High-flexibility structure nonlinear aerodynamic damping estimation method and system based on Sage-Husa algorithm and square root cubature Kalman filtering and storage medium

Abstract

The invention discloses a high-flexibility structure nonlinear aerodynamic damping estimation method based on a Sage-Husa algorithm and square root cubature Kalman filtering. According to the method, aerodynamic damping with nonlinear characteristics can be effectively identified from free vibration data, forced vibration data, steady-state vibration data and random vibration data of high-flexibility structures such as high-rise buildings and fan towers under crosswind excitation, and process noise can be automatically adjusted according to the current state; the interested parameters of the high-dimensional system are accurately predicted, the noise level does not need to be known sufficiently, and a theoretical basis can be provided for evaluating the structural response by calculating the aerodynamic damping of the high-flexibility structure more conveniently and accurately in actual engineering. The invention further discloses a high-flexibility structure nonlinear aerodynamic damping estimation system based on the Sage-Husa algorithm and the square root cubature Kalman filter and a storage medium.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerodynamic analysis, and specifically relates to a highly flexible structure nonlinear aerodynamic damping estimation method, system and storage medium based on a Sage-Husa algorithm and square root volume Kalman filtering. Background Art

[0002] Aerodynamic damping refers to the energy dissipation effect on structural vibration caused by fluid flowing through a blunt body, and is an important aerodynamic parameter that affects structural vibration. Since its generation mechanism is affected by multiple factors such as structural shape, flow field characteristics and amplitude dependence, theoretical analysis and research on aerodynamic damping is very difficult. For high-flexible structures (such as high-rise buildings, wind turbine towers, etc.), aerodynamic damping usually appears as a negative value near the locking range of vortex-induced vibration, and has significant amplitude dependence. In order to accurately evaluate the response of such structures under crosswind in engineering practice, the key is to achieve accurate modeling of aerodynamic damping. An accurate aerodynamic damping model can not only improve the accuracy and reliability of the evaluation results, but also provide an effective basis for the wind-resistant design of the structure, thereby enhancing the safety and durability of the building.

[0003] In recent years, the identification methods of aerodynamic damping have made significant progress, mainly focusing on experiments, numerical simulations and data-driven methods. In the experimental method, the free vibration test effectively extracts the aerodynamic damping through wind tunnel experiments combined with technologies such as Hilbert transform (HT), especially in capturing nonlinear aerodynamic damping characteristics. The forced vibration test uses random decrement technology (RDT) to obtain linear damping, but there are limitations in identifying nonlinear damping. At the same time, the application of computational fluid dynamics (CFD) technology has also provided new ideas for the extraction of nonlinear aerodynamic damping, and more accurate aerodynamic damping values ​​can be obtained by simulating the complex process of interaction between airflow and structure.

[0004] In terms of statistical and data-driven methods, the least squares method, neural network and other techniques are applied to damping identification, processing complex nonlinear features and improving identification accuracy. In addition, nonlinear Kalman filter (NKF) and unscented Kalman filter (UKF) have been used for real-time identification of aerodynamic damping, effectively processing noise and nonlinear characteristics in dynamic systems. In some studies, an iterative unscented Kalman filter (UKF) is further used to extract the aerodynamic damping ratio from free vibration data, thereby significantly enhancing the robustness of the identification process when the initial conditions change. This method improves the system's adaptability to noise and parameter changes by optimizing the iterative process. However, in the current research on aerodynamic damping identification, there is still an urgent need for a comprehensive and in-depth understanding of the vibration system. This in-depth analysis is crucial to accurately specify the characteristics of process noise, because the nature of the noise directly affects the reliability of the estimation results. Only on the basis of a full grasp of the dynamic characteristics of the vibration system and the source of noise can the validity of the model and the accuracy of the results be ensured.

[0005] Compared with other nonlinear Kalman filtering methods, the square root cubic Kalman filter (SRCKF) shows higher accuracy and efficiency in processing high-dimensional nonlinear systems. However, the premise for obtaining ideal results is to have a proper understanding of the characteristics of process noise. In practical applications, the noise characteristics are often unknown and dynamically changing, which makes it possible for inaccurate noise models to significantly reduce the estimation accuracy and even cause the system to diverge. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a method, system and storage medium for estimating nonlinear aerodynamic damping of highly flexible structures based on the Sage-Husa algorithm and square root volume Kalman filtering, which can automatically adjust the process noise according to the current state and accurately predict the parameters of interest of the high-dimensional system without having a sufficient understanding of the noise level, and can provide a theoretical basis for more accurate calculation of the aerodynamic damping of flexible structures in actual engineering.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] The present invention firstly proposes a method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter, which is characterized by comprising the following steps:

[0009] Step 1: Based on the crosswind response equation of the high-flexibility structure and the harmonic balance technology, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is obtained;

[0010] Step 2: Define the measurement equation through vibration displacement, velocity and acceleration; consider the displacement, velocity, frequency, unknown structural aerodynamic damping parameters and external loads of the high-flexible structure, and define the state space equation;

[0011] Step 3: Time Update: First define the initial state estimate And the initial state covariance matrix P0, using the spherical radial volume law to generate volume points X k / k ; Then propagate the volume point through the state transition function f(·) to predict the state mean and the square root of the state covariance S k+1 / k ;

[0012] Step 4: Measurement update: First use and S k+1 / k Recalculate the volume points and then propagate them through the measurement function h(·) to get the predicted mean Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k ;

[0013] Step 5: State update: Calculate Kalman gain K k+1 , update the state matrix and the square root of the covariance S k+1 .

[0014] Step 6: Noise update: Evaluate whether the state-space equation parameters have stabilized. If so, it indicates that the estimation has achieved the best performance, keeping the process noise unchanged. If not, it indicates that the state-space equation parameters continue to fluctuate. The Sage-Husa estimator is used to update the process noise Q in real time until the state-space equation parameters reach a stable state.

[0015] Step 7: Repeat steps 3 to 6 for each sample point until all sample points are processed and stable nonlinear aerodynamic damping parameters are obtained;

[0016] Step 8: Calculate the nonlinear aerodynamic damping by using the obtained stable nonlinear aerodynamic damping parameters.

[0017] Furthermore, in step 1, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is:

[0018]

[0019] Where: a is the nonlinear aerodynamic damping; ρ is the air density; m is the structure width; m s Represents the effective structural mass per unit height; y max is the structural vibration amplitude; B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and they are all constants.

[0020] Further, the measurement equation is defined as:

[0021]

[0022] Among them: y, and Represent displacement, velocity, and acceleration;

[0023] The state space equation is:

[0024]

[0025] Where: B1′, B2′, B3′, B4′ and B′5 are the structural aerodynamic damping parameters; S is the defined zero-mean Gaussian white noise external load; ω s =2πf s represents the modal circular frequency, f s is the frequency; and: B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and they are all constants.

[0026] Furthermore, in step 3, the method steps for updating the time are as follows:

[0027] 31) Define the initial state estimate And the initial state covariance matrix P0 is defined as:

[0028]

[0029] Where: X0 represents the initial state space equation; E(·) represents taking the expectation; COV(·) represents taking the covariance.

[0030] Get the state space vector and measurement vector:

[0031] X k =f(X k-1 )+w k

[0032] Z k =h(X k )+v k

[0033] Where: X k ∈R n and Z k ∈R m are the state vector and measurement vector at time step k, respectively; f(·) and h(·) represent the nonlinear state transfer function and nonlinear measurement function; k is the current time step; w k ∈R n and vk ∈R m The covariance matrices are and uncorrelated zero-mean Gaussian white noise; Q k is the process noise covariance; R k is the measurement noise covariance;

[0034] 32) Generate volume point X using the spherical radial volume law k / k :

[0035]

[0036] Where: S k / k YesP k / k The orthogonal-triangular decomposition of k / k is the state covariance matrix; ξ is the volume point set; e i is the identity matrix I n The i-th column of .

[0037] 33) Propagate volume points through the state transition function f(·):

[0038]

[0039] in: is the new volume point at time step k+1 obtained by propagating the state transition function; X i,k / k is the volume point at time step k.

[0040] 34) Predict state mean and the square root of the state covariance S k+1 / k :

[0041]

[0042] in:

[0043] S Q =chol(Q)

[0044]

[0045] Where chol represents the Cholesky decomposition function; Tria(·) represents the QR decomposition of the matrix; S Q is the Cholesky decomposition of Q; Q is the process noise; is the weight matrix.

[0046] Further, in step 4, the method steps for measuring update are:

[0047] 41) Use state mean and the square root of the state covariance Sk+1 / k Recalculate volume points:

[0048]

[0049] 42) Propagate volume points through the measurement function h(·):

[0050] Z i,k+1 / k =h(X i,k+1 / k ),i=1,2,...,2n

[0051] 43) Predict the mean value from the transformed volume points Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k

[0052]

[0053] Where: S R is the Cholesky decomposition of R, R is the measurement noise; η k+1 / k is the measurement weight matrix; Z k+1 / k is the new volume point obtained by propagating the measurement function.

[0054] Further, in step 5, the Kalman gain K k+1 for:

[0055]

[0056] State Matrix Updated to:

[0057]

[0058] The square root of the state covariance S k+1 Updated to:

[0059] S k+1 = Tria([χ k+1 / k -K k+1 η k+1 / k ,K k+1 S R ]).

[0060] Further, in step six, the noise updating method is:

[0061] The Sage-Husa estimator is used to update the process noise Q:

[0062]

[0063] in:

[0064]

[0065] Where: b is the forgetting factor; α1 is the introduced empirical proportional factor; e k+1 is the new information sequence;

[0066] After the Sage-Husa estimator is used to iteratively update the process noise Q for the preset k times, the data accumulated during the preset k iterations are used to evaluate whether the state space equation parameters have stabilized:

[0067] If in the current j-th iteration, j>k, if the ratio of the standard deviation to the mean value of the parameter satisfies:

[0068]

[0069] Among them: std j represents the standard deviation of the parameters of the jth iteration; mean j represents the average value of the parameters of the jth iteration; std(X j-k:j ) is the standard deviation of the parameters from the current jth iteration to the previous jkth iteration; mean(X j-k:j ) is the average parameter value from the current jth to the previous jk iterations; δ is the preset threshold.

[0070] Then the state space equation parameters have stabilized and the process noise remains unchanged:

[0071] Q j+1 =Q j

[0072] Otherwise, it indicates that the state space equation parameters are unstable and the process noise Q is updated as:

[0073]

[0074] Among them: α2 is the introduced empirical proportional factor.

[0075] The present invention also proposes a highly flexible structure nonlinear aerodynamic damping estimation system based on the Sage-Husa algorithm and the square root volume Kalman filter, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program and implements the highly flexible structure nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and the square root volume Kalman filter as described above.

[0076] The present invention also proposes a storage medium having a computer program stored thereon. When the computer program is executed by a processor, the highly flexible structural nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and square root volume Kalman filtering as described above is implemented.

[0077] The beneficial effects of the present invention are:

[0078] The key to improving the application effect of SRCKF is to deeply study the dynamic characteristics of noise characteristics and build a noise model that is more suitable for actual conditions. The Sage-Husa estimator is used to estimate noise statistics in real time. By introducing the Sage-Husa estimator, NKF can estimate the process noise covariance matrix in nonlinear systems in real time. Combining the Sage-Husa estimator with SRCKF helps to further explore the accuracy of filter estimation and system stability under dynamic noise conditions. Therefore, the integration study of SRCKF and Sage-Husa estimator is of great significance, which not only helps to improve the performance of the filter in unknown noise environments, but also provides new theoretical support for real-time and accurate estimation of high-dimensional nonlinear systems. That is: the nonlinear aerodynamic damping estimation method for high-flexible structures based on the Sage-Husa algorithm and square root volume Kalman filtering of the present invention can not only effectively identify aerodynamic damping with nonlinear characteristics from the free vibration data, forced vibration data, steady-state vibration data and random vibration data of high-rise buildings, wind turbine towers and other high-flexible structures under crosswind excitation, but also can automatically adjust the process noise according to the current state and accurately predict the parameters of interest of the high-dimensional system without having a sufficient understanding of the noise level. It can provide a theoretical basis for more convenient and accurate calculation of the aerodynamic damping of high-flexible structures to evaluate the structural response in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0080] Figure 1 This is a schematic diagram of the Gaoruo round tower structure;

[0081] Figure 2 It is a flow chart of a method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter (SSRCKF) of the present invention;

[0082] Figure 3 is the structural damping ξ s = 0.5% and random crosswind response data with reduced wind speed U / fB = 11.7;

[0083] Figure 4 It is a comparison diagram between the measured displacement and the displacement estimated by SSRCKF;

[0084] Figure 5 Comparison chart of measured speed and SSRCKF estimated speed;

[0085] Figure 6 The comparison diagram between the parameter values ​​of nonlinear aerodynamic damping estimated by SSRCKF and the target values;

[0086] Figure 7 is the comparison between the estimated aerodynamic damping values ​​at different times estimated by SSRCKF and the target values;

[0087] Figure 8 is the structural damping ξ s = 0.5% and different types of response data of reduced wind speed U / fB = 11.7;

[0088] Fig. 9 Comparison of aerodynamic damping extracted by SSRCKF using different types of data with the target value. DETAILED DESCRIPTION

[0089] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0090] In this embodiment, the proposed high-flexible structure nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and the square root volume Kalman filter (SSRCKF) is used to calculate the nonlinear aerodynamic damping of a high-flexible round tower structure, and the effectiveness and accuracy of the estimated nonlinear aerodynamic damping are evaluated by comparing with the true value. Specifically, the round tower structure has a height H of 200m, an aspect ratio H / B=13.3, and a mass parameter m s / ρB 2 =172, modal circular frequency ω s =1.26, the structural damping ratio is ξ s = 0.5%, 1% and 2%, assuming that the basic mode vibration shape is linear along the height of the structure, that is, φ(y) = y / H, such as Figure 1 shown.

[0091] like Figure 2 As shown, the nonlinear aerodynamic damping estimation method for a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter (SSRCKF) in this embodiment includes the following steps.

[0092] Step 1: Based on the crosswind response equation of the high-flexibility structure and the harmonic balance technology, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is obtained.

[0093] Specifically, the relationship between aerodynamic damping and structural vibration amplitude is derived and expressed by the structural crosswind response equation and harmonic balance technology. The crosswind response equation of the flexible structure based on the first modal response is expressed as:

[0094]

[0095] Where: y1 represents the generalized displacement of the structure (linear or torsional displacement); for speed; is the acceleration; ω s =2πf s represents the modal circular frequency, f s is the frequency; s represents the structural damping ratio; ξ a represents the aerodynamic damping ratio; Q(t) represents the generalized crosswind force; M s Represents generalized quality.

[0096] When conducting high-frequency force balance model tests and estimating the generalized crosswind force Q(t) from the base bending moment M(t), the relationship is:

[0097]

[0098] Where: η b is the empirical mode vibration correction factor. For linear mode vibration, η is generally set b =1; H is the structure height; ρ is the air density; B is the structure width; m s represents the effective structural mass per unit height; U is the wind speed at the top of the structure; η is the dimensionless parameter of the modal vibration type, for the linear modal vibration type η=3; C Mb (t) represents the base moment coefficient.

[0099] Pneumatic damping a It is expressed as:

[0100]

[0101] Where: B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and are all constants; y = y1 (t) / B represents the normalized dimensionless displacement. Low-order or high-order polynomial models can be used according to requirements.

[0102] Using harmonic balance technology y=y max sin(ωt), the relationship between nonlinear aerodynamic damping and structural vibration amplitude is:

[0103]

[0104] Where: a is the nonlinear aerodynamic damping; ρ is the air density; B is the structure width; m s Represents the effective structural mass per unit height; y max is the structural vibration amplitude; B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and they are all constants.

[0105] In this embodiment, a third-order polynomial model is used to estimate the nonlinear aerodynamic damping of the high-flexible round tower structure.

[0106] That is, the nonlinear aerodynamic damping ξ represented by the third-order polynomial model a for:

[0107]

[0108] Where: B1, B2, B3 are the parameters estimated by SSRCKF.

[0109] Using harmonic balance technology y=y max sin(ωt), establishes the aerodynamic damping ξ a The relationship with the vibration amplitude is:

[0110]

[0111] Step 2: Define the measurement equation through vibration displacement, velocity and acceleration; consider the displacement, velocity, frequency, unknown structural aerodynamic damping parameters and external loads of the highly flexible structure, and define the state space equation.

[0112] Considering the structural displacement, velocity, frequency, unknown structural aerodynamic damping parameters and external loads, the state space equation is:

[0113]

[0114] Where: y represents the structural displacement; is the velocity; B′1, B′2, B′3, B′4 and B′5 are the structural aerodynamic damping parameters; S is the defined zero-mean Gaussian white noise external load, and:

[0115]

[0116] The nonlinear state-space equation that can be solved by the fourth-order Runge-Kutta method is expressed as:

[0117]

[0118] According to the measured displacement or acceleration time history, the vibration velocity time history is obtained by differentiation or integration, and then the SSRCKF method is used for post-processing.

[0119] Using vibration displacement, velocity and acceleration as measurement variables can improve the accuracy of the estimation. Specifically, the measurement equation is defined as:

[0120]

[0121] Among them: y, and Represents displacement, velocity, and acceleration.

[0122] Specifically, in this embodiment, after the third-order polynomial model is used for calculation, the measurement equation and the state space equation are expressed as:

[0123] Considering the structural displacement, velocity, frequency, unknown structural aerodynamic damping parameters and external loads, the state space equation is:

[0124]

[0125] Where: y represents the displacement of the top of the round tower structure, is the speed, ω s represents the modal circular frequency, and S is the defined zero-mean Gaussian white noise external load.

[0126] The nonlinear state-space equation that can be solved by the fourth-order Runge-Kutta method is expressed as:

[0127]

[0128] In actual engineering, the measurement values ​​that can be obtained for built structures generally only obtain vibration accelerations accompanied by large noise; in wind tunnel tests, vibration displacement or vibration acceleration can be directly measured, and the noise level can be reduced. In subsequent applications, the vibration velocity time history can be obtained by differentiation or integration based on the displacement or acceleration time history obtained by actual measurement or experiment, and the influence of noise can be processed, and then the SSRCKF method can be used for post-processing.

[0129] Step 3: Time Update: First define the initial state estimate And the initial state covariance matrix P0, using the spherical radial volume law to generate volume points X k / k ; Then propagate the volume point through the state transition function f(·) to predict the state mean and the square root of the state covariance S k+1 / k .

[0130] In this embodiment, the structural damping ξ s = 0.5% and the random crosswind response data of the reduced wind speed U / fB = 11.7, the acquisition frequency is 250Hz, that is, Δt = 0.04s, such as Figure 3 As shown in Figure 2, the accuracy of the SSRCKF method in identifying nonlinear aerodynamic damping is verified. The target value of the aerodynamic damping parameter under this condition is:

[0131] [B1 B2 B3]=[-4.59 123.95 -484.39]

[0132] Specifically, in this embodiment, the method steps for updating time are:

[0133] 31) Define the initial state estimate before updating the time And the initial state covariance matrix P0:

[0134]

[0135] Where: X0 represents the initial state space equation; E(·) represents taking the expectation; COV(·) represents taking the covariance.

[0136] Using the SSRCKF technique, the initial state space vector can be set to any value without affecting the final estimate. In this embodiment, the initial value X0 = [0 0.2 0 0 0 0 0] T The initial covariance matrix P0 can also be taken arbitrarily, but its size will affect the convergence speed of SSRCKF estimation. It is recommended to use a larger P0 value to accelerate convergence, and take P0 = 10 3 diag([1 1 1 1 11 1]). In addition, define the covariance Q of the process noise k and the measurement noise covariance R k . The selection of process noise Q in nonlinear Kalman filtering is of great significance for accurate estimation. However, the characteristics of process noise have always been unknown and difficult to accurately model. Inappropriate process noise will not only reduce the calculation accuracy, but also cause the filter to diverge, which is particularly problematic in high-dimensional systems. In this embodiment, the Sage-Husa estimator can be used to estimate and dynamically update the process noise in real time based on the statistical characteristics of the process noise. Therefore, the process noise can take any value because it will automatically converge to a suitable value. In this embodiment, the initial process noise Q0=10 is selected. 3 diag([1 1 1 1 1 1 1]). The measurement noise can be set smaller, take R0 = 10 - 3 diag([1 1 1]).

[0137] In a nonlinear discrete system, the state space vector and measurement vector are obtained:

[0138] X k =f(X k-1 )+w k

[0139] Z k =h(X k )+v k

[0140] Where: X k ∈R n and Z k ∈R m are the state vector and measurement vector at time step k, respectively; f(·) and h(·) represent the nonlinear state transfer function and nonlinear measurement function; k is the current time step; w k ∈R n and vk ∈R m The covariance matrices are and uncorrelated zero-mean Gaussian white noise; Q k is the process noise covariance; R k is the measurement noise covariance.

[0141] 32) Generate volume point X using the spherical radial volume law k / k , for state dimension n, the volume point is defined as:

[0142]

[0143] Where: S k / k YesP k / k The orthogonal-triangular decomposition of k / k is the state covariance matrix; ξ is the volume point set; e i is the identity matrix I n The i-th column of .

[0144] 33) Propagate volume points through the state transition function f(·):

[0145]

[0146] in: is the new volume point at time step k+1 obtained by propagating the state transition function; X i,k / k is the volume point at time step k.

[0147] 34) Predict state mean and the square root of the state covariance S k+1 / k :

[0148]

[0149] in:

[0150] S Q =chol(Q)

[0151]

[0152] Where chol represents the Cholesky decomposition function; Tria(·) represents the QR decomposition of the matrix; S Q is the Cholesky decomposition of Q; Q is the process noise; is the weight matrix.

[0153] Step 4: Measurement update: First use and S k+1 / kRecalculate the volume points and then propagate them through the measurement function h(·) to get the predicted mean Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k .

[0154] Specifically, in this embodiment, the steps of the measurement update method are:

[0155] 41) Use state mean and the square root of the state covariance S k+1 / k Recalculate volume points:

[0156]

[0157] 42) Propagate volume points through the measurement function h(·):

[0158] Z i,k+1 / k =h(X i,k+1 / k ),i=1,2,...,2n

[0159] 43) Predict the mean value from the transformed volume points Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k

[0160]

[0161] Where: S R is the Cholesky decomposition of R, R is the measurement noise; η k+1 / k is the measurement weight matrix; Z k+1 / k is the new volume point obtained by propagating the measurement function.

[0162] Step 5: State update: Calculate Kalman gain K k+1 , update the state matrix and the square root of the covariance S k+1 .

[0163] Specifically, the Kalman gain K k+1 for:

[0164]

[0165] State Matrix Updated to:

[0166]

[0167] The square root of the state covariance S k+1 Updated to:

[0168] S k+1 = Tria([χk+1 / k -K k+1 η k+1 / k ,K k+1 S R ])

[0169] Step 6: Noise update: Evaluate whether the state-space equation parameters have stabilized: If so, it indicates that the estimation has achieved the best performance and the process noise remains unchanged; if not, it indicates that the state-space equation parameters continue to fluctuate, and the Sage-Husa estimator is used to update the process noise Q in real time until the state-space equation parameters reach a stable state.

[0170] Specifically, the noise update method is:

[0171] The Sage-Husa estimator is used to update the process noise Q:

[0172]

[0173] in:

[0174]

[0175] Wherein: b is the forgetting factor, and in this embodiment, b=0.95; α1 is the introduced empirical proportional factor, and according to numerical simulation and experimental verification, in this embodiment, α1=1; e k+1 is the new information sequence.

[0176] After the Sage-Husa estimator is used to iteratively update the process noise Q for the preset k times, the data accumulated during the preset k iterations are used to evaluate whether the state space equation parameters have stabilized:

[0177] If in the current j-th iteration, j>k, if the ratio of the standard deviation to the mean value of the parameter satisfies:

[0178]

[0179] Among them: std j represents the standard deviation of the parameters of the jth iteration; mean j represents the average value of the parameters of the jth iteration; std(X j-k:j ) is the standard deviation of the parameters from the current jth iteration to the previous jkth iteration; mean(X j-k:j ) is the average parameter value from the current jth to the previous jk iterations; δ is the preset threshold;

[0180] Then the state space equation parameters have stabilized and the process noise remains unchanged:

[0181] Q j+1 =Q j

[0182] Otherwise, it indicates that the state space equation parameters are unstable and the process noise Q is updated as:

[0183]

[0184] Where: α2 is the empirical proportional factor introduced. In order to accelerate the stabilization of the parameters, the variation range of the process noise must be reduced. Therefore, α2 in this embodiment is set to 10 -6 .

[0185] In this embodiment, the preset number of iterations in the noise update process is k=1000, which means that the parameter stability is evaluated after 40 seconds of free iteration. In the first 1000 free iteration steps of the data, SSRCKF not only updates the process noise Q in real time, but also accumulates data for subsequent evaluation to see if the parameters have stabilized.

[0186] After j (j>k=1000) iterations, the stability of the state space vector parameters is evaluated using the previously accumulated data. The stability criterion is that the ratio of the standard deviation to the mean value of the parameter in the current j-th iteration and the previous k=1000 iterations satisfies:

[0187]

[0188] Among them: std j represents the standard deviation of the parameters of the jth iteration; mean j represents the average value of the parameters of the jth iteration; std(X j-k:j ) is the standard deviation of the parameters from the current jth iteration to the previous j-1000 iterations; mean(X j-k:j ) is the average value of the parameters from the current jth iteration to the previous j-1000th iteration; δ is the preset threshold. In this embodiment, δ=5%.

[0189] Step 7: Repeat steps 3 to 6 for each sample point until all sample points are processed and stable nonlinear aerodynamic damping parameters are obtained.

[0190] In this embodiment, the first 600s of displacement data are estimated to obtain the parameter value of nonlinear aerodynamic damping. The time step Δt = 0.04s, then the four steps of time update, measurement update, state update and noise update are iterated for 15,000 steps in sequence to obtain the parameter value of nonlinear aerodynamic damping estimated by SSRCKF. Figure 4 The figure shows the comparison between the measured displacement and the SSRCKF estimated displacement. Figure 5 The figure shows the comparison between the measured velocity and the velocity estimated by SSRCKF. It can be found that the measured displacement and velocity are almost consistent with the estimated values ​​by SSRCKF. Figure 6The figure shows the comparison between the three aerodynamic damping parameter values ​​B1, B2, and B3 estimated by SSRCKF and the actual values. It can be found that the parameter values ​​estimated by SSRCKF are almost consistent with the actual target values ​​of aerodynamic damping when they converge to stability. These comparison figures all show the accuracy of SSRCKF in response estimation.

[0191] Step 8: Calculate the nonlinear aerodynamic damping by using the obtained stable nonlinear aerodynamic damping parameters.

[0192] Specifically, the obtained stable nonlinear aerodynamic damping parameters B1, B2, B3, B4 and B5 are substituted into the relationship between the aerodynamic damping ratio and the structural vibration amplitude:

[0193]

[0194] The amplitude-dependent nonlinear aerodynamic damping can be obtained by adjusting the amplitude and aerodynamic damping parameters.

[0195] In this embodiment, the three aerodynamic damping parameter values ​​B1, B2, and B3 obtained through the iterative process in step 7 are substituted into the relationship between the aerodynamic damping ratio and the structural vibration amplitude:

[0196]

[0197] In order to evaluate the performance of SSRCKF estimation, the parameter estimates at five different times, i.e., t = 0s, 40s, 100s, 400s, and 500s, are used to calculate the nonlinear aerodynamic damping and compared with the target nonlinear aerodynamic damping values, as shown in Figure 7 As shown. It can be found that when the parameter values ​​are stable, that is, at t = 400s and 500s, the estimated value of aerodynamic damping is almost consistent with the target value. In order to obtain a more accurate estimate of aerodynamic damping, the specific values ​​of the parameters B1, B2, and B3 can be obtained by taking the average value of the time period after the estimated parameters converge and stabilize.

[0198] SSRCKF can not only estimate the nonlinear aerodynamic damping more accurately from the displacement data of random vibration, but also obtain the aerodynamic damping value from other types of data, such as Figure 8 The free vibration data, steady-state data, and forced vibration data (respectively as Case 1, Case 2, and Case 3) shown in Figure 1 can also accurately obtain the aerodynamic damping value. Fig. 9 The figure shows the comparison between the aerodynamic damping values ​​obtained by SSRCKF from these three different vibration conditions and the target values. It can be found that SSRCKF can also accurately estimate the nonlinear aerodynamic damping from different types of vibration data.

[0199] This embodiment is based on the Sage-Husa algorithm and the square root volume Kalman filter (SSRCKF) high flexible structure nonlinear aerodynamic damping estimation method, which is used to estimate the nonlinear aerodynamic damping of flexible structures. The method can iterate the data points in sequence through the steps of time update, measurement update, state update and noise update, and accurately predict the actual value, thereby obtaining the parameters of the relevant nonlinear aerodynamic damping. The characteristics of this implementation method are that the process noise can be automatically adjusted according to the current state, and the parameters of interest of the high-dimensional system can be accurately predicted without sufficient understanding of the noise level, which can be more convenient when setting the initial value. Moreover, the method of this embodiment can obtain the parameters of nonlinear aerodynamic damping from different types of vibration data, which can provide a theoretical basis for more convenient and accurate calculation of the aerodynamic damping of high flexible structures such as towers in actual engineering to evaluate the structural response. Finally, the method of this embodiment is applied to estimate the nonlinear aerodynamic damping of a high flexible round tower structure with a height of 200m under different vibration conditions. It can be found that the state value of the vibration data can be more accurately predicted by SSRCKF, and the parameter value estimation of the aerodynamic damping can finally converge to almost the same as the actual value. For different types of vibration data, such as free vibration data, steady-state data, and forced vibration data, the aerodynamic damping parameters can be well estimated, and nonlinear aerodynamic damping that is almost consistent with the target value can be obtained. It should be noted that the nonlinear aerodynamic damping estimation method for high-flexible structures based on the Sage-Husa algorithm and the square root volume Kalman filter (SSRCKF) in this embodiment is not only applicable to high-flexible round tower structures, but also to other high-flexible structures, such as wind turbine towers, high-rise buildings, and single-degree-of-freedom vibrations of long-span bridges.

[0200] This embodiment also proposes a highly flexible structure nonlinear aerodynamic damping estimation system based on the Sage-Husa algorithm and the square root volume Kalman filter, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the computer program and implements the highly flexible structure nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and the square root volume Kalman filter as described above in this embodiment.

[0201] This embodiment further proposes a storage medium having a computer program stored thereon. When the computer program is executed by a processor, the highly flexible structure nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and square root volume Kalman filter as described above in this embodiment is implemented.

[0202] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and square root volumetric Kalman filtering, characterized in that: The steps include: Step 1: Based on the crosswind response equation of the high-flexibility structure and the harmonic balance technology, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is obtained; Step 2: Define the measurement equation through vibration displacement, velocity and acceleration; consider the displacement, velocity, frequency, unknown structural aerodynamic damping parameters and external loads of the high-flexible structure, and define the state space equation; Step 3: Time Update: First define the initial state estimate And the initial state covariance matrix P0, using the spherical radial volume law to generate volume points X k / k ; Then propagate the volume point through the state transition function F(·) to predict the state mean and the square root of the state covariance S k+1 / k ; Step 4: Measurement update: First use and S k+1 / k Recalculate the volume points and then propagate them through the measurement function h(·) to get the predicted mean Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k ; Step 5: State update: Calculate Kalman gain K k+1 , update the state matrix and the square root of the covariance S k+1 . Step 6: Noise update: Evaluate whether the state space equation parameters have stabilized: If so, it means that the estimation has achieved the best performance, keeping the process noise constant; If not, it indicates that the state-space equation parameters continue to fluctuate, and the Sage-Husa estimator is used to update the process noise Q in real time until the state-space equation parameters reach a stable state; Step 7: Repeat steps 3 to 6 for each sample point until all sample points are processed and stable nonlinear aerodynamic damping parameters are obtained; Step 8: Calculate the nonlinear aerodynamic damping by using the obtained stable nonlinear aerodynamic damping parameters.

2. According to claim 1, the method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter is characterized by: In step 1, the relationship between nonlinear aerodynamic damping and structural vibration amplitude is: Where: a is the nonlinear aerodynamic damping; ρ is the air density; B is the structure width; m s Represents the effective structural mass per unit height; y max is the structural vibration amplitude; B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and they are all constants.

3. According to claim 1, the method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter is characterized by: The measurement equation is defined as: Among them: y, and Represent displacement, velocity, and acceleration; The state space equation is: Where: B′1, B′2, B′3, B′4 and B′5 are the structural aerodynamic damping parameters; S is the defined zero-mean Gaussian white noise external load; ω s =2πf s represents the modal circular frequency, f s is the frequency; and: B1, B2, B3, B4 and B5 are nonlinear aerodynamic damping parameters, and they are all constants.

4. According to claim 1, the method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter is characterized by: In step 3, the time updating method steps are as follows: 31) Define the initial state estimate And the initial state covariance matrix P0 is defined as: Where: X0 represents the initial state space equation; E(·) represents taking the expectation; COV(·) represents taking the covariance. Get the state space vector and measurement vector: X k =f(X k-1 )+w k Z k =h(X k )+v k Where: X k ∈R n and Z k ∈R m are the state vector and measurement vector at time step k, respectively; f(·) and h(·) represent the nonlinear state transfer function and nonlinear measurement function; k is the current time step; w k ∈R n and v k ∈R m The covariance matrices are and uncorrelated zero-mean Gaussian white noise; Q k is the process noise covariance; R k is the measurement noise covariance. 32) Generate volume point X using the spherical radial volume law k / k : Where: S k / k YesP k / k The orthogonal-triangular decomposition of k / k is the state covariance matrix; ξ is the volume point set; e i is the identity matrix I n The i-th column of . 33) Propagate volume points through the state transition function f(·): in: is the new volume point at time step k+1 obtained by propagating the state transition function; X i,k / k is the volume point at time step k. 34) Predict state mean and the square root of the state covariance S k+1 / k : in: S Q =chol(Q) Where chol represents the Cholesky decomposition function; Tria(·) represents the QR decomposition of the matrix; S q is the Cholesky decomposition of Q; Q is the process noise; is the weight matrix.

5. According to claim 1, the method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and the square root volume Kalman filter is characterized by: In step 4, the measurement update method steps are: 41) Use state mean and the square root of the state covariance S k+1 / k Recalculate volume points: 42) Propagate volume points through the measurement function h(·): Z i,k+1 / k =h(X i,k+1 / k ),i=1,2,...,2n 43) Predict the measured mean from the transformed volume points Innovation covariance square root S zz,k+1 / k and the cross-covariance P xz,k+1 / k : Where: S R is the Cholesky decomposition of R, R is the measurement noise; η k+1 / k is the measurement weight matrix; Z k+1 / k is the new volume point obtained by propagating the measurement function.

6. The method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and square root volumetric Kalman filter according to claim 1, characterized in that: In step 5, the Kalman gain K k+1 for: State Matrix Updated to: The square root of the state covariance S k+1 Updated to: S k+1 =Tria([x k+1 / k -K k+1 or k+1 / k ,K k+1 S R ])。 7. The method for estimating nonlinear aerodynamic damping of a highly flexible structure based on the Sage-Husa algorithm and square root volumetric Kalman filter according to claim 1, characterized in that: In step 6, the noise updating method is: The Sage-Husa estimator is used to update the process noise Q: in: Where: b is the forgetting factor; α1 is the introduced empirical proportional factor; e k+1 is the new information sequence; After the Sage-Husa estimator is used to iteratively update the process noise Q for the preset k times, the data accumulated during the preset k iterations are used to evaluate whether the state space equation parameters have stabilized: If in the current j-th iteration, j>k, if the ratio of the standard deviation to the mean value of the parameter satisfies: Among them: std j represents the standard deviation of the parameters of the jth iteration; mean j represents the average value of the parameters of the jth iteration; std(X j- k: j ) is the standard deviation of the parameters from the current jth iteration to the previous jk iterations; mean(X j- k: j ) is the average parameter value from the current jth to the previous jk iterations; δ is the preset threshold. Then the state space equation parameters have stabilized and the process noise remains unchanged: Q j+1 =Q j Otherwise, it indicates that the state space equation parameters are unstable and the process noise Q is updated as: Among them: α2 is the introduced empirical proportional factor.

8. A highly flexible structural nonlinear aerodynamic damping estimation system based on the Sage-Husa algorithm and square root volumetric Kalman filter, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program and implements a highly flexible structure nonlinear aerodynamic damping estimation method based on the Sage-Husa algorithm and the square root volume Kalman filter as described in any one of claims 1 to 7.

9. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by a processor, implements a highly flexible structural nonlinear aerodynamic damping estimation method based on a Sage-Husa algorithm and a square root volume Kalman filter as described in any one of claims 1 to 7.

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