Time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform

Abstract

The invention discloses a time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, and the method comprises the following steps: 1), obtaining related parameters of a structure and an incoming flow condition; 2) using CFD-based fluid-structure interaction numerical simulation to output wind-induced response time history data of the structure under the action of wind; 3) according to the obtained displacement and wind pressure information, instantaneous displacement-load parameter extraction is carried out based on a wavelet transform theory; 4) performing transient aerodynamic damping identification based on a harmonic balance theory; 5) establishing a time-varying nonlinear aerodynamic damping model based on a hybrid modeling strategy; and 6) based on the time-varying nonlinear aerodynamic damping model, performing response prediction of the tensile membrane structure considering the fluid-solid coupling effect, and performing performance evaluation. According to the time-varying nonlinear aerodynamic damping recognition and modeling method for the flexible engineering structure, the time-varying nonlinear aerodynamic damping model capable of considering the time-varying fluctuation effect and the nonlinear characteristics at the same time is constructed, and compared with a traditional aerodynamic damping model capable of only considering nonlinearity, the time-varying nonlinear aerodynamic damping model has the advantages that the time-varying fluctuation effect is greatly improved; according to the method, the inherent time-varying fluctuation characteristics of aerodynamic damping can be described better, the prediction precision of the wind-induced response of the flexible engineering structure considering the fluid-structure interaction effect is remarkably improved, the applicability is improved from the source, the accuracy of structural wind-induced response evaluation analysis is improved, and reliable support is provided for wind resistance design and structural optimization of the structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wind-resistant analysis and design of flexible engineering structures, and particularly relates to a time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform. BACKGROUND

[0002] With the development of technology and engineering practice, modern engineering structures are gradually evolving towards large-scale and high flexibility. However, such structures are prone to large vibrations under wind loads. In addition to the dynamic characteristics of the structure itself, negative aerodynamic damping induced by fluid-structure coupling is also one of the important factors that cause strong vibration. Aerodynamic damping, as an inherent aerodynamic characteristic of flexible engineering structures, often manifests as a self-excited aerodynamic force acting on the structure, and is a key parameter that cannot be ignored in wind-induced response analysis and wind-resistant design. Accurate evaluation of aerodynamic damping is of great engineering significance for response prediction accuracy and structural safety.

[0003] In recent years, the aerodynamic damping characteristics of flexible engineering structures have gradually become a research focus. Studies have shown that at higher wind speeds, the aerodynamic damping of such structures can be negative, leading to a decrease in the total damping of the system, amplifying the wind-induced response, and even inducing aeroelastic instability. In addition, aerodynamic damping has a significant time-varying characteristic, i.e., it fluctuates continuously with the vibration process at a specific wind speed, exhibiting time-varying nonlinear characteristics. This phenomenon is due to the geometric nonlinearity of flexible engineering structures: large deformations of the structure cause continuous changes in the geometric shape and dynamic characteristics of the structure, forming a nonlinear equilibrium path. Geometric nonlinearity not only causes time-domain fluctuations in structural parameters, directly leading to transient changes in aerodynamic damping forces, but also disturbs the flow field by changing the structure's shape, further enhancing the time-varying behavior of aerodynamic damping. Therefore, accurately understanding and modeling the time-varying characteristics of aerodynamic damping is crucial for accurate prediction of wind-induced responses of flexible engineering structures.

[0004] Although existing research has explored the time-varying characteristics of aerodynamic damping, systematic understanding is still lacking. The main reason is that the identification of time-varying aerodynamic damping during free vibration is theoretically and technically challenging. Existing identification methods are mostly based on the harmonic balance method, which calculates the average aerodynamic damping through energy balance of multi-cycle vibrations. The results are steady-state equivalent damping, which cannot reflect the instantaneous variation law. To overcome this limitation, some studies use forced vibration methods based on modal decomposition, which identify steady-state damping and establish its relationship with amplitude by applying a pre-set harmonic excitation to indirectly represent the time-varying characteristics. However, this method relies on artificial excitation rather than real wind-induced vibration, and its energy transfer mechanism differs fundamentally from the actual fluid-structure coupling process, leading to uncertainties between the identified results and the real time-varying aerodynamic damping.

[0005] With the development of aeroelastic analysis technology, it is gradually possible to directly identify the instantaneous aerodynamic damping in the process of free vibration, which provides a new way of thinking for understanding the time-varying characteristics of aerodynamic damping. Existing researches have successfully identified time-varying aerodynamic damping in bridge segment models based on Hilbert transform, and established a model of damping changing with time by extracting instantaneous amplitude. However, this method is only applicable to low Reynolds number and single frequency vibration, and is difficult to be directly extended to high Reynolds number and multi-frequency vibration with significant characteristics. In this context, the continuous wavelet transform method with multi-frequency transient resolution shows potential applicability and is expected to become an effective tool for identifying time-varying aerodynamic damping. However, there is no systematic research at present, and it is urgent to establish a time-varying aerodynamic damping identification and modeling method suitable for complex dynamic characteristics of flexible engineering structures. SUMMARY

[0006] In view of the above problems existing in the prior art, the purpose of the present application is to provide a time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, so as to solve the problem of response evaluation distortion caused by the insufficient precision of the traditional aerodynamic damping model applied in the existing aerodynamic damping evaluation and wind-induced dynamic response prediction technology of flexible engineering structures.

[0007] In order to solve the above technical problems, the technical scheme adopted by the present application is as follows: A time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, comprising the following steps, Step 1) obtaining relevant parameters of the structure and the flow field; Step 2) using fluid-structure coupling numerical simulation based on CFD to output wind-induced response time history data of the structure under the action of wind; Step 3) based on the obtained displacement and wind pressure information, instantaneous displacement-load parameter extraction based on wavelet transform theory; Step 4) time-varying aerodynamic damping identification based on harmonic balance theory; Step 5) establishing a time-varying nonlinear aerodynamic damping model based on a hybrid modeling strategy; Step 6) response prediction of the tensile membrane structure considering fluid-structure coupling effect based on the time-varying nonlinear aerodynamic damping model, and performance evaluation.

[0008] As an optimization, in step 1), the parameters include structural size parameters, inherent structural property parameters, dominant modal natural frequency and flow velocity parameters.

[0009] As an optimization, in step 2), a method combining nonlinear finite element modeling and three-dimensional large eddy simulation is used to construct a fluid-structure coupling numerical model of the structure under the action of the flow field, so as to realize the output of the generalized wind-induced response time history data of the structure under the action of wind.

[0010] As optimization, step 3) includes the following steps: Step 3.1) Wavelet decomposition is performed on the structural vibration generalized displacement time history and the generalized load time history obtained in step 2) to obtain the wavelet transform coefficients of displacement and load, i.e., In the formula, W d , W F are the wavelet transform coefficients of displacement and load, respectively, d G and F G are the generalized displacement and generalized force, respectively, a is a scale parameter, inversely proportional to frequency, b is a time shift parameter, Ψ * is the complex conjugate of the mother wavelet function Ψ . Step 3.2) Based on the idea of inverse wavelet transform, the generalized load, generalized displacement parameter instantaneous value of the structure is extracted, including the load amplitude instantaneous value, the displacement amplitude instantaneous value and the load-displacement phase difference instantaneous value, i.e., In the formula, f d is the dominant frequency common to displacement and load, Δ f is the corresponding wavelet transform bandwidth at the dominant frequency, A d and A F are the amplitudes of the displacement time history and the wind load time history, respectively, Φ is the phase difference of the wind load leading displacement.

[0011] As optimization, in step 4), the transient aerodynamic damping is determined based on the harmonic balance method, i.e., In the formula, Ξ a t is the structural transient aerodynamic damping ratio, Ω r is the circular frequency of vibration, M G is the generalized mass of the structure corresponding to its dominant mode, and Ω s is the corresponding natural frequency.

[0012] As optimization, step 5) includes the following steps: ​Step 5.1) Perform probability density function fitting on the generalized displacement time history obtained in Step 2) using a probability density function model to construct a nonlinear aerodynamic damping model; Step 5.2) Perform time domain statistical analysis on the instantaneous aerodynamic damping obtained in Step 4) to establish a time-varying aerodynamic damping model; Step 5.3) Combine the results of Step 5.1) and Step 5.2) to construct an aerodynamic damping model that takes into account time-varying nonlinearity.

[0013] As an optimization, Step 5.1) includes the following steps: Step 5.1.1) Determine the dimensionless aerodynamic damping coefficient expression, i.e., where, a c is the dimensionless aerodynamic damping coefficient, m s is the structural mass coefficient, Ρ air is the air density, U r is the reduced wind speed of the incoming flow; Step 5.1.2) Determine the generalized Van der Pol oscillator form of the nonlinear aerodynamic damping model, i.e., where, a c,steady is the nonlinear aerodynamic damping model, A c , B c and β c is the dimensionless parameter to be determined; Step 5.1.3) Determine the probability density function model of the structural wind-induced displacement containing the undetermined parameters in Step 5.1.2), i.e., where, p A is the probability density function of the amplitude, which has the form: where, C is the normalization constant, S 0 is the power spectral density of the white noise random process, is the phase angle variable, b 0 and b 1 are related to A c and B c respectively, which is expressed as: ​ Step 5.1.4) establish the probability density function curve of the generalized displacement time history obtained in step 2), and adopt the least square method to fit the curve with the probability density function model in step 5.1.3) as the target, and output the optimal parameters obtained after fitting to obtain the nonlinear aerodynamic damping model in step 5.1.2).

[0014] As optimization, step 5.2) includes the following steps: Step 5.2.1) determine the Strouhal number of the structure based on the structural shape characteristics St , and determine the aerodynamic damping oscillation frequency constant f ac , that is, In the formula, U H is the incoming flow wind speed, H is the structure height; Step 5.2.2) statistically analyze the fluctuation value of the transient aerodynamic damping under different wind speeds obtained in step 4), and determine the aerodynamic damping fluctuation amplitude constant Δ a c ; Step 5.2.3) establish the time-varying aerodynamic damping model, that is, In the formula, a c,fluctuating is the time-varying aerodynamic damping model.

[0015] As optimization, step 5.3) includes the following steps: Step 5.3.1) establish the time-varying nonlinear aerodynamic damping model by combining step 5.1) and step 5.2), that is, In the formula, the aerodynamic damping is a function of displacement and time; Step 5.3.2) convert the aerodynamic damping into the amplitude and time function form; In the formula, Γ is the gamma function.

[0016] As optimization, the time-varying nonlinear aerodynamic damping model is used for structure wind-induced response time domain iterative solving in step 5), and the root mean square, fourth moment, peak value and peak value factor results of the predicted response are compared with the actual aeroelastic test results to evaluate the performance of the time-varying nonlinear aerodynamic damping model.

[0017] Compared with the prior art, the present application has the following advantages: 1. The harmonic balance-wavelet transform-based instantaneous aerodynamic damping identification method of the present scheme can more accurately identify the real-time aerodynamic damping in the vibration process of flexible engineering structures, and based on the superiority of wavelet transform multi-frequency processing, this method can be used in the case of multi-modal coupling coexistence at the same time, and has wide applicability.

[0018] 2. The strategy of mixed modeling of the present scheme constructs a time-varying nonlinear aerodynamic damping model of flexible engineering structures that can simultaneously consider time-varying fluctuation effects and nonlinear characteristics. Compared with the traditional aerodynamic damping model that can only consider nonlinearity, the model in this paper can better describe the inherent time-varying fluctuation characteristics of aerodynamic damping, and significantly improve the prediction accuracy of wind-induced response of structures considering fluid-structure coupling effects, thus improving the applicability and accuracy of wind-induced response evaluation and analysis of flexible engineering structures, and providing reliable support for wind-resistant design and structure optimization. 3. The present scheme constructs a nonlinear aerodynamic damping model based on the fitting mode of the probability density function model, and constructs a nonlinear aerodynamic damping model based on the form of simple harmonic oscillation. The efficiency of this model construction method is significantly higher than that of the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The present application is a typical flexible engineering structure-tensioned membrane structure schematic diagram; Figure 2 The present application is a generalized displacement and load time history diagram in the fluid-structure coupling process of flexible engineering structures; Figure 3 The present application is a load and displacement amplitude diagram identified by wavelet transformation; Figure 4 The present application is a displacement amplitude, load amplitude and displacement load phase difference time history diagram identified by the present application; Figure 5 The present application is an instantaneous aerodynamic damping time history diagram identified under different wind speeds; Figure 6 The present application is a nonlinear aerodynamic damping model established in the present application; Figure 7 The present application is a comparison diagram of the time-varying nonlinear aerodynamic damping model and the traditional aerodynamic damping model; Figure 8 The present application is a response time history prediction comparison diagram of the time-varying nonlinear aerodynamic damping model and the traditional nonlinear model; Figure 9 The present application is a response fluctuation value prediction comparison diagram of the time-varying nonlinear aerodynamic damping model and the traditional nonlinear model; Figure 10 The present application is a response fourth moment prediction comparison diagram of the time-varying nonlinear aerodynamic damping model and the traditional nonlinear model; Figure 11A comparison chart of response peak value prediction of the time-varying nonlinear aerodynamic damping model and a traditional nonlinear model; Figure 12 A comparison chart of response peak value factor prediction of the time-varying nonlinear aerodynamic damping model and a traditional nonlinear model. DETAILED DESCRIPTION

[0020] The application will be further described below in conjunction with the drawings and embodiments.

[0021] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present application.

[0022] It should be noted that similar reference numerals and letters indicate similar items in the following drawings, and therefore, once an item is defined in one drawing, it need not be further defined and explained in subsequent drawings. In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the present application is usually placed during use, and are only for the convenience of describing the present application and simplifying the description, and therefore, cannot be understood as indicating or implying that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore, cannot be understood as limiting the present application. In addition, the terms "first", "second", "third", and the like are only used for differentiation in description, and cannot be understood as indicating or implying relative importance. In addition, the terms "horizontal", "vertical", and the like do not mean that the components must be absolutely horizontal or vertical, but can be slightly inclined. For example, "horizontal" only means that its direction is relatively more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined. In the description of the present application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "arrange", "mount", "connect", "connect" should be understood broadly, for example, can be fixedly connected, or can be detachably connected, or integrally connected; can be mechanically connected, or can be electrically connected; can be directly connected, or can be indirectly connected through an intermediate medium, or can be connected inside two elements. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0023] Embodiment: see Figures 1-12 , A time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, comprising the following steps, Step 1) Obtain the relevant parameters of the structure and the flow field; take a typical flexible engineering structure-tensioned membrane structure as an application case, wherein the parameters include the span, width and building height of the tensioned membrane structure, and the thickness, area mass, elastic modulus, Poisson's ratio, damping ratio and natural frequency of each mode of the membrane material. Specifically, in this embodiment, a typical closed one-way tensioned membrane structure is taken as the research object, and the tensioned membrane structure is pre-tensioned along the windward direction of both ends. Specifically, in this embodiment, the height of the tensioned membrane structure model is 0.1875m, the span is 0.3m, the width is 0.1m, and the flow wind speed is 2-7m / s. The thickness of the membrane material is 0.2mm, the area mass is 0.2066kg / m, the Young's modulus is 4.1×10 N / m, the Poisson's ratio is 0.32, and the numerical model of the tensioning stiffness is 81.9N / m. H L B U H h m s 2 E 5 2 μ Eh

[0024] Step 2) A method combining nonlinear finite element modeling and three-dimensional large eddy simulation is used to construct a structure-fluid coupling numerical model. Based on the two-way fluid-structure coupling simulation strategy, the structure domain, the fluid domain and the interface domain are solved separately. In the structure domain, based on thin shell element discretization and temperature pre-tensioning technology, a tensioned membrane structure finite element model of geometrically nonlinear elastic body is constructed to calculate its large deformation displacement response. In the fluid domain, three-dimensional large eddy simulation method is used to capture the unsteady vortex in the coupling process and obtain the membrane surface wind load. In the coupling interface domain, the data transmission between different area grids on the fluid-structure interface is realized based on the mapping interpolation algorithm, and the fairing body moving grid technology is introduced to complete the high-quality moving grid update. The wind-induced response time history data of the typical tensioned membrane structure under wind action are output, including the membrane surface generalized wind load time history and the generalized displacement time history.

[0025] Step 3) According to the obtained displacement and wind pressure information, the instantaneous displacement-load parameters are extracted based on the wavelet transform theory; Step 3.1) The wavelet decomposition of the structure vibration generalized displacement time history and the generalized load time history obtained in step 2) is carried out, and the wavelet transform coefficients of displacement and load are obtained, that is,​​​​​​​​​​​​ where, W d 、 W F are the wavelet transform coefficients of displacement and load respectively, d G and F G are the generalized displacement and generalized force respectively, a is the scale parameter, inversely proportional to the frequency, b is the time shift parameter, Ψ * is the complex conjugate of mother wavelet function Ψ ; Step 3.2) Extract the instantaneous values of generalized load and generalized displacement parameters of the structure based on the idea of inverse wavelet transform, including the instantaneous values of load amplitude, displacement amplitude and load-displacement phase difference, i.e., where, f d is the dominant frequency of displacement and load, f is the wavelet transform bandwidth corresponding to the dominant frequency, A d and A F are the amplitudes of displacement time history and wind load time history respectively, Φ is the phase difference of wind load leading displacement.

[0026] Step 4) Identify the transient aerodynamic damping based on the harmonic balance theory. Specifically, the generalized motion equation of the tensile membrane structure under wind action is, where, M Gj 、 C Gj and K Gj are the generalized mass, generalized damping and generalized stiffness of the membrane structure corresponding to its j th mode shape respectively, 、 and are the generalized displacement, velocity and acceleration of the structure respectively, F Wj ( t ) is the aerodynamic load component caused by the incoming turbulent flow fluctuation, C aj ( t ) is the time-varying aerodynamic damping, which is a function of time, K aj (U r ) is the linear aerodynamic stiffness, which is only a function of the incoming wind speed and is independent of time.

[0027] The relationship between the transient aerodynamic damping ratio and the structural amplitude-displacement instantaneous parameters is determined based on the harmonic balance method, i.e. The aerodynamic damping ratio can be obtained as where Ξ a ( t ) is the structural transient aerodynamic damping ratio, Ω r is the vibration circular frequency, M G is the generalized mass of the structure corresponding to its dominant vibration mode, and is the corresponding Ω s natural frequency.

[0028] Step 5) constructing a time-varying nonlinear aerodynamic damping model based on a hybrid modeling strategy; Step 5.1) using a probability density function model to fit the generalized displacement time history obtained in step 2) to construct a nonlinear aerodynamic damping model; Step 5.1.1) determining the dimensionless aerodynamic damping coefficient expression, i.e. where a c is the dimensionless aerodynamic damping coefficient, m s is the area mass of the membrane, Ρ air is the air density, U r is the reduced wind speed of the incoming flow.

[0029] Step 5.1.2) determining the generalized Van der Pol oscillator form of the nonlinear aerodynamic damping model, i.e. where a c,steady is the nonlinear aerodynamic damping model, A c , B c and β c are the dimensionless parameters to be determined.

[0030] Step 5.1.3) determining the probability density function model of the wind-induced displacement of the tensile membrane structure containing the undetermined parameters in step 5.1.2), i.e. where, p A is the probability density function of the amplitude, which is given by: where, C is a normalization constant, S 0 is the power spectral density of the white noise random process, is the phase angle variable, b 0 and b 1 are the mean and standard deviation of the phase angle variable, respectively, A c and B c are related by: Step 5.1.4) Establish the probability density function curve of the generalized displacement time history obtained in Step 2), and use the least squares method to fit the curve with the probability density function model in Step 5.1.3) as the target, and output the optimal parameters obtained after fitting to Step 5.1.2) to obtain the nonlinear aerodynamic damping model.

[0031] Table 1 lists the undetermined parameters of the nonlinear aerodynamic damping model in the form of generalized van der pol oscillator obtained by fitting based on the probability density function for the unidirectional tensioned membrane structure example in the range of U r =1.20~1.73. A c , B c and β c are the optimal fitting values of the unidirectional tensioned membrane structure example.

[0032] Table 1 GVDP model parameters based on PDF fitting Table 1 Identified GVPO model parameters for the steady-stateaerodynamic damping mode Step 5.2, based on the time-domain statistical analysis of the instantaneous aerodynamic damping obtained in Step 4), a time-varying aerodynamic damping model is established.

[0033] Step 5.2.1) Determine the Strouhal number of the unidirectional tensioned membrane structure example based on the shape characteristics St is 0.06, and the aerodynamic damping oscillation frequency constant f ac is​ Step 5.2.2) fluctuation analysis is performed on the transient aerodynamic damping at different wind speeds obtained in step 3), and the fluctuation amplitude constant Δ of the aerodynamic damping is determined at a confidence interval of 95% a c to cover the fluctuation of the aerodynamic damping at all wind speeds.

[0034] Step 5.2.3) a time-varying aerodynamic damping model of the tensile membrane structure is established, that is, wherein, a c,fluctuating is the time-varying aerodynamic damping model.

[0035] Step 5.3) the time-varying nonlinear aerodynamic damping model is constructed by combining the results of step 5.1) and step 5.2); Step 5.3.1) the time-varying nonlinear aerodynamic damping model is established by combining step 5.1) and step 5.2), that is, wherein, the aerodynamic damping is a function of displacement and time.

[0036] Step 5.3.2) the aerodynamic damping is converted into a function of amplitude and time; wherein, Γ is the gamma function.

[0037] Step 6) the aerodynamic damping model in the form of displacement and time function is substituted into the generalized motion equation, and the fourth-order Runge-Kutta method is used for time-domain iterative calculation to predict the response time history, and the fluctuation value, the fourth moment, the peak value and the peak factor of the predicted displacement time history result are calculated, and the calculated results are compared with the aeroelastic test results to evaluate the performance of the aerodynamic damping model.

[0038] Figure 8 is the comparison of the response prediction time history result and the aeroelastic test result, Figures 9-12 is the comparison of the predicted response statistical value and the aeroelastic result and the prediction result of the traditional model, and it can be seen that the time-varying nonlinear aerodynamic damping model established in the present application performs better in the prediction of response fluctuation value, kurtosis, peak response and peak factor.

[0039] The application provides a time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, which can accurately consider the time-varying nonlinear fluctuation effect of aerodynamic damping caused by structural complexity, and efficiently and accurately model the feature, thereby improving the accuracy and optimization rate of aerodynamic load analysis and response evaluation, and further optimizing the wind-resistant design of the structure, and providing reliable support for safe use and structural optimization of the structure.

[0040] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application and not to limit the technical solutions, and those of ordinary skill in the art should understand that those who modify or equivalently replace the technical solutions of the present application without departing from the purpose and scope of the technical solutions should be covered in the scope of claims of the present application.

Claims

1. A time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform, characterized in that, Comprising the following steps, Step 1) obtaining the relevant parameters of the structure and the flow condition; Step 2) using CFD-based fluid-structure coupling numerical simulation to output the wind-induced response time history data of the structure under wind action; Step 3) based on the obtained displacement and wind pressure information, using wavelet transform theory to extract the instantaneous displacement-load parameters; Step 4) using harmonic balance theory to identify the transient aerodynamic damping; Step 5) using a hybrid modeling strategy to establish a time-varying nonlinear aerodynamic damping model; Step 6) using the time-varying nonlinear aerodynamic damping model to predict the response of the tensile membrane structure considering fluid-structure coupling effects and to evaluate the performance.

2. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, In step 1), the parameters include structural size parameters, inherent structural property parameters, dominant modal natural frequency, and incoming flow wind speed parameters.

3. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, In step 2), a method combining nonlinear finite element modeling and three-dimensional large eddy simulation is used to construct a fluid-structure coupling numerical model of the structure under the action of the incoming flow field, so as to realize the output of the generalized wind-induced response time history data of the structure under wind action.

4. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, In step 3), it includes: Step 3.1) wavelet decomposition of the structure vibration generalized displacement time history and the generalized load time history obtained in step 2) to obtain the wavelet transform coefficients of displacement and load, i.e., In the formula, W d , W F These are the wavelet transform coefficients for displacement and load, respectively. d G and F G These are generalized displacement and generalized force, respectively. a This is a scale parameter, inversely proportional to frequency. b For time shift parameters, ψ * Mother wavelet function ψ The complex conjugate; Step 3.2) based on the inverse wavelet transform idea to extract the generalized load and generalized displacement parameter instantaneous values of the structure, including the load amplitude instantaneous value, the displacement amplitude instantaneous value and the load-displacement phase difference instantaneous value, i.e., where, f d is the dominant frequency common to the displacement and the load, f is the corresponding wavelet transform bandwidth at the dominant frequency, A d and A F are the amplitudes of the displacement time history and the wind load time history, respectively, φ is the phase difference of the wind load leading the displacement.

5. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, In step 4), the transient aerodynamic damping is determined based on the harmonic balance method, i.e., wherein ξ a t is the structural transient aerodynamic damping ratio, ω r is the vibration circular frequency, M G is the structural generalized mass corresponding to its dominant mode of vibration, and is the corresponding ω s natural frequency of vibration.​ 6. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, In step 5), it includes the following steps: Step 5.1) using the probability density function model to fit the generalized displacement time history obtained in step 2) to construct a nonlinear aerodynamic damping model; Step 5.2) performing time-domain statistical analysis on the instantaneous aerodynamic damping obtained in step 4) to establish a time-varying aerodynamic damping model; Step 5.3) combining the results of step 5.1) and step 5.2) to construct an aerodynamic damping model considering time-varying nonlinearity.

7. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 6, characterized in that, Step 5.1) includes the following steps: Step 5.1.1) determining the dimensionless aerodynamic damping coefficient expression, i.e., wherein a c is the dimensionless aerodynamic damping coefficient, m s is the structural mass coefficient, ρ air is the air density, U r is the reduced wind speed of the incoming flow; Step 5.1.2) determining the generalized Van der Pol oscillator form of the nonlinear aerodynamic damping model, i.e., wherein a c,steady is a nonlinear aerodynamic damping model, A c , B c and β c is a dimensionless parameter to be determined; Step 5.1.3) determining the probability density function model of the structure wind-induced displacement containing the undetermined parameters in step 5.1.2), i.e., wherein p A is the probability density function of the amplitude, which has the form​ wherein C is a normalization constant, S 0 is the power spectral density of the white noise random process, is a phase angle variable, b 0 and b 1 are respectively associated with A c and B c are related and are expressed as: Step 5.1.4) establishing the probability density function curve of the generalized displacement time history obtained in step 2), and using the least squares method to fit the curve with the probability density function model in step 5.1.3) as the target, and outputting the optimal parameters obtained after fitting to the nonlinear aerodynamic damping model in step 5.1.2).

8. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 6, characterized in that, Step 5.2) includes the following steps: Step 5.2.1 ) determining its Storhaug number based on structural form features St and from this the aerodynamic damping oscillation frequency constant f ac i.e., wherein U H is the incoming wind speed, H is the structure height; Step 5.2.2) Statistical analysis of the fluctuation value of the transient aerodynamic damping at different wind speeds obtained in step 4) to determine the fluctuation amplitude constant of the aerodynamic damping Δ a c ; Step 5.2.3) establishing a time-varying aerodynamic damping model of the structure, i.e., In the formula, a c,fluctuating is a time-varying aerodynamic damping model.

9. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 6, characterized in that, Step 5.3) includes the following steps: Step 5.3.1) combining step 5.1) and step 5.2) to establish a time-varying nonlinear aerodynamic damping model, i.e., In the formula, the aerodynamic damping is a function of displacement and time; Step 5.3.2) converting the aerodynamic damping into a function of amplitude and time; where Γ is the gamma function.

10. The time-varying nonlinear aerodynamic damping identification method based on harmonic balance and wavelet transform according to claim 1, characterized in that, Step 6) Time domain iterative solution of the structural wind-induced response based on the time-varying nonlinear aerodynamic damping model is performed, and the root mean square, fourth moment, peak value and peak factor results of the predicted response are compared with the actual aeroelastic test results to evaluate the performance of the time-varying nonlinear aerodynamic damping model.

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