model modal frequency, damping ratio, mode shape and equivalent physical mass matrix by the corresponding scale parameter to obtain the corresponding prototype building frequency, damping ratio, mode shape and equivalent physical mass matrix, and then inversely deducing the equivalent physical stiffness and damping matrix of the prototype building. Since the scale ratio of each element in the model equivalent physical stiffness and damping matrix is not the same, the application will directly analyze the results of the equivalent physical stiffness and damping matrix of the corresponding prototype building.

[0101] The physical stiffness and damping matrix are not strictly symmetric matrices, and will change significantly with the change of the reduced wind speed. In addition, it is worth noting that the non-symmetry of the 2x2 translational direction stiffness matrix and damping matrix in the upper left corner and becomes very significant when the reduced wind speed reaches V r = 9.5 and V r = 12.0. It shows that the wind-structure interaction can produce asymmetric aerodynamic stiffness and damping matrix, making the total physical stiffness and damping matrix of the building asymmetric, and its non-symmetry becomes more significant at high reduced wind speed.

[0102] Assuming that the equivalent physical mass of the prototype building is unchanged, based on the equivalent physical mass matrix of the prototype building and the equivalent physical stiffness and damping matrix of the prototype building at a specific reduced wind speed, the modal parameters of the prototype building at the corresponding reduced wind speed can be obtained. This paper uses modal assurance criterion (MACX) to describe the similarity of complex modal shape, which is defined as follows

[0103]

[0104] Where ψ1 and ψ2 are two sets of mode shapes, H is the conjugate transpose, and T is the transpose. The MACX value is between 0 and 1, and when the two mode shapes are completely consistent, the MACX value is 1. The calculated modal parameters of the prototype building at three reduced wind speeds are shown in Table 1. Among them, f1, f2 and f3 are the first three order frequencies, ζ1, ζ2 and ζ3 are the first three order damping ratios, and MACX j is the MACX value of the jth order mode shape of the prototype building under a certain working condition and the jth order mode shape of the prototype building under the low reduced wind speed (V r = 4.8) (j is 1, 2 or 3), and MACX 1-2MACX value of the first and second order mode shape of the building under a certain working condition. It can be seen that the change of the prototype building physical stiffness and damping matrix with the scaled wind speed will lead to significant changes in the first three order modal frequency, the first three order damping ratio and the first order mode shape of the building. In addition, the first two order mode shapes of the prototype building will become very similar at the vortex-induced resonance scaled wind speed of 9.5. Considering that the second order mode shape of the building under different scaled wind speeds is basically unchanged, it can be considered that the first order mode shape of the prototype building will be close to the second order mode shape at the vortex-induced resonance scaled wind speed of 9.5. This close phenomenon also occurs at a high scaled wind speed of 12.0.

[0105] Table 1 Comparison of modal parameters under low, medium and high scaled wind speeds

[0106]

[0107] The equivalent physical stiffness and damping matrix of the prototype building will change significantly with the scaled wind speed, and the change of the physical stiffness and damping matrix will significantly affect the modal parameters. It will be a very meaningful work to analyze the change rule of each element in the physical stiffness and damping matrix with the scaled wind speed. However, before summarizing the change rule of these elements, it is necessary to determine the influence of the change of each element on the specific modal parameters, otherwise, even if we summarize the change rule of these elements, we cannot understand the significance behind these change rules.

[0108] The equivalent physical stiffness and damping matrix of the prototype building under low scaled wind speed (4.8 when the wide side is windward, 6.6 when the narrow side is windward) can be regarded as the original physical stiffness and damping matrix of the prototype building, and the modal parameters obtained based thereon can be regarded as the original modal parameters. Therefore, the value of a certain element in the stiffness matrix and damping matrix under a certain scaled wind speed can be used to replace the value of the corresponding element in the stiffness matrix and damping matrix under low scaled wind speed to obtain new assumed stiffness matrix and damping matrix. By comparing the first three order frequency, the first three order damping ratio, MACX1, MACX2, MACX3, MACX 1-2 value of the new assumed stiffness matrix and damping matrix, the influence of the change of the corresponding element on the modal parameters can be obtained.

[0109] It is too cumbersome to show all the results of all elements under all scaled wind speeds, so here we directly give the general conclusion obtained: the change of the diagonal elements in the physical stiffness matrix mainly affects the modal frequency and damping ratio, and the smaller the value is, the smaller the modal frequency is; the change of the diagonal elements in the damping matrix mainly affects the damping ratio, and the smaller the value is, the smaller the damping ratio is; the difference between k yx and k xy and the difference between c yx and c xyThe difference of the diagonal elements of the translational stiffness matrix, i.e., the asymmetry of the translational stiffness matrix, mainly affects the coupling of the fundamental translational modes, k yx , k xy and c yx , c xy The change of the off-diagonal elements of the translational stiffness matrix and the translational damping matrix affects the damping ratio, but has little effect on the frequency; k xθ , k yθ The change of the off-diagonal elements of the translational stiffness matrix and the translational damping matrix has little effect on the modal parameters, c xθ , c yθ The change of the off-diagonal elements of the translational stiffness matrix and the translational damping matrix affects the third-order mode; k θx , k θy and c θx , c θy The change of the off-diagonal elements of the translational stiffness matrix and the translational damping matrix has little effect on the modal parameters. It is worth mentioning that the elements that can significantly affect the modal frequency are only the diagonal elements in the stiffness matrix, so it can be said that the modal frequency is mainly determined by the diagonal elements in the physical stiffness matrix.

[0110] Based on the complex modal basic theory, the equivalent physical stiffness and damping matrices of a 3-DOF (x translational direction, y translational direction and θ torsional direction) prototype building of a multi-DOF aeroelastic model are obtained by back-stepping from the complex modal parameters, and the influence of wind-structure interaction is explored in detail. The basic conclusions are as follows:

[0111] The diagonal elements of the equivalent physical stiffness matrix mainly affect the modal frequency and damping ratio, and the modal frequency is mainly determined by the diagonal elements in the physical stiffness matrix. The diagonal elements of the equivalent physical damping matrix mainly affect the damping ratio. The diagonal elements k xx , k yy and k θθ of the equivalent physical stiffness matrix change with the scaled wind speed in a similar way to f1, f2 and f3, respectively. The diagonal elements c xx , c yy and c θθ of the equivalent physical damping matrix change with the scaled wind speed in a similar way to ζ1, ζ2 and ζ3, respectively.

[0112] In the translational direction, the force generated by the unit displacement / unit velocity in the crosswind direction in the downwind direction is basically unchanged with the scaled wind speed, and the force generated by the unit displacement / unit velocity in the downwind direction in the crosswind direction changes greatly with the scaled wind speed, making the asymmetry of the translational stiffness matrix and the translational damping matrix more obvious at high scaled wind speed, and further making the coupling of the fundamental translational modes of the building significant, and making the downwind mode close to the crosswind mode.

[0113] For other elements in the equivalent physical stiffness and damping matrices, c xθ , c yθThe change of a will affect the third order mode, k xθ , k yθ , k θx , k θy and c θx , c θy The change of the element has little effect on the modal parameters.

[0114] The embodiment of the application also provides a device for identifying equivalent physical stiffness and damping matrix of super high-rise building. The device comprises:

[0115] The acquisition module acquires design parameters of the target super high-rise building based on the finite element model, wherein the design parameters at least include mass, moment of inertia, translational stiffness and torsional stiffness of each floor;

[0116] The degree of freedom condensation module adopts a static force condensation method to perform degree of freedom condensation processing on the target super high-rise building to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtains an equivalent mass matrix;

[0117] The decoupling module decouples physical time history signals measured at the condensed position of the target super high-rise building by using a complex second-order blind identification method to obtain modal signals and complex modes; wherein the number of physical time history signals, the number of modal signals and the number of complex modes are consistent with the number of degrees of freedom of the equivalent system;

[0118] The identification module is used for identifying modal parameters of the above-mentioned modal signals by using an improved Bayesian spectral density method to obtain frequencies and damping ratios; wherein the number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system;

[0119] The determination module obtains the equivalent physical stiffness and damping matrix based on the complex modal basic theory, the obtained complex modal parameters and the equivalent mass matrix.

[0120] In an optional embodiment of the application, the complex second-order blind identification method is used to decouple the physical time history signals, the improved Bayesian spectral density method is used to identify the modal parameters of the modal signals, and the equivalent physical stiffness and damping matrix are obtained in combination with the equivalent mass matrix, comprising:

[0121] The complex second-order blind identification method is used to decouple the physical time history signals to obtain modal signals and complex modes

[0122] The improved Bayesian spectral density method is used to identify the modal parameters of the modal signals to obtain modal frequencies and damping ratios;

[0123] The eigenvalues are obtained based on the frequencies and the damping ratios, the complex eigenvectors are obtained based on the eigenvalues and the complex modes, and the target matrix is solved by using the eigenvalue matrix and the complex eigenvector matrix to obtain the equivalent physical stiffness and damping matrix according to the target matrix and in combination with the equivalent mass matrix.

[0124] In an optional embodiment of the present application, the decoupling module decouples the physical time history signal measured at the condensation position of the target super high-rise building by using a complex second-order blind identification method, and when each modal signal obtained by decoupling contains only one modal frequency, it indicates that the physical signal has been successfully decoupled.

[0125] In an optional embodiment of the present application, when the damping is non-proportional damping, the decoupling is performed by using a complex modal method.

[0126] The identification device for the equivalent physical stiffness and damping matrix of the super high-rise building provided by the embodiments of the present application is used to implement the above-mentioned identification method for the equivalent physical stiffness and damping matrix of the super high-rise building. The specific limitations of the identification device for the equivalent physical stiffness and damping matrix of the super high-rise building can be referred to the limitations of the identification method for the equivalent physical stiffness and damping matrix of the super high-rise building in the foregoing, and will not be described here. Each part in the above-mentioned identification device for the equivalent physical stiffness and damping matrix of the super high-rise building can be realized by software, hardware and combinations thereof, in whole or in part. The above-mentioned modules can be embedded in or independent of the processor in the device in hardware form, or can be stored in the memory in the device in software form, so as to be called and executed by the processor to perform the operations corresponding to each module.

[0127] Each technical feature of the above-mentioned embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of each technical feature in the above-mentioned embodiments are not described, however, as long as the combination of these technical features does not exist contradictory, it should be considered as the scope of the present application.

[0128] The above-mentioned embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of the present application. Therefore, the scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for identifying equivalent physical stiffness and damping matrices of a super high-rise building, characterized in that, The method comprises: obtaining design parameters of the target super high-rise building based on a finite element model, wherein the design parameters at least include mass of each floor, moment of inertia, translational stiffness and torsional stiffness; performing degree of freedom condensation on the target super high-rise building by using a static condensation method to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtaining an equivalent mass matrix; decoupling physical time history signals measured at the condensation position of the target super high-rise building by using a complex second-order blind identification method to obtain modal signals and complex modes; wherein the number of physical time history signals, the number of modal signals and the number of complex modes are consistent with the number of degrees of freedom of the equivalent system; identifying modal parameters of the above modal signals by using an improved Bayesian spectral density method to obtain frequencies and damping ratios; wherein the number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system; obtaining equivalent physical stiffness and damping matrices based on the obtained complex modal parameters and the equivalent mass matrix according to the complex modal basic theory; performing degree of freedom condensation on the super high-rise building, decoupling the physical time history signals and identifying the modal parameters of the modal signals, and then obtaining the equivalent physical stiffness and damping matrices in combination with the equivalent mass matrix, comprising: obtaining a low degree of freedom equivalent system based on the design parameters of the target building by using a static condensation method, and obtaining an equivalent mass matrix; decoupling the physical time history signals by using a complex second-order blind identification method to obtain modal signals and complex modes; identifying modal parameters of the modal signals by using an improved Bayesian spectral density method to obtain modal frequencies and damping ratios; obtaining eigenvalues based on the frequencies and the damping ratios, obtaining complex eigenvectors based on the eigenvalues and the complex modes, and then solving the target matrix by using the matrix of the eigenvalues and the matrix of the complex eigenvectors, and obtaining the equivalent physical stiffness and damping matrices in combination with the equivalent mass matrix.

2. The identification method according to claim 1, characterized in that, The decoupling of the physical time history signals measured at the condensation position of the target super high-rise building by using the complex second-order blind identification method comprises: When each modal signal obtained by decoupling contains only one modal frequency, it indicates that the physical time history signals have been successfully decoupled.

3. The identification method according to claim 1, characterized in that, When the damping is non-proportional damping, decoupling is performed by using a complex modal method.

4. A device for identifying equivalent physical stiffness and damping matrices of a super high-rise building, characterized by, The device comprises: an obtaining module configured to obtain design parameters of a target super high-rise building based on a finite element model, wherein the design parameters at least include mass of each floor, moment of inertia, translational stiffness and torsional stiffness; a degree of freedom condensation module configured to perform degree of freedom condensation on the target super high-rise building by using a static condensation method to obtain a low degree of freedom equivalent system corresponding to the target super high-rise building, and obtain an equivalent mass matrix; a decoupling module configured to decouple physical time history signals measured at the condensation position of the target super high-rise building by using a complex second-order blind identification method to obtain modal signals and complex modes; wherein the number of physical time history signals, the number of modal signals and the number of complex modes are consistent with the number of degrees of freedom of the equivalent system; an identification module configured to identify modal parameters of the above modal signals by using an improved Bayesian spectral density method to obtain frequencies and damping ratios; wherein the number of frequencies and the number of damping ratios are consistent with the number of degrees of freedom of the equivalent system; The determining module obtains equivalent physical stiffness and damping matrix based on the complex modal fundamental theory, the obtained complex modal parameters and the equivalent mass matrix; The device further comprises: The degree of freedom condensation module adopts a static force condensation method, obtains a low degree of freedom equivalent system based on design parameters of the target building, and obtains an equivalent mass matrix; The decoupling module adopts a complex second-order blind identification method to decouple the physical time history signal to obtain a modal signal and a complex mode shape; The identification module adopts an improved Bayesian spectral density method to identify modal parameters of the modal signal to obtain a modal frequency and a damping ratio; The determining module obtains an eigenvalue based on the frequency and the damping ratio, obtains a complex eigenvector based on the eigenvalue and the complex mode shape, and further solves the target matrix by using a matrix of the eigenvalue and a matrix of the complex eigenvector to obtain the equivalent physical stiffness and damping matrix.

5. The identification device of claim 4, wherein, The decoupling module decouples the physical time history signal measured at the condensation position of the target super high-rise building by using the complex second-order blind identification method, and the decoupling includes: When each order of the modal signal obtained by decoupling only contains one modal frequency, it indicates that the physical time history signal has been successfully decoupled.

6. The identification device of claim 4, wherein, When the damping is non-proportional damping, the decoupling is performed by using a complex modal method.

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