Method, system and storage medium for identifying aerodynamic derivatives of a bending-torsion coupled motion based on a pressure measurement method

Abstract

This invention discloses a method, system, and storage medium for identifying aerodynamic derivatives in bending-torsional coupled motion based on pressure measurement. The method includes: acquiring wind pressure and displacement time-history signals to extract aerodynamic and displacement characteristic parameters; introducing an approximate assumption about the effective angle of attack to reduce the dimensionality of the eight unknown aerodynamic derivatives in the Scanlan self-excited force model to four independent aerodynamic derivatives; substituting the characteristic parameters into an analytical closed-form formula constructed based on the dynamic equations and trigonometric expansion matching to directly calculate the four independent aerodynamic derivatives; and then substituting back into the approximate assumption to deduce the remaining four aerodynamic derivatives, completing the identification of all eight aerodynamic derivatives. This invention, by introducing physical assumptions to construct a closed-form analytical formula, achieves non-iterative, high-precision direct calculation of aerodynamic derivatives, solving the underdetermined solution problem caused by insufficient information in the pressure measurement method. It boasts high computational efficiency and clear physical meaning of the results.

Description

Technical Field

[0001] This invention belongs to the field of structural wind-resistant engineering and aerodynamics, specifically relating to an analytical identification method, system, and storage medium for the aerodynamic derivatives of the bending-torsional coupled motion of structural cross sections based on pressure measurement. It is particularly suitable for solving the self-excited force parameters and analyzing the fluid-structure interaction mechanism of highly flexible structures under vortex-induced vibration or soft flutter conditions. Background Technology

[0002] Long-span bridges and tall structures are highly susceptible to aerodynamic instability phenomena such as vortex-induced resonance and flutter under wind loads. To accurately analyze the flutter stability and self-excited vibration response of bridges in the frequency domain, the linear self-excited aerodynamic model proposed by Scanlan is widely used in engineering. Considering the coupled vertical and torsional motions of the bridge cross-section, this model includes eight key aerodynamic derivatives (…). , ).

[0003] Currently, the primary method for obtaining these aerodynamic derivatives is wind tunnel testing. Traditional free vibration methods (system identification methods) mainly rely on measuring the displacement response envelope of the structure for inversion, failing to capture the true aerodynamic force distribution acting on the model surface. With the widespread adoption of high-frequency pressure measurement technologies such as electronic scanning valves, researchers can directly measure the unsteady pulsating wind pressure on the structure surface and then integrate it to obtain the self-excited lift and lift moment. However, applying pressure measurement to the aerodynamic derivative identification of two-degree-of-freedom bending-torsional coupled motion presents a fundamental mathematical challenge: the measured self-excited lift and lift moment, after frequency domain extraction, only provide four known physical quantities (lift amplitude, lift phase, lift moment amplitude, and lift moment phase), while the Scanlan self-excited force model contains eight unknown aerodynamic derivatives. This is a classic example of an underdetermined equation solving problem.

[0004] To address this challenge, existing technologies mainly employ the following two approaches.

[0005] (1) Iterative optimization path: usually relies on complex nonlinear optimization search algorithms (such as least squares method) to approximate parameters. Although such methods can solve the problem to a certain extent, they are not only computationally time-consuming, but also prone to getting trapped in local optima due to the multi-peak characteristics of the objective function, resulting in the extraction of aerodynamic derivatives lacking physical rationality.

[0006] (2) Data-driven approach: Identifying aerodynamic equations by constructing machine learning models such as sparse dictionaries or neural networks. Although this approach avoids some of the defects of traditional optimization, its "black box" nature leads to poor physical interpretability of the results, and the model's generalization ability and dependence on training data are strong, making it difficult to guarantee the stability of identification under different working conditions.

[0007] In summary, existing technologies have failed to fundamentally overcome the "underdetermined" problem in addressing the identification of bending-torsional coupling aerodynamic derivatives under pressure measurement. Neither iterative numerical optimization methods nor data-driven machine learning methods can achieve analytical identification with clear physical meaning without iteration. Therefore, there is an urgent need for an analytical identification method that can fundamentally solve this underdetermined problem, eliminate iterative search, and provide clear physical meaning. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide an analytical identification method, system and storage medium for the aerodynamic derivatives of the bending-torsional coupling motion of structural cross sections based on the pressure measurement method. By introducing the effective angle of attack assumption to establish a closed analytical derivation system, the non-iterative and high-precision direct calculation of aerodynamic derivatives is realized, providing an efficient parameter identification means for structural wind engineering.

[0009] To achieve the above objectives, the present invention provides the following technical solution: This invention first proposes an analytical identification method for the aerodynamic derivatives of the bending-torsional coupling motion of a structural cross-section based on pressure measurement, comprising the following steps: Step 1: Collect surface wind pressure time history signals and structural vibration displacement time history signals of the structural cross-section; Step 2: Integrate the surface wind pressure time history signal to obtain the self-excited lift time history and the self-excited lift moment time history. Then, extract features from the self-excited lift time history, the self-excited lift moment time history, and the structural vibration displacement time history signals to obtain aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state. The aerodynamic characteristic parameters include the lift coefficient amplitude, lift phase, lift moment coefficient amplitude, and lift moment phase. The displacement characteristic parameters include torsional amplitude, vertical amplitude, phase difference between vertical and torsional motion, and vibration circular frequency. Step 3: Introduce approximate assumptions about aerodynamic derivatives based on effective angle of attack to reduce the dimensionality of the 8 unknown aerodynamic derivatives in the Scanlan self-excited force model to 4 independent aerodynamic derivatives to be determined; Step 4: Substitute the aerodynamic characteristic parameters and displacement characteristic parameters extracted in Step 2 into the analytical closed formula constructed based on the matching principle of structural dynamics equations and trigonometric series expansion to directly calculate the four independent aerodynamic derivatives. Step 5: Substitute the 4 independent aerodynamic derivatives obtained in Step 4 back into the aerodynamic derivative approximation relationship, and reverse-engineer the remaining 4 aerodynamic derivatives to complete the identification of all 8 aerodynamic derivatives of the structural section under bending-torsional coupled motion.

[0010] Furthermore, in step two, the self-excited lift time history and self-excited lift moment time history Represented as: The lift coefficient time history was obtained after dimensionless processing. and lift moment coefficient time history : in: For the structural surface, the first Zero-mean pulsating pressure at each pressure measurement point; For the first The representative length of each pressure measurement point along the perimeter of the cross section; For the first The distance of each pressure measurement point from the center of the cross section; air density; The width of the structural cross-section; This refers to wind speed.

[0011] Furthermore, in step two, the aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state are obtained, including: Torsional displacement and speed time history Represented as: Vertical displacement and speed time history Represented as: in: and These are the torsional amplitude and the vertical amplitude, respectively. This represents the phase difference between the vertical and torsional motions. It is the angular frequency of vibration; The fundamental frequency component that resonates with the structural vibration is extracted through frequency domain analysis, and the lift coefficient time history is analyzed. and lift moment coefficient time history Represented as: in: and These are the magnitudes of the lift coefficient and the lift moment coefficient, respectively. and These are the lift phase and the lift torque phase, respectively. It is the angular frequency of vibration.

[0012] Furthermore, in step three, the approximate assumption of the aerodynamic derivative relationship is as follows: The Scanlan self-excited force model is expressed as follows: in: , , , , , , and It is the aerodynamic derivative; , is the width of the structural cross section Half of; To reduce the frequency; It is the angular frequency of vibration; air density; The width of the structural cross-section; Wind speed; and These are the time histoscopic displacement and velocity time histories, respectively. and The time histories are vertical displacement and velocity, respectively.

[0013] Furthermore, in step four, the analytical closure formula is calculated. , , and The four independent aerodynamic derivatives are expressed as: in: It is the amplitude ratio; and These are the torsional amplitude and the vertical amplitude, respectively. and These are the magnitudes of the lift coefficient and the lift moment coefficient, respectively. This represents the phase difference between the vertical and torsional motions. This is the phase of the lift torque.

[0014] Furthermore, in step five, the remaining four aerodynamic derivatives are derived by reverse calculation: in: This is the lift phase.

[0015] This invention also proposes a structural cross-section bending-torsional coupling motion aerodynamic derivative analysis and identification system based on pressure measurement method, including a memory, a processor, and a computer program stored in the memory and run on the processor. When the processor executes the computer program, it implements the bending-torsional coupling motion aerodynamic derivative identification method based on pressure measurement method as described above.

[0016] The present invention also proposes a storage medium storing a computer program, which, when executed by a processor, implements the above-described method for identifying aerodynamic derivatives of bending-torsional coupling motion based on pressure measurement.

[0017] The beneficial effects of this invention are as follows: This invention presents an analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on the pressure measurement method. By introducing the effective angle of attack approximation assumption, it reduces the eight unknown aerodynamic derivatives in the traditional Scanlan model to four independent aerodynamic derivatives, thus mathematically solving the underdetermined solution problem caused by insufficient information in the pressure measurement method. Building upon this, the method further establishes a set of analytical closed-form formulas based on the structural dynamics equations and the matching principle of trigonometric expansion, which can directly calculate the reduced aerodynamic derivatives. All eight derivatives are then derived by substituting the approximate relationships in reverse. This invention achieves non-iterative, direct analytical solution of aerodynamic derivatives, completely avoiding the problems of traditional nonlinear optimization algorithms, such as getting trapped in local optima, computational time consumption, and lack of physical meaning in the results. Compared with existing technologies, this invention has significant advantages in computational efficiency, identification accuracy, and physical interpretability, providing an efficient and reliable parameter identification method for wind-resistant structural engineering. This invention can be directly disassembled and applied to different pressure measurement holes on the cross-section surface to conduct a detailed study on the spatial contribution distribution of the upper and lower surfaces of the cross-section and the windward side to the overall aerodynamic derivatives (aerodynamic damping, aerodynamic stiffness), providing an extremely powerful analytical tool for the optimized design of the aerodynamic shape of the structure. Attached Figure Description

[0018] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a schematic diagram of the cross-sectional structure of an example bridge; Figure 2 This is a flowchart of the aerodynamic derivative identification method for bending-torsional coupling motion based on pressure measurement according to the present invention; Figure 3 The vibration displacement time history signals of the bridge structure measured in wind tunnel tests; (a) vertical displacement; (b) torsional displacement; Figure 4Time history diagrams of aerodynamic coefficients of bridge structures obtained by pressure measurement method; (a) time history of lift coefficient; (b) time history of lift moment coefficient; Figure 5 Comparison diagrams of aerodynamic hysteresis loops reconstructed by back-calculation of the obtained aerodynamic derivatives: (a) Lift hysteresis loop under vertical motion; (b) Lift torque hysteresis loop under vertical motion; (c) Lift hysteresis loop under torsional motion; (d) Lift torque hysteresis loop under torsional motion. Detailed Implementation

[0019] 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.

[0020] In this embodiment, a proposed aerodynamic derivative identification method based on pressure measurement for bending-torsional coupled motion is applied. The aerodynamic derivatives are identified based on the surface wind pressure time history signal and the structural vibration displacement time history signal measured in a wind tunnel test of the bridge structure. Specifically, the bridge model cross-section used is as follows: Figure 1 As shown, the bridge model is a double box girder structure with a cross-sectional width of 569 mm, a height of 49.5 mm, and a length of 2096 mm. Multiple pressure measuring holes are arranged along the cross-section for obtaining wind pressure time history.

[0021] like Figure 2 As shown in the flowchart, this embodiment of the aerodynamic derivative identification method for bending-torsional coupling motion based on pressure measurement includes the following steps.

[0022] Step 1: Collect surface wind pressure time history signals and structural vibration displacement time history signals of the structural cross section through wind tunnel tests, that is, obtain the surface self-excited aerodynamic time history signals and the corresponding structural dynamic displacement time history signals when the structure undergoes bending-torsional coupled motion.

[0023] Step 2: Integrate the surface wind pressure time history signal to obtain the self-excited lift time history and the self-excited lift moment time history. Then, extract features from the self-excited lift time history, the self-excited lift moment time history, and the structural vibration displacement time history signals to obtain aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state. The aerodynamic characteristic parameters include the lift coefficient amplitude, lift phase, lift moment coefficient amplitude, and lift moment phase. The displacement characteristic parameters include torsional amplitude, vertical amplitude, phase difference between vertical and torsional motion, and vibration circular frequency.

[0024] Specifically, in this embodiment, a torsional vortex-induced vibration with coupled vertical vibration at a wind speed of 4.57 m / s and an angle of attack of 0 degrees is used as an example. Aerodynamic information is used to identify the aerodynamic derivative. A pressure measuring valve is pre-embedded inside the model to measure the surface wind pressure time history signal. Vertical and torsional displacement data are collected outside the model using a laser displacement meter. Figure 3This represents the vibration displacement time history signal of the bridge structure measured in a wind tunnel test. Figure 3 (a) is the time history diagram of vertical displacement. Figure 3 (b) is the time history diagram of torsional displacement. This was achieved by measuring the zero-mean pulsating pressure at various pressure measurement points on the structural surface. Combined with the first The representative length of each pressure measurement point along the perimeter of the cross section. and its distance from the center of the cross section The self-excited lift time history is obtained through integration. and self-excited lift moment time history The lift coefficient time history was then obtained after dimensionless processing. and lift moment coefficient time history .

[0025] Specifically, the self-excited lift time history and self-excited lift moment time history Represented as: The lift coefficient time history was obtained after dimensionless processing. and lift moment coefficient time history : in: For the structural surface, the first Zero-mean pulsating pressure at each pressure measurement point; For the first The representative length of each pressure measurement point along the perimeter of the cross section; For the first The distance of each pressure measurement point from the center of the cross section; air density; The width of the structural cross-section; For wind speed. Specifically, such as... Figure 4 As shown in (a), the black line represents the measured lift coefficient time history, as... Figure 4 As shown in (b), the black line represents the time history of the lift torque coefficient. It can be seen that both lift and lift torque have a frequency doubling effect, which causes the time history to fluctuate greatly.

[0026] In this embodiment, feature extraction is performed on the self-excited lift time history, self-excited lift moment time history, and structural vibration displacement time history signals to obtain aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state.

[0027] Specifically, torsional displacement and speed time history Represented as: Furthermore, the vertical displacement and speed time history Represented as: in: and These are the torsional amplitude and the vertical amplitude, respectively. This represents the phase difference between the vertical and torsional motions. The angular frequency of vibration. In this embodiment, the phase difference between the vertical and torsional displacement data measured in the wind tunnel test is... 21.1°. At this wind speed, the vibration exhibits a torsional mode branch of bending-torsional coupling vibration. The vibration frequency is 1.583 Hz. Vertical amplitude... 5.494×10 -3 The vertical structure damping ratio is 0.20%; Torsional amplitude 1.74°, torsional damping ratio is 2.04%.

[0028] Frequency domain analysis is used to extract the fundamental frequency component that resonates with the structural vibration. Specifically, by performing frequency domain analysis on the measured self-excited aerodynamic time history, higher harmonics can be effectively filtered out, thus extracting the fundamental frequency component that resonates with the structural vibration. Further analysis of the lift coefficient time history... and lift moment coefficient time history Represented as: in: and These are the magnitudes of the lift coefficient and the lift moment coefficient, respectively. and These are the lift phase and the lift torque phase, respectively. It is the angular frequency of vibration.

[0029] In this embodiment, aerodynamic coefficients and displacement time history signals that are absolutely aligned in time can be obtained through pre-synchronization processing (e.g., phase difference correction methods), thereby obtaining... and In this embodiment, the phase of the self-excited force is corrected using lift torque and torsional displacement to obtain... 5.075×10 -3 ; 42.8° 5.164×10 -2 ; 200.5°.

[0030] The following formula can be used to effectively suppress high-order harmonic interference and extract the target's motion frequency components from measured data: in: and These are aerodynamic coefficients based on measured data, which include higher harmonic components; = ; = ; The number of cycles.

[0031] like Figure 4 As shown, the red line represents the time history of the lift coefficient and lift moment coefficient, which are extracted from the motion frequency by filtering out high-order harmonic interference. It can be seen that after extracting the components with the same frequency as the motion, the high-frequency sawtooth fluctuations in the aerodynamic time history signal are filtered out, the curve is smoother, and the low-frequency response characteristics of the structure are clearly displayed.

[0032] Step 3: Introduce the approximate assumption relationship of aerodynamic derivative based on effective angle of attack, and reduce the dimensionality of the 8 unknown aerodynamic derivatives in the Scanlan self-excited force model to 4 independent aerodynamic derivatives to be determined.

[0033] Specifically, addressing the underdetermined solution problem caused by the Scanlan self-excited force model containing eight unknown aerodynamic derivatives while measured aerodynamic forces only provide four known quantities, an approximate assumption based on the effective angle of attack is introduced to reduce the eight unknown aerodynamic derivatives to four independent aerodynamic derivatives to be solved. Scanlan proposed using aerodynamic derivatives to express two-degree-of-freedom linear self-excited forces, assuming that the aerodynamic derivatives are only related to the geometry of the cross-section and the reduced frequency. Self-excited lift per unit length. (Downward is positive) and lift torque (Upward is positive) is expressed as: in: , It is the aerodynamic derivative; ; For the reduced frequency.

[0034] As shown in the above equation, the Scanlan self-excited force model includes eight aerodynamic derivatives, namely... and 1, 2, 3, 4 To determine these aerodynamic derivatives, this embodiment uses an approximate relationship between the aerodynamic derivatives proposed by Matsumoto et al., based on the effective angle of attack of vertical and torsional vibrations: The Scanlan self-excited force model can be simplified as follows: in: , , , , , , and It is the aerodynamic derivative; , is the width of the structural cross section Half of; To reduce the frequency; It is the angular frequency of vibration; air density; The width of the structural cross-section; Wind speed; and These are the time histoscopic displacement and velocity time histories, respectively. and The time histories are vertical displacement and velocity, respectively.

[0035] At this point, the 8 unknown aerodynamic derivatives are reduced to 4 independent aerodynamic derivatives to be determined.

[0036] Step 4: Substitute the aerodynamic characteristic parameters and displacement characteristic parameters extracted in Step 2 into the analytical closed formula constructed based on the matching principle of structural dynamics equations and trigonometric series expansion to directly calculate the four independent aerodynamic derivatives.

[0037] Substituting the displacement and velocity time histories into the Scanlan self-excited force model, which includes the above approximation, and using the sine and cosine terms of trigonometric functions, the relationship with... In-phase aerodynamic stiffness terms and In-phase aerodynamic damping term; then, the measured self-excited aerodynamic force expression form. The coefficients are strictly aligned with those of the same term in the theoretical model. Specifically, the vertical displacement... and torsional displacement and the expression for velocity and Substituting into the simplified Scanlan self-excited force model, we get: in: It represents the amplitude ratio.

[0038] Substituting the above equation into the equation: have to: According to the principle of physical uniqueness, the trigonometric function coefficients corresponding to the theoretical equations and the experimental equations must be strictly equal, thus establishing the core set of equations. coefficients and sum The coefficients need to be aligned. For lift, we can obtain: Regarding the lifting torque, we can obtain: This allows us to obtain the aerodynamic derivative: Substituting the values ​​of each parameter into the formula yields the aerodynamic derivative values. , , , .

[0039] Step 5: Substitute the 4 independent aerodynamic derivatives obtained in Step 4 back into the aerodynamic derivative approximation relationship, and reverse-engineer the remaining 4 aerodynamic derivatives to complete the identification of all 8 aerodynamic derivatives of the structural section under bending-torsional coupled motion.

[0040] The identified , , and Substituting the approximate relationship between the aerodynamic derivatives, we can obtain: achievable , Therefore, the aerodynamic derivative can be obtained from the self-excited aerodynamic coefficients and the amplitude and phase of the displacement. , .

[0041] To differentiate between the use of aerodynamic and displacement information to identify aerodynamic derivatives, this embodiment uses the "Aerodynamic Method," while the closed-loop solution using displacement information is named the "Vibration Method." The aerodynamic derivatives obtained by both methods are listed in Table 1. The results show that only... There are differences, but the remaining aerodynamic derivatives are very similar. The error originates from the approximate relationship between aerodynamic derivatives: It is not strictly true.

[0042] Table 1. Aerodynamic derivatives obtained by the two methods Using the obtained aerodynamic derivatives, the lift and lift moment caused by vertical and torsional motion can be calculated according to the Scanlan self-excited force model, such as... Figure 5 As shown. For aerodynamic forces and displacements of a single frequency, the aerodynamic hysteresis loop is a standard ellipse when a phase difference exists; otherwise, it is a line segment. The presence of a phase difference between aerodynamic forces and displacements is also known as the hysteresis effect. When the aerodynamic force phase leads the displacement [0° 90°], the direction of the major axis of the hysteresis loop ellipse is located in the first and third quadrants; when the aerodynamic force phase leads the displacement [90° 180°], the direction of the major axis of the hysteresis loop ellipse is located in the second and fourth quadrants. Figure 5 The results show that the lift moments calculated by the two methods agree well; however, the lift hysteresis loop identified using the aerodynamic method has a phase difference with the result from the vibration method, resulting in a 2.02% error in the lift amplitude. The lift phase error identified by the aerodynamic method mainly originates from... ,right The calculation error will cause the phase difference error in the back calculation of lift.

[0043] This embodiment overcomes the mathematical underdeterminacy problem under bending-torsional coupling. Addressing the bottleneck of traditional pressure measurement methods, which can only provide four aerodynamic knowns and cannot solve for eight aerodynamic derivatives, this embodiment creatively introduces an effective angle-of-attack approximation relationship for parameter dimensionality reduction. This successfully transforms complex statically indeterminate / underdetermined systems into solvable algebraic systems, removing obstacles from the theoretical level. It achieves a completely closed-loop analytical derivation and solution, eliminating local optima: it derives and constructs a solution containing… , , and This embodiment presents a complete set of analytical closed-form formulas. Compared with traditional system identification methods or nonlinear optimization search algorithms, the core of this embodiment lies in balancing coefficients through strict trigonometric expansion. This method eliminates the need to guess initial values ​​and cumbersome iterative processes, resulting in an exponential increase in computational speed. Furthermore, it fundamentally eliminates the risk of the algorithm getting trapped in local optima, and the calculation results exhibit extremely high mathematical stability and physical definiteness. Moreover, this formula system can be directly decomposed and applied to different pressure measurement holes on the cross-sectional surface for refined study of the spatial contribution distribution of the upper and lower surfaces of the cross-section and the windward side to the overall aerodynamic derivatives (aerodynamic damping, aerodynamic stiffness), providing an extremely powerful analytical tool for the optimized design of structural aerodynamic shapes.

[0044] This embodiment also proposes a structural cross-section bending-torsional coupling motion aerodynamic derivative analysis and identification system based on pressure measurement method, including a memory, a processor, and a computer program stored in the memory and run on the processor. When the processor executes the computer program, it implements the bending-torsional coupling motion aerodynamic derivative identification method based on pressure measurement method as described in this embodiment.

[0045] This embodiment also proposes a storage medium storing a computer program, which, when executed by a processor, implements the bending-torsional coupling motion aerodynamic derivative identification method based on pressure measurement as described in this embodiment.

[0046] 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 method for analytical identification of aerodynamic derivatives of bending-torsional coupled motion of structural cross sections based on pressure measurement, characterized in that: Includes the following steps: Step 1: Collect surface wind pressure time history signals and structural vibration displacement time history signals of the structural cross-section; Step 2: Integrate the surface wind pressure time history signal to obtain the self-excited lift time history and the self-excited lift moment time history. Then, extract features from the self-excited lift time history, the self-excited lift moment time history, and the structural vibration displacement time history signals to obtain aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state. The aerodynamic characteristic parameters include the lift coefficient amplitude, lift phase, lift moment coefficient amplitude, and lift moment phase. The displacement characteristic parameters include torsional amplitude, vertical amplitude, phase difference between vertical and torsional motion, and vibration circular frequency. Step 3: Introduce approximate assumptions about aerodynamic derivatives based on effective angle of attack to reduce the dimensionality of the 8 unknown aerodynamic derivatives in the Scanlan self-excited force model to 4 independent aerodynamic derivatives to be determined; Step 4: Substitute the aerodynamic characteristic parameters and displacement characteristic parameters extracted in Step 2 into the analytical closed formula constructed based on the matching principle of structural dynamics equations and trigonometric series expansion to directly calculate the four independent aerodynamic derivatives. Step 5: Substitute the 4 independent aerodynamic derivatives obtained in Step 4 back into the aerodynamic derivative approximation relationship, and reverse-engineer the remaining 4 aerodynamic derivatives to complete the identification of all 8 aerodynamic derivatives of the structural section under bending-torsional coupled motion.

2. The analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement method according to claim 1, characterized in that: In step two, the self-excited lift time history and self-excited lift moment time history Represented as: The lift coefficient time history was obtained after dimensionless processing. and lift moment coefficient time history : in: For the structural surface, the first Zero-mean pulsating pressure at each pressure measurement point; For the first The representative length of each pressure measurement point along the perimeter of the cross section; For the first The distance of each pressure measurement point from the center of the cross section; air density; The width of the structural cross-section; This refers to wind speed.

3. The analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement method according to claim 1, characterized in that: In step two, the aerodynamic characteristic parameters and displacement characteristic parameters under the fundamental frequency state are obtained, including: Torsional displacement and speed time history Represented as: Vertical displacement and speed time history Represented as: in: and These are the torsional amplitude and the vertical amplitude, respectively. This represents the phase difference between the vertical and torsional motions. It is the angular frequency of vibration; The fundamental frequency component that resonates with the structural vibration is extracted through frequency domain analysis, and the lift coefficient time history is analyzed. and lift moment coefficient time history Represented as: in: and These are the magnitudes of the lift coefficient and the lift moment coefficient, respectively. and These are the lift phase and the lift torque phase, respectively. It is the angular frequency of vibration.

4. The analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement method according to claim 1, characterized in that: In step three, the approximate assumption of the aerodynamic derivative relationship is as follows: The Scanlan self-excited force model is expressed as follows: in: , , , , , , and It is the aerodynamic derivative; , is the width of the structural cross section Half of; To reduce the frequency; It is the angular frequency of vibration; air density; The width of the structural cross-section; Wind speed; and These are the time histoscopic displacement and velocity time histories, respectively. and The time histories are vertical displacement and velocity, respectively.

5. The analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement method according to claim 4, characterized in that: In step four, the analytical closure formula is calculated. , , and The four independent aerodynamic derivatives are expressed as: in: It is the amplitude ratio; and These are the torsional amplitude and the vertical amplitude, respectively. and These are the magnitudes of the lift coefficient and the lift moment coefficient, respectively. This represents the phase difference between the vertical and torsional motions. This is the phase of the lift torque.

6. The analytical identification method for aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement method according to claim 5, characterized in that: In step five, the remaining four aerodynamic derivatives are calculated by reverse derivation: in: This is the lift phase.

7. A system for analytical identification of aerodynamic derivatives of structural cross-section bending-torsional coupling motion based on pressure measurement, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the bending-torsional coupling motion aerodynamic derivative identification method based on pressure measurement 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 method for identifying aerodynamic derivatives of bending-torsional coupling motion based on pressure measurement as described in any one of claims 1-6.

Images