Nonlinear aerodynamic damping identification method, system and storage medium for self-excited hysteresis vibration

Abstract

The application discloses a kind of nonlinear aerodynamic damping identification methods, system and storage medium for self-excited hysteresis vibration, comprising: obtaining structural wind-induced vibration response data;Aerodynamic damping is modeled as non-monotonic high-order function about amplitude, and construct the extended state vector and state space model containing damping parameter and load term;Recursive estimation of state vector is utilized filtering algorithm, and damping parameter is identified simultaneously;According to parameter calculation damping-amplitude curve;Using full amplitude domain splicing strategy, the high-precision identification result in small amplitude interval is fused to correct the identification curve in large amplitude interval, and obtain high-precision target damping curve;By analyzing the intersection and slope of the curve and structural damping line, stable and unstable equilibrium points are identified.The application solves the problem that traditional method cannot accurately describe multi-stable hysteresis phenomenon and the identification precision is insufficient in small amplitude interval, realizes high-precision identification of nonlinear aerodynamic damping and quantitative analysis of hysteresis mechanism.

Description

Technical Field

[0001] This invention belongs to the field of structural wind engineering and structural health monitoring technology, specifically a nonlinear aerodynamic damping identification method, system and storage medium for self-excited hysteretic vibrations with two or more stable amplitude characteristics. Background Technology

[0002] Long-span bridges, high-rise buildings, and wind turbine towers are prone to wind-induced vibrations under fluid-structure interaction due to their high flexibility and low damping characteristics. Among these, vortex-induced vibration (VIV) is a crucial factor directly affecting structural safety and user comfort. For some aerodynamically blunt structures (such as separated double-box girder bridges), wind tunnel tests and field measurements have revealed a "displacement hysteresis phenomenon" within a specific wind speed range. This means that under the same wind speed and structural parameters, the bridge may exhibit two or more different stable amplitudes. This nonlinear phenomenon of multiple steady states not only increases the uncertainty of structural response but also poses a severe challenge to wind-resistant design.

[0003] Traditional linear or simple nonlinear aerodynamic damping models, due to their assumption that damping varies monotonically with amplitude, cannot explain and simulate this hysteretic behavior involving multiple stable states. Therefore, it is necessary to introduce higher-order nonlinear models that can characterize the non-monotonic variation of aerodynamic damping with amplitude. Regarding parameter identification, although nonlinear identification methods based on Kalman filtering frameworks (such as the Unscented Kalman Filter (UKF)) have solved the problem of identifying strongly nonlinear parameters and decoupling loads to some extent (by expanding the unknown load into a state variable), these existing methods still have identification defects: because the signal-to-noise ratio of response data in the small amplitude range is relatively low, and when identifying all data containing large amplitude transitions at once, the parameters in the small amplitude region are easily affected by the large amplitude data, resulting in significant identification errors and insufficient accuracy in the final aerodynamic damping curve in the small amplitude stable region. This error in the small amplitude region directly affects the accurate judgment of the critical instability point (the unstable equilibrium point), thus failing to accurately reveal the entire hysteresis mechanism.

[0004] Therefore, how to establish a high-order nonlinear damping model that can accurately describe hysteresis and propose a global correction and identification strategy to eliminate identification errors in small amplitude ranges and ensure the high accuracy of the target damping curve in the full amplitude domain is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a nonlinear aerodynamic damping identification method, system, and storage medium for self-excited hysteretic vibrations, in order to solve the problems that traditional damping models cannot accurately describe multi-steady-state hysteretic phenomena and that existing identification methods lack accuracy in the small amplitude range; by constructing a non-monotonic high-order damping model and combining filtering algorithms with a full-amplitude domain splicing strategy, high-precision aerodynamic damping identification is achieved across the entire amplitude range, thereby accurately revealing the stable and unstable equilibrium states of hysteretic vibrations.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A nonlinear aerodynamic damping identification method for self-excited hysteretic vibration includes the following steps:

[0008] Step 1: Obtain vibration response data of the structure exhibiting displacement hysteresis characteristics under wind load;

[0009] Step 2: Model the aerodynamic damping as a non-monotonic high-order function with respect to amplitude, and construct a nonlinear dynamic state-space model for hysteresis characteristics;

[0010] Step 3: Based on the state-space model, the state vector is recursively estimated using a filtering algorithm, and nonlinear aerodynamic damping parameters are identified simultaneously.

[0011] Step 4: Calculate the curve of aerodynamic damping as a function of amplitude based on the nonlinear aerodynamic damping parameters calculated by recursion and iteration.

[0012] Step 5: Employ a full-amplitude domain stitching and recognition strategy, and combine the recognition results of the small amplitude range to correct and fuse the full-amplitude curve, so as to eliminate the recognition error in the small amplitude range and obtain a high-precision target aerodynamic damping curve.

[0013] Step 6: By solving for the intersection point and slope of the target aerodynamic damping curve and the structural damping line, multiple stable amplitudes and unstable equilibrium points that lead to self-excited hysteresis vibration are identified.

[0014] Furthermore, in step one, the vibration response data is dynamic data collected within the wind speed range where displacement hysteresis occurs, specifically for structures with bluff body characteristics. This data includes unsteady transition processes, and the core physical quantity collected is displacement time history data.

[0015] Furthermore, in step two, the method for constructing the nonlinear dynamic state-space model comprises the following steps:

[0016] 21) Considering only the fundamental mode shape, the equation of motion for the lateral wind-induced vibration of the building structure is:

[0017]

[0018]

[0019]

[0020] in: and These refer to the height and width of the building structure, respectively. For normalized displacement, the generalized modal coordinates This refers to the top displacement of the building structure; and Located at vibration velocity and acceleration, respectively; , is the structural angular frequency; It is the natural frequency; and These are structural damping and aerodynamic damping caused by vortex-induced forces, respectively. The modal shape varies along the height; For height position; The empirical modal correction coefficients are needed to deduce the generalized modal force from the base bending moment; The mass per unit height that varies along the altitude; Effective mass per unit height; The base moment coefficient; These are parameters related to the modal shape. air density; Wind speed;

[0021] 22) Express aerodynamic damping as a higher-order polynomial function of the absolute value of vibration displacement or the absolute value of vibration velocity:

[0022]

[0023]

[0024] in: and These are the parameters of the aerodynamic damping constant; ; ; , where is the reduced frequency;

[0025] 23) By using the relationship of work done by aerodynamic forces over one cycle, the displacement-dependent aerodynamic damping model is transformed into an amplitude-dependent aerodynamic damping model:

[0026]

[0027] in: , which is the normalized amplitude; This represents the actual amplitude. The feature width;

[0028] 24) Construct a high-dimensional extended state vector :

[0029]

[0030] in: For external loads;

[0031] 25) Construct the state transition equation, using displacement, velocity, and acceleration as test and observation quantities, and measure the vector. Represented as:

[0032]

[0033] State space variables and observation vector Expressed using discrete-time equations:

[0034]

[0035]

[0036] Where: subscript Indicates a time step; for Regarding the next time step The mapping function, i.e., the state transition function; for Regarding the next time step The mapping function, i.e., the measurement function; For including the covariance matrix A zero-mean Gaussian white noise vector; For including the covariance matrix A zero-mean Gaussian white noise vector; For expectation operators.

[0037] Furthermore, in step three, the filtering algorithm is an unscented Kalman filter algorithm. The method steps for recursively iteratively estimating the state vector and simultaneously identifying nonlinear aerodynamic damping parameters are as follows:

[0038] 31) Generating sigma points through unscented transformation:

[0039]

[0040]

[0041]

[0042]

[0043] in: for sigma point matrix of time step The first in List; To expand the state vector in the th The average matrix of time steps; For the first The covariance matrix of the time step; State-space variables The dimension; The first square root of the matrix OK; For scaling parameters; Decision made Distribution of nearby sigma points; This is the second scaling parameter;

[0044] 32) Update the sigma point over time using the state transition equation and calculate the mean of the state-space variables. and its covariance matrix , represented as:

[0045]

[0046]

[0047]

[0048] in: It is a nonlinear state transition equation; and These are the weighting coefficients; This is the noise matrix;

[0049] 33) Estimated vectors of displacement, velocity, and acceleration With observation vector Update the variance matrix of the state-space variables. Covariance Matrix :

[0050]

[0051]

[0052]

[0053]

[0054] in: This is the measurement error matrix;

[0055] 34) Using the Kalman gain matrix and total observation vector Update the state space vector and its covariance matrix :

[0056]

[0057]

[0058] .

[0059] Furthermore, in step four, calculating the curve of aerodynamic damping as a function of amplitude includes: constructing an amplitude vector from zero to the maximum identified amplitude, substituting the identified nonlinear aerodynamic damping parameters into the amplitude-dependent nonlinear aerodynamic damping model, and calculating and plotting the curve of aerodynamic damping change on the amplitude calculation vector.

[0060] Furthermore, in step five, the full-amplitude domain stitching recognition strategy includes the following steps:

[0061] 51) Perform identification on the response data under the small amplitude steady state to obtain the first set of aerodynamic damping coefficients and the corresponding aerodynamic damping curves for the small amplitude segment;

[0062] 52) Perform identification on response data containing large amplitude steady state or large transition process to obtain the second set of aerodynamic damping coefficients and the corresponding aerodynamic damping curves for the full amplitude range;

[0063] 53) Using the high-precision data of the small amplitude segment aerodynamic damping curve in the overlapping amplitude range, replace and / or correct the corresponding part of the full amplitude segment aerodynamic damping curve in the small amplitude range, and splice them together to form a complete aerodynamic damping curve with consistent accuracy in the full amplitude domain.

[0064] Furthermore, in step six, identifying stable amplitudes and unstable equilibrium points specifically involves: when the total damping curve crosses the zero axis with a positive slope, the corresponding intersection point is a stable equilibrium point; when the total damping curve crosses the zero axis with a negative slope, the corresponding intersection point is an unstable equilibrium point; by analyzing the energy balance state on both sides of the intersection point, the multistable hysteresis mechanism is revealed.

[0065] The present invention also proposes a nonlinear aerodynamic damping identification system for self-excited hysteretic vibration, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor. The processor executes the computer program and implements the nonlinear aerodynamic damping identification method for self-excited hysteretic vibration as described above.

[0066] The present invention also proposes a storage medium storing a computer program, which, when executed by a processor, implements the nonlinear aerodynamic damping identification method for self-excited hysteresis vibration as described above.

[0067] The beneficial effects of this invention are as follows:

[0068] The present invention provides a nonlinear aerodynamic damping identification method for self-excited hysteretic vibrations, which has the following main technical advantages:

[0069] (1) Effective modeling of self-excited hysteresis phenomenon is achieved: By explicitly modeling aerodynamic damping as a non-monotonic higher-order function with respect to amplitude, the constructed model itself has the ability to describe the non-monotonic change of damping value with amplitude and the possibility that the curve may cross the zero axis multiple times, thus laying the mathematical model foundation for characterizing the core hysteresis phenomenon of "multiple steady states coexisting".

[0070] (2) A systematic parameter identification and curve construction method is provided: This invention uses a filtering algorithm to recursively estimate the extended state vector containing damping parameters, and calculates the curve of continuous aerodynamic damping with amplitude based on the identification results, forming a complete and operable identification process from data to model parameters.

[0071] (3) Significantly improves the global recognition accuracy of aerodynamic damping curves: This invention proposes a “full amplitude domain splicing recognition strategy”, which processes small amplitude data and full amplitude data separately, and uses the high-precision results of the former to correct the latter in the low amplitude region. This directly addresses and effectively alleviates the inherent defect of “large amplitude data affecting small amplitude accuracy” in traditional one-time recognition, thereby obtaining a more reliable aerodynamic damping curve in the full amplitude range.

[0072] (4) It realizes the direct judgment of system stability: Based on the high-precision damping curve obtained in the end, by solving the intersection point with the structural damping line, and by distinguishing the stable equilibrium point from the unstable equilibrium point according to the positive and negative slope of the intersection point, the multistable structure and critical state that cause hysteresis can be directly analyzed from the identification results, providing a clear criterion for understanding the vibration mechanism.

[0073] In summary, this invention reveals and quantifies the multi-steady-state hysteresis mechanism. Unlike traditional monotonic damping models, the high-order nonlinear model constructed in this invention can accurately describe the multiple zero-point crossings of the aerodynamic damping curve. Thus, for the first time, it quantifies the "instability boundary point" and "multiple stable points" leading to amplitude jumps from a data-driven perspective, providing a powerful theoretical tool for accurately explaining the complex displacement hysteresis phenomena of blunt body structure cross-sections. Addressing the problem of insufficient accuracy in identifying small-amplitude intervals from large-amplitude data, this invention proposes a full-amplitude domain stitching identification strategy. When using large-amplitude data for identification, filtering algorithms often suffer from local errors in the near-zero small-amplitude region (due to reduced signal-to-noise ratio or weakened nonlinearity). This invention identifies aerodynamic damping in small-amplitude stable states (high-precision coverage of the low-amplitude region) and large-amplitude stable states (covering the entire domain but with slightly lower accuracy at the lower end) separately, and then optimizes and stitches these two identifications together. This strategy cleverly combines the advantages of different data sources, thereby obtaining highly accurate nonlinear amplitude-dependent aerodynamic damping curves across the entire range from zero to maximum amplitude, providing more comprehensive and reliable data support for structural health monitoring and damage identification. Attached Figure Description

[0074] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0075] Figure 1 A structural diagram of a square column-shaped building structure;

[0076] Figure 2 This is a flowchart of an embodiment of the nonlinear aerodynamic damping identification method for self-excited hysteresis vibration according to the present invention;

[0077] Figure 3 For structural damping and amplitude-dependent aerodynamic damping;

[0078] Figure 4 For structural damping The displacement response time histories released with different initial amplitudes; where: Figure 4 (a) indicates that when the initial amplitude is given as 0.001, the structural response amplitude will continuously increase to a stable equilibrium amplitude; Figure 4 (b) indicates that when the initial amplitude is given as 0.2, the structural response amplitude will shrink to the value of 0.2. Figure 4 (a) shows the same amplitude of a stable equilibrium. Figure 4 (c) indicates that when the initial amplitude is given as 0.25, the structural response amplitude increases to a value greater than... Figure 4 (a) has a larger equilibrium amplitude than the stable equilibrium amplitude; Figure 4 (d) indicates that when the initial amplitude is given as 0.5, the structural response amplitude will shrink to the value of 0.5. Figure 4(c) shows the same amplitude of a stable equilibrium. Figure 4 (e) represents the transition of vibration displacement between two steady states under a given initial amplitude of 0.001 and the action of a random chattering force, where, Figure 4 Regions 1 and 3 in (e) represent two small stable amplitude states. Figure 4 Region 2 in (e) represents a large stable amplitude state;

[0079] Figure 5 For structural damping The displacement response time history released with different initial amplitudes; Figure 5 (a) and Figure 5 (b) indicates that under given minimum initial amplitude (0.001) and maximum initial amplitude (0.2), the structural response amplitude will increase or decrease to a stable equilibrium amplitude.

[0080] Figure 6 A comparison graph showing the measured displacement and the UKF estimated displacement under different amplitudes; where: Figure 6 (a) indicates that the displacement curve predicted by UKF under small amplitude steady state is highly consistent with the original measured displacement data points; Figure 6 (b) indicates that the displacement curve predicted by UKF under large amplitude steady state is highly consistent with the original measured displacement data points;

[0081] Figure 7 Output the parameter results of the nonlinear aerodynamic damping estimated by UKF; where: Figure 7 (a) indicates that under small amplitude conditions, all parameters gradually converge and stabilize near a specific constant value; Figure 7 (b) indicates that under large amplitude conditions, all parameters gradually converge and stabilize near a specific constant value;

[0082] Figure 8 The aerodynamic damping estimate is obtained through a high-order non-monotonic aerodynamic damping model; Figure 8 (a) shows the aerodynamic damping identification results for the small amplitude stable state; Figure 8 (b) shows the aerodynamic damping identification results for the large amplitude stable state;

[0083] Figure 9 This represents the estimated aerodynamic damping value obtained by splicing across the entire amplitude domain. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0085] This embodiment uses a rectangular column structure as an example. It applies the nonlinear aerodynamic damping identification method for self-excited hysteretic vibration proposed in this invention to calculate the nonlinear aerodynamic damping of a rectangular column structure. Based on the response data of the rectangular column structure with multiple stable amplitudes, the multisteady hysteresis mechanism is revealed and quantified. Simultaneously, the effectiveness and accuracy of the estimated nonlinear aerodynamic damping value are evaluated by comparing it with the true value. Specifically, the height of the rectangular column... 200 m, width B = 15 m; natural frequency of the structure is 0.2 Modal shape Assuming it varies linearly along the height, that is Dimensionless mass 172; This refers to the cross-sectional width; 0.09; 0.1572; 0.28, 0.85, structural damping ratio has Square column structure, such as Figure 1 As shown.

[0086] like Figure 2 As shown, this embodiment describes a nonlinear aerodynamic damping identification method for self-excited hysteresis vibration, which includes the following steps.

[0087] Step 1: Acquire vibration response data of the structure exhibiting displacement hysteresis characteristics under wind load. Specifically, the characteristics of acquiring vibration response data of the structure exhibiting displacement hysteresis characteristics under wind load are: for structures with bluff body characteristics, this is carried out in wind tunnel tests or actual structural monitoring, focusing on the wind speed range in which the structure exhibits displacement hysteresis. The key to the acquisition is capturing dynamic data containing unsteady transition processes, such as the process of the model evolving from a static state to a small-amplitude steady state after being disturbed, or the transition process from a small-amplitude state to a large-amplitude steady state after being disturbed by a large disturbance. The core physical quantity acquired is displacement time history data, and acceleration signals are acquired simultaneously when conditions permit to assist in observation and verification.

[0088] In this embodiment, for the square column example, the top wind speed When the wind speed is 1.1 times the vortex-induced resonance speed, that is 1.1 The aerodynamic damping ratio is then assumed to be a dimensionless polynomial nonlinear function of the amplitude, as shown in the following equation:

[0089]

[0090] Figure 3The relationship between the aerodynamic damping ratio and the vibration amplitude is shown. The aerodynamic damping ratio exhibits a non-monotonic change with amplitude: when the vibration amplitude is between 0 and 0.148, the aerodynamic damping ratio increases with increasing amplitude; then, before the amplitude reaches 0.302, the damping ratio decreases with increasing amplitude; after exceeding this critical amplitude, the damping ratio increases again with increasing amplitude.

[0091] As can be seen, when the structural damping ratio At 0.5%, the total system damping 0 corresponds to 3 amplitudes, namely 0.076 0.235 and 0.358. when At 0.076, 0; when 0.076 0.235, 0; when 0.235 At 0.358, 0; when At 0.358, 0. The structure will reach different stable states when released under different initial amplitudes. Specifically, when the initial amplitude... At 0.076, since the total system damping is negative, the amplitude will continue to increase to 0.076; when 0.076... At 0.235, the amplitude will decay to 0.076; when 0.235 At 0.358, the amplitude will increase to 0.358, reaching another stable equilibrium state with a larger amplitude; when At 0.358, the amplitude decays to 0.358. This is due to structural damping. At 0.5%, there are two stable amplitudes. 0.076 and 0.358. Amplitude 0.235 represents an unstable amplitude. For structural damping... In the case of 1.5%, the total system damping 0 corresponds to 1 steady-state amplitude. 0.038.

[0092] The response time history under different initial amplitudes was calculated using the fourth-order Runge-Kutta method. For example... Figure 4 As shown, this is structural damping. The displacement response time histories released with different initial amplitudes show that the structural damping... The lower structure has two steady-state amplitudes. For example... Figure 4 As shown in (a), when the initial amplitude is given as 0.001, the structural response amplitude will continuously increase to a stable equilibrium amplitude; as Figure 4 As shown in (b), when the initial amplitude is given as 0.2, the structural response amplitude will shrink to [value missing]. Figure 4 (a) shows the same amplitude of a stable equilibrium. Figure 4 As shown in (c), when the initial amplitude is given as 0.25, the structural response amplitude will not shrink to the same value. Figure 4 The same stable equilibrium amplitude shown in (a) will instead continue to increase to a larger stable equilibrium amplitude; as Figure 4 As shown in (d), when the initial amplitude is given as 0.5, the structural response amplitude will also shrink to the same value. Figure 4 (c) shows the same amplitude of a stable equilibrium. Figure 4 As shown in (e), given an initial amplitude of 0.001, besides the influence of the initial amplitude, under the action of random beatout force, the vibration displacement transitions between two steady states, where, Figure 4 Regions 1 and 3 in (e) represent two small stable amplitude states. Figure 4 Region 2 in (e) represents a large stable amplitude state.

[0093] like Figure 5 As shown, this is structural damping. The displacement response time histories released with different initial amplitudes show that, regardless of... Figure 5 (a) shows a given very small initial amplitude value, or as shown in (a) Figure 5 (b) shows that given a large initial amplitude, the structural response amplitude will continuously increase or decrease to the same stable equilibrium amplitude, and only a steady state can be observed.

[0094] Step 2: Model the aerodynamic damping as a non-monotonic high-order function with respect to amplitude, and construct a nonlinear dynamic state-space model for hysteresis characteristics. Specifically, in this embodiment, the method for constructing the nonlinear dynamic state-space model is as follows.

[0095] 21) When constructing a non-monotonic high-order aerodynamic damping model for hysteresis characteristics, considering only the basic mode shape, the lateral wind-induced vibration of the building structure has the following equations of motion:

[0096]

[0097]

[0098]

[0099] in: and These refer to the height and width of the building structure, respectively. , for normalized displacement; generalized modal coordinates This refers to the top displacement of the building structure; , is the structural angular frequency; It is the natural frequency; and These are structural damping and aerodynamic damping caused by vortex-induced forces, respectively. The modal shape varies along the height; For height position; The empirical modal correction coefficients are needed to deduce the generalized modal force from the base bending moment; for linear modal shapes, , 1; The mass per unit height that varies along the altitude; Effective mass per unit height; The base moment coefficient; For parameters related to modal shape, for linear modal shape, 3; air density; This refers to wind speed.

[0100] 22) To describe the hysteresis phenomenon, aerodynamic damping is expressed as a high-order polynomial function of the absolute value of the vibration displacement:

[0101]

[0102] Or a higher-order polynomial function expressing the absolute value of vibration velocity:

[0103]

[0104] in: and These are the parameters of the aerodynamic damping constant; ; ; , where is the reduced frequency. It is important to emphasize that the displacement and velocity of the vibration must be expressed in absolute values.

[0105] Specifically, this embodiment uses a fourth-order polynomial function:

[0106]

[0107] Or it can be expressed as a polynomial function of vibration velocity:

[0108]

[0109] 23) By using the relationship of work done by aerodynamic forces over one cycle, the displacement-dependent aerodynamic damping model is transformed into an amplitude-dependent aerodynamic damping model:

[0110]

[0111] in: , which is the normalized amplitude; This represents the actual amplitude. For the characteristic width; specifically, for square building structures, the characteristic width is... It is equal to the width of the building structure. .

[0112] In this embodiment, taking a fourth-order polynomial damping model as an example, the amplitude-dependent aerodynamic damping can be obtained as follows:

[0113]

[0114] Specifically, in some other implementations, the order of the polynomial can be adjusted. This model allows the damping curve to exhibit an "N"-shaped or inverse "N"-shaped variation, thus enabling it to cross the zero axis multiple times.

[0115] 24) State Vector Definition: The state vector in a traditional Kalman filter typically only contains... To achieve parameter identification and load decoupling, this embodiment constructs a high-dimensional extended state vector. :

[0116]

[0117] Specifically, taking the fourth-order polynomial damping model as an example, the state-space equation can be expressed as:

[0118]

[0119] Among them, the number of displacement-dependent damping coefficients depends on the order of damping; For external loads, in the case of uniform flow, The numerical calculations used to initiate the filtering algorithm still need to be retained; this expansion strategy, by incorporating the unknown load into the state space, enables the decoupled identification of damping parameters and external loads under a single working condition and unknown incoming turbulence intensity.

[0120] 25) Constructing the state transition equation: The state-space equation involving state-space variables can be calculated using numerical methods such as the fourth-order Runge-Kutta method. Displacement, velocity, and acceleration are selected as the test and observation quantities, respectively. The values ​​of velocity and acceleration can be obtained by differentiating the displacement data. The measurement vector... This can be expressed as:

[0121]

[0122] State space variables and observation vector It can be expressed using discrete-time equations:

[0123]

[0124]

[0125] Where: subscript Indicates a time step; for Regarding the next time step The mapping function can be called the state transition function; for Regarding the next time step The mapping function is called the measurement function; For including the covariance matrix A zero-mean Gaussian white noise vector; For including the covariance matrix A zero-mean Gaussian white noise vector; For expectation operators.

[0126] Step 3: Based on the state-space model, a filtering algorithm is used to recursively iteratively estimate the state vector, simultaneously identifying the nonlinear aerodynamic damping parameters. In this embodiment, the unscented Kalman filter (UKF) algorithm is used.

[0127] Specifically, before using the UKF method to identify aerodynamic damping, it is necessary to analyze the noise matrix. Measurement error matrix Covariance Matrix initial value To elaborate further: Noise matrix This can be understood as noise inherent to the system itself. In wind tunnel tests, the structural model, or the numerical model discussed in this chapter, can be considered to have sufficiently accurate system equations and a high signal-to-noise ratio. In this case, the noise matrix can be... The values ​​corresponding to the displacement, velocity, and damping model coefficients are set to zero. Noise matrix. When the terms corresponding to the internal and external loads are also set to zero, the covariance matrix in the UKF calculation process... The matrix may be non-positive definite, making Cholesky decomposition impossible and resulting in an error, thus interrupting the calculation. Therefore, the noise matrix... The corresponding value for Chinese and foreign loads is set to a small value, here it is 10. -12 Measurement error matrix For the numerical calculation data or wind tunnel test data used in this embodiment, the measurement error matrix The values ​​should also be small and cannot be zero; otherwise, the covariance matrix will be problematic. An error was reported due to the non-positive definite matrix, thus interrupting the UKF calculation process. Measurement error matrix As the numerical values ​​increase, the errors between the UKF-predicted displacement, velocity, and acceleration and the measured values ​​increase. (Initial values ​​for the covariance matrix are then used.) and the constantly updated covariance matrix Used to control the rate of fluctuation of state variables over time. Increase the covariance matrix. This can accelerate the convergence of the unknown damping model coefficients to the target value. (Noise matrix) Measurement error matrix Initial values ​​of the covariance matrix The parameters can be coordinated to ensure the UKF calculation process is not interrupted. Different combinations are possible, affecting how quickly the predicted values ​​of the observed variables converge to the actual observed values, and the speed at which the damping model parameters are identified. However, the identified damping result is unique. This embodiment provides one suitable set of parameters for each example.

[0128] The UKF parameters are the same for both small-amplitude and large-amplitude steady states: the initial values ​​of the state-space variables are set to... = [0 00 0 0 0 0 0] T Noise matrix diag[0 0 0 0 0 0 0 10 -12 ]; Observe the displacement, velocity, and acceleration error matrices. =diag[10 -10 10 -10 10 -10 Initial values ​​of the covariance matrix diag[1 1 10 -5 10 -3 10 1 10 3 10 3 10 1 ].

[0129] In this embodiment, a structure with two steady-state amplitudes and damping is utilized. Using 0.5% of the displacement response data as computational data, recursive iterative calculations using unscented Kalman filtering are performed on the displacement data of the small-amplitude stable segment and the large-amplitude stable segment respectively. The steps for synchronously estimating the state vector are as follows:

[0130] 31) Generating sigma points through unscented transformation: Assume the extended state vector initial value The average matrix is , The covariance matrix is Based on the system's state distribution, the mean and covariance of the states are represented by a set of sigma points with specific weights. These points are generated from the initial estimate of the states and their covariance matrices. Using scaling and unscented transformation, a model was generated. 1 sample sigma point, State-space variables Dimensions. sigma point matrix of time step The first in List This can be expressed as:

[0131]

[0132]

[0133]

[0134]

[0135] in: for The first sigma point in the time step sigma matrix List; To expand the state vector in the th The average matrix of time steps; For the first The covariance matrix of the time step; State-space variables The dimension; The first square root of the matrix OK; For scaling parameters; Decision made The distribution of nearby sigma points is set to 1; The second scaling parameter is set to 0.

[0136] 32) Time Update: Update the sigma point in time using the state transition equation and calculate the mean of the state-space variables. and its covariance matrix Specifically, in this step, each sigma point is determined through a nonlinear state transition equation. Calculate the estimate for the next time step, for example, using the fourth-order Runge-Kutta method or Newmark. Numerical methods such as the method, namely:

[0137]

[0138] By recombining the sigma points, we obtain State-space variables at time steps Mean and its covariance matrix :

[0139]

[0140]

[0141] in: and Weighting coefficients:

[0142]

[0143]

[0144] in: In the Gaussian process, the parameter that produces higher-order effects in covariance estimation is set to 2.

[0145] 33) Measurement Update: Through the estimated vectors of displacement, velocity, and acceleration With observation vector Update the variance matrix of the state-space variables. Covariance Matrix Specifically, in this step, the estimated vectors of displacement, velocity, and acceleration are used. With observation vector The comparison updates the variance matrix of the state-space variables. Covariance Matrix Specifically:

[0146]

[0147]

[0148]

[0149]

[0150] 34) State update: using the Kalman gain matrix and total observation vector Update # State space vector at time step and its covariance matrix :

[0151]

[0152]

[0153]

[0154] After performing recursive iterative calculations using unscented Kalman filtering on the response data for both large-amplitude and small-amplitude stable states, the updated extended state vector can be obtained. This includes the predicted displacement and velocity data, as well as the predicted parameters of the nonlinear aerodynamic damping model. For example... Figure 6 The figure shows a comparison between the measured displacement and the UKF estimated displacement under different amplitudes. It can be clearly observed from the figure that, regardless of the amplitude, the measured displacement is lower than that estimated by the UKF. Figure 6 The small-amplitude stable state shown in (a) is still as... Figure 6 (b) shows the large-amplitude steady state, where the displacement curves predicted by the UKF all highly coincide with the original measured displacement data points. This indicates that the designed observer can track the dynamic displacement changes of the system in real time and accurately. Figure 7 The output values ​​of the nonlinear aerodynamic damping parameters estimated by UKF are shown. Observing the parameter curves, it can be seen that in the initial stage, each parameter exhibits certain transient fluctuations, which is the algorithm's adjustment process to adapt to the initial error. Over time, regardless of... Figure 7 The small amplitude condition shown in (a) is still as follows Figure 7 (b) shows that under the large amplitude condition, all parameters gradually converge and stabilize near a specific constant value.

[0155] Step 4: Calculate the curve of aerodynamic damping as a function of amplitude based on the nonlinear aerodynamic damping parameters calculated by recursion and iteration.

[0156] In this embodiment, the calculation of the curve of aerodynamic damping as a function of amplitude includes:

[0157] 41) Define the amplitude calculation interval and construct an amplitude vector from zero to the maximum identification amplitude: In order to plot a continuous and smooth curve of aerodynamic damping as a function of amplitude, it is necessary to construct an amplitude vector specifically for display and calculation. By obtaining the maximum amplitude value of the displacement data of the recognition algorithm, and by setting a small step size to divide the data from 0 to the maximum amplitude value, sufficient point density is ensured, thereby accurately reflecting the subtle nonlinear characteristics of aerodynamic damping as a function of amplitude;

[0158] 42) Substitute the nonlinear aerodynamic damping parameters calculated by recursion into the amplitude-dependent nonlinear aerodynamic damping model, calculate and plot the variation curve of nonlinear aerodynamic damping in the amplitude calculation interval.

[0159] The parameters of the nonlinear aerodynamic damping model corresponding to time periods of 50s, 100s, 200s, and 300s were taken respectively, and the parameters were substituted into the higher-order non-monotonic aerodynamic damping model. The calculated amplitude-dependent aerodynamic damping results are as follows. Figure 8 As shown.

[0160] Step 5: Employ a full-amplitude domain splicing and recognition strategy, and combine the recognition results of the small amplitude range to correct and fuse the full-amplitude curve, so as to eliminate the recognition error in the small amplitude range and obtain a high-precision target aerodynamic damping curve.

[0161] Specifically, in this embodiment, the full amplitude domain stitching recognition strategy includes the following steps.

[0162] 51) For the response data under the small amplitude steady state, execute the recognition algorithm to obtain the first set of high-precision aerodynamic damping coefficients in the small amplitude range, and substitute them into the high-order nonlinear aerodynamic damping model to calculate the curve of aerodynamic damping with amplitude in the small amplitude range.

[0163] 52) Perform identification on the full-amplitude response data of large-amplitude stable state or containing large-amplitude transition process to obtain the second set of aerodynamic damping coefficients in the full-amplitude range. Substitute them into the high-order nonlinear aerodynamic damping model to calculate the curve of aerodynamic damping as a function of amplitude in the full-amplitude range.

[0164] 53) By using the high-precision data of the nonlinear aerodynamic damping curve in the small amplitude segment within the overlapping amplitude range, the results of the curve directly identified from the full amplitude data in the small amplitude range are replaced and corrected, and finally spliced ​​together to form a complete curve with consistent and optimized accuracy in the full amplitude domain.

[0165] Specifically, by Figure 8 (a) It can be seen that the predicted aerodynamic damping in a small-amplitude steady state can accurately identify the aerodynamic damping at 300s. The accuracy of the aerodynamic damping identified by the UKF method should be determined by the aerodynamic damping calculated from the damping model coefficients, not by the damping model coefficients themselves. The same conclusion can also be drawn in... Figure 8 (b) This was obtained from the aerodynamic damping identification results of the large-amplitude steady state. It should be noted that... Figure 8 In (b), the UKF method identifies the effective amplitude range of aerodynamic damping from zero to the maximum displacement (amplitude), which differs from the minimum to maximum amplitude range in the PDF method. Errors within a very small amplitude range are caused by damping coefficient identification errors. To obtain a more accurate aerodynamic damping curve across the entire amplitude range, a full-amplitude splicing method is used. Data from the first segment of the aerodynamic damping curve within the overlapping amplitude range is used to replace or correct the portion of the second segment of the aerodynamic damping curve within the corresponding small amplitude range, thus splicing together a target aerodynamic damping curve with high accuracy across the entire amplitude range. For example... Figure 9 The figure shows the estimated aerodynamic damping value obtained by splicing across the entire amplitude domain at 300s. It can be seen that through this splicing strategy, the final global damping curve maintains optimal accuracy in both small and large amplitude regions, and is essentially identical to the target aerodynamic damping value, eliminating potential local errors from a single data source.

[0166] Step 6: By solving for the intersection points and slopes of the nonlinear aerodynamic damping curve and the structural damping line, multiple stable amplitudes and unstable equilibrium points that lead to self-excited hysteresis vibration are identified.

[0167] By analyzing the intersection of the nonlinear aerodynamic damping curve and the negative structural damping curve (i.e., the equilibrium point where the total system damping is zero), the hysteresis phenomenon is revealed from the perspective of energy balance. Specifically, in this embodiment, identifying stable amplitudes and unstable equilibrium points includes the following:

[0168] 61) When the total damping curve crosses the zero axis with a positive slope (from bottom to top), this intersection constitutes a stable equilibrium point. To the left of this point (small amplitude region), the total damping is negative, and the aerodynamic energy absorption exceeds the structural energy dissipation, driving the amplitude to increase to the stable equilibrium point. To the right of this point (large amplitude region), the total damping is positive, and the system's net energy dissipation causes the amplitude to decay. The system will eventually be "locked" at the stable equilibrium point amplitude, forming a stable oscillation.

[0169] 62) When the total damping curve crosses the zero axis with a negative slope (from top to bottom), this intersection constitutes an unstable equilibrium point. Small perturbations near this point can cause energy imbalance in the system, causing the amplitude to deviate further from the equilibrium point, either decaying to a stable point in a lower energy state or diverging to a stable point in a higher energy state. Specifically, to the left of this point (small amplitude region), the total damping is positive, aerodynamic energy absorption is less than structural energy dissipation, resulting in net energy dissipation of the system, causing the amplitude to decay to the stable equilibrium point (if present in a smaller amplitude stage) or directly shrink to 0. To the right of this point (large amplitude region), the total damping is negative, aerodynamic energy absorption is greater than structural energy dissipation, driving the amplitude to increase to the stable equilibrium point amplitude (if present in a larger amplitude stage) or directly diverging.

[0170] pass Figure 9 As shown in the figure, when the structural damping ratio At 0.5%, the total system damping 0 corresponds to 3 amplitudes, namely , and . when hour, 0; when , 0; when hour, 0; when hour, 0. The structure will reach different stable states under different excitation states. Specifically, when the initial amplitude... At that time, since the total damping of the system is negative, the aerodynamic energy absorption is greater than the structural energy dissipation, driving the amplitude to increase to the stable equilibrium point. .when When the total damping is positive, the system loses net energy, causing the amplitude to decay. Ultimately, the system will be "locked" at the amplitude of its stable equilibrium point. .when At this point, the total damping is negative, the aerodynamic energy absorption exceeds the structural energy dissipation, and the driving amplitude increases to a large amplitude stable equilibrium point. .when When the total damping is positive, the system loses net energy, causing the amplitude to decay. Ultimately, the system will be "locked" at a stable equilibrium point with large amplitude. .

[0171] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A nonlinear aerodynamic damping identification method for self-excited hysteretic vibration, characterized in that: Includes the following steps: Step 1: Obtain vibration response data of the structure exhibiting displacement hysteresis characteristics under wind load; Step 2: Model the aerodynamic damping as a non-monotonic high-order function with respect to amplitude, and construct a nonlinear dynamic state-space model for hysteresis characteristics; Step 3: Based on the state-space model, the state vector is recursively estimated using a filtering algorithm, and nonlinear aerodynamic damping parameters are identified simultaneously. Step 4: Calculate the curve of aerodynamic damping as a function of amplitude based on the nonlinear aerodynamic damping parameters calculated by recursion and iteration. Step 5: Employ a full-amplitude domain splicing and recognition strategy, and combine the recognition results of the small amplitude range to correct and fuse the full-amplitude curve, so as to eliminate the recognition error in the small amplitude range and obtain a high-precision target aerodynamic damping curve. The full amplitude domain stitching and recognition strategy includes the following steps: 51) Perform identification on the response data under the small amplitude steady state to obtain the first set of aerodynamic damping coefficients and the corresponding aerodynamic damping curves for the small amplitude segment; 52) Perform identification on response data containing large amplitude steady state or large transition process to obtain the second set of aerodynamic damping coefficients and the corresponding aerodynamic damping curves for the full amplitude range; 53) Using the high-precision data of the small amplitude segment aerodynamic damping curve in the overlapping amplitude range, replace and / or correct the corresponding part of the full amplitude segment aerodynamic damping curve in the small amplitude range, and splice them together to form a complete aerodynamic damping curve with consistent accuracy in the full amplitude domain. Step 6: By solving for the intersection point and slope of the target aerodynamic damping curve and the structural damping line, multiple stable amplitudes and unstable equilibrium points that lead to self-excited hysteresis vibration are identified.

2. The nonlinear aerodynamic damping identification method for self-excited hysteretic vibration according to claim 1, characterized in that: In step one, the vibration response data is dynamic data collected within the wind speed range where displacement hysteresis occurs for structures with bluff body characteristics, including unsteady transition processes. The core physical quantity collected is displacement time history data.

3. The nonlinear aerodynamic damping identification method for self-excited hysteretic vibration according to claim 1, characterized in that: In step two, the method for constructing the nonlinear dynamic state-space model consists of the following steps: 21) Considering only the fundamental mode shape, the equation of motion for the lateral wind-induced vibration of the building structure is: in: and These refer to the height and width of the building structure, respectively. , for normalized displacement; generalized modal coordinates This refers to the top displacement of the building structure; and Located at vibration velocity and acceleration, respectively; , is the structural angular frequency; It is the natural frequency; and These are structural damping and aerodynamic damping caused by vortex-induced forces, respectively. The modal shape varies along the height; For height position; The empirical modal correction coefficients are needed to deduce the generalized modal force from the base bending moment; The mass per unit height that varies along the altitude; Effective mass per unit height; The base moment coefficient; These are parameters related to the modal shape. air density; Wind speed; 22) Express aerodynamic damping as a higher-order polynomial function of the absolute value of vibration displacement or the absolute value of vibration velocity: in: and These are the parameters of the aerodynamic damping constant; ; ; , where is the reduced frequency; 23) By using the relationship of work done by aerodynamic forces over one cycle, the displacement-dependent aerodynamic damping model is transformed into an amplitude-dependent aerodynamic damping model: in: , which is the normalized amplitude; This represents the actual amplitude. The feature width; 24) Construct a high-dimensional extended state vector : in: For external loads; 25) Construct the state transition equation, using displacement, velocity, and acceleration as test and observation quantities, and measure the vector. Represented as: State space variables and observation vector Expressed using discrete-time equations: Where: subscript Indicates a time step; for Regarding the next time step The mapping function, i.e., the state transition function; for Regarding the next time step The mapping function, i.e., the measurement function; For including the covariance matrix A zero-mean Gaussian white noise vector; For including the covariance matrix A zero-mean Gaussian white noise vector; For expectation operators.

4. The nonlinear aerodynamic damping identification method for self-excited hysteretic vibration according to claim 1, characterized in that: In step three, the filtering algorithm is an unscented Kalman filter algorithm. The method steps for recursively iteratively estimating the state vector and simultaneously identifying nonlinear aerodynamic damping parameters are as follows: 31) Generating sigma points through unscented transformation: in: for The first sigma point in the time step matrix List; To expand the state vector in the th... The average matrix of time steps; For the first The covariance matrix of the time step; State-space variables The dimension; The first square root of the matrix OK; For scaling parameters; Decision made Distribution of nearby sigma points; This is the second scaling parameter; 32) Update the sigma point over time using the state transition equation and calculate the mean of the state-space variables. and its covariance matrix , is represented as: in: It is a nonlinear state transition equation; and These are the weighting coefficients; This is the noise matrix; 33) Estimated vectors of displacement, velocity, and acceleration With observation vector Update the variance matrix of the state-space variables. Covariance Matrix : in: This is the measurement error matrix; 34) Using the Kalman gain matrix and total observation vector Update the state space vector and its covariance matrix : 。 5. The nonlinear aerodynamic damping identification method for self-excited hysteretic vibration according to claim 1, characterized in that: In step four, calculating the curve of aerodynamic damping as a function of amplitude includes: constructing an amplitude vector from zero to the maximum identified amplitude, substituting the identified nonlinear aerodynamic damping parameters into the amplitude-dependent nonlinear aerodynamic damping model, and calculating and plotting the curve of aerodynamic damping change on the amplitude calculation vector.

6. The nonlinear aerodynamic damping identification method for self-excited hysteretic vibration according to claim 1, characterized in that: In step six, identifying stable amplitudes and unstable equilibrium points specifically involves: when the total damping curve crosses the zero axis with a positive slope, the corresponding intersection point is a stable equilibrium point; when the total damping curve crosses the zero axis with a negative slope, the corresponding intersection point is an unstable equilibrium point; by analyzing the energy balance state on both sides of the intersection point, the multistable hysteresis mechanism is revealed.

7. A nonlinear aerodynamic damping identification system for self-excited hysteretic vibration, characterized in that: It includes a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor executing the computer program and implementing the nonlinear aerodynamic damping identification method for self-excited hysteretic vibration as described in any one of claims 1-6.

8. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by a processor, implements the nonlinear aerodynamic damping identification method for self-excited hysteresis vibration as described in any one of claims 1-6.

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