Efficient and high-precision prediction method for bridge section flutter

Abstract

The invention discloses an efficient and high-precision prediction method for bridge section flutter, and relates to the technical field of bridge wind resistance. The efficient and low-cost prediction method for the flutter characteristics of the bridge section is constructed. Accurate prediction of the flutter characteristic of the section can be realized only by about 1 / 5 of wind tunnel experiment train number of a classic flutter derivative model interpolation prediction method; the method for predicting the flutter characteristics of the section of the bridge is constructed, safer modeling is achieved only by depending on experimental data under low wind speed and subcritical conditions, test sampling is conducted only from experiments before flutter, tiny vibration and even non-vibration, and physical information of unsteady aerodynamic force is extracted; a two-time symbol regression method is utilized to realize a process of firstly reducing dimensions and then modeling, the dimension reduction enables the symbol regression method to reduce the overfitting risk, the robustness of the modeling method is enhanced, and the prediction precision can be improved by one order of magnitude.

Description

Technical Field

[0001] The invention relates to the technical field of bridge wind resistance, and in particular to a high-efficiency and high-precision prediction method for bridge section flutter. Background Art

[0002] The increase in bridge span reduces bridge stiffness and damping, significantly increasing the risk of flutter. Therefore, before flutter or dangerous vibration occurs, it is necessary to quickly and accurately warn of flutter boundaries and amplitudes to assist in engineering structure design.

[0003] The flutter derivative method is the mainstream method for evaluating the unsteady aerodynamic and flutter characteristics of bridges. At present, there are two means of predicting the unsteady aerodynamic and flutter derivatives of bridge sections in the bridge design industry. The first is the numerical simulation method, which has a serious imbalance between efficiency and accuracy by discretely solving the NS equations, and there is no absolutely accurate turbulence model at this stage to meet the engineering accuracy requirements. The second is the wind tunnel test. Although it has high accuracy, the wind tunnel test for the entire bridge and two-dimensional sections is costly and has a long cycle, and it is necessary to repeatedly apply excitation at different wind speeds to collect flutter derivatives. In addition, all current flutter derivative prediction methods rely on data after the critical wind speed (supercritical) of flutter, which greatly increases the risk of experiments and tests. Therefore, it is necessary to develop a method using machine learning, which only uses a small number of experimental data points before the critical wind speed (subcritical) of flutter to achieve safe, low-cost, and efficient flutter prediction of engineering structures. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a high-efficiency and high-precision prediction method for bridge section flutter, which solves the problem of not utilizing machine learning and only using a small number of experimental data points before the critical wind speed of flutter to achieve efficient and high-precision flutter prediction.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: An efficient and high-precision prediction method for bridge section flutter is provided, which comprises the following steps: S1. Based on the wind speed data and frequency data of the bridge section operation, collect the flutter data of the bridge section under the low wind speed subcritical condition; S2, based on the chatter data, construct a chatter single-valued function using the symbolic regression method; S3. Based on the flutter single-valued function, a cross-section flutter prediction model is constructed using the symbolic regression method; S4. Couple the structural motion equations, solve the cross-section flutter prediction model, and obtain the flutter response, i.e. the prediction result.

[0006] Furthermore, the flutter data in step S1 include flutter derivative aerodynamic data of different amplitudes and different wind speeds; the wind speed data are different dimensionless wind speeds in the pre-flutter state; and the frequency data are forced vibration or free response amplitudes.

[0007] Further, step S2 includes the following steps: S2-1, selecting flutter derivative aerodynamic data, wind speed data and frequency data that meet the first screening condition; S2-2, select the initial symbolic expression based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model; S2-3, constructing multiple candidate expressions of candidate association parameters using a symbolic regression method based on the initial symbolic expression, the selected wind speed data, and the selected frequency data; S2-4, taking the candidate correlation parameters as independent variables and the selected flutter derivative aerodynamic data as dependent variables, and constructing the polynomial fitting functions corresponding to each candidate expression by using the polynomial fitting method; S2-5, constructing a dimensionality reduction loss function based on multiple polynomial fitting functions and the selected flutter derivative aerodynamic data, and solving it to obtain the fitness corresponding to each candidate expression; S2-6, based on each fitness, performing inheritance, mutation, and crossover processing on each candidate expression to obtain a processed candidate expression; S2-7. Repeat steps S2-3 to S2-6 until the number of iterations or the accuracy meets the requirements, and filter all processed candidate expressions based on the second filtering condition to obtain the best expression, that is, the chatter single-valued function.

[0008] Furthermore, the first screening condition is: screening flutter derivative aerodynamic data, wind speed data and frequency data that are not less than the overall threshold, less than the amplitude vibration threshold and far away from the corresponding flutter critical point; The second screening condition is to satisfy the minimum dimensionality reduction loss function, that is, to use the expression as the independent variable and the flutter derivative as the dependent variable, so that the flutter derivative is expressed as a single-valued function, and the corresponding expression satisfies the principle of simplicity.

[0009] Furthermore, the cross-section flutter prediction model in step S3 adopts the classic flutter derivative Scanlan model.

[0010] Further, step S3 includes the following steps: S3-1, determining the associated parameters and flutter derivative aerodynamic data corresponding to the flutter single-valued function of step S2; S3-2, based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model, select the initial modeling symbolic expression for flutter derivative modeling; S3-3, based on the initial modeling symbolic expression, the associated parameters of step S3-1 and the flutter derivative aerodynamic data, a modeling candidate expression of the flutter derivative dimensionality reduction space is constructed using a symbolic regression method, that is, an initial cross-section flutter prediction model is constructed; S3-4, calculating the bi-norm error between the calculation result of the flutter derivative prediction model and the flutter derivative training data, that is, calculating the modeling loss function, and obtaining the fitness of the corresponding modeling candidate expression; S3-5, based on each fitness, performing genetic, mutation, and crossover processing on each modeling candidate expression to obtain a processed modeling candidate expression; S3-6. Repeat steps S3-3 to S3-5 until the number of iterations or the accuracy meets the requirements, and filter all processed modeling candidate expressions based on the third filtering condition to obtain the best modeling candidate expression, that is, the cross-section flutter prediction model.

[0011] Furthermore, the third screening condition is to satisfy the minimum modeling loss function, that is, the establishment of the flutter derivative prediction model can have a high prediction accuracy for the training data, and the corresponding expression satisfies the principle of simplicity.

[0012] Furthermore, the formula after coupling the structural motion equation in step S4 with the cross-section flutter prediction model obtained in step S3 is:

[0013] in,, , , denote the torsional vibration angle, angular velocity and angular acceleration respectively, represents the torsional structure damping ratio, represents the circular frequency of the torsion structure, represents the mass moment of inertia, represents the incoming flow density, represents the reduction frequency, , represents the flutter derivatives of the two torsional degrees of freedom, represents the half chord length of the section, Indicates the incoming flow velocity.

[0014] The beneficial effects of the present invention are: 1. The present invention constructs an efficient and low-cost prediction method for the flutter characteristics of bridge sections. It only requires about 1 / 5 of the number of wind tunnel tests of the classic flutter derivative model interpolation prediction method to achieve accurate prediction of the flutter characteristics of the section; 2. The present invention constructs a prediction method for bridge section flutter characteristics that relies only on experimental data at low wind speed and subcritical conditions, achieving safer modeling. The present invention only takes test samples from pre-flutter, small vibration or even no vibration experiments to extract physical information of unsteady aerodynamic forces; 3. The present invention uses the double symbolic regression method to achieve the process of first reducing dimension and then modeling. Dimensionality reduction enables the symbolic regression method to reduce the risk of overfitting, enhance the robustness of the modeling method, and improve the prediction accuracy by an order of magnitude. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a method flow chart; Figure 2 This is a typical cross-section diagram of the Yanji Yangtze River Bridge; Figure 3 is the cross-sectional variable wind speed and amplitude torsional flutter derivative Graphs; Figure 4 is the cross-sectional variable wind speed and amplitude torsional flutter derivative Graphs; Figure 5 for Sampling flutter derivative correlation parameters Dimensionality reduction structure and prediction model prediction result curve graph; Figure 6 for Sampling flutter derivative correlation parameters Dimensionality reduction structure and prediction model prediction result curve graph; Figure 7 for Comparison curve between the prediction results of flutter characteristics under sampling and the prediction of classic flutter derivatives; Figure 8 for Sampling flutter derivative correlation parameters Dimensionality reduction structure and prediction model prediction result diagram; Fig. 9 for Sampling flutter derivative correlation parameters Dimensionality reduction structure and prediction model prediction result curve graph; Fig.10 for Comparison curve between the flutter characteristic prediction results under sampling and the classic flutter derivative prediction. DETAILED DESCRIPTION

[0016] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0017] like Figure 1 As shown, a high-efficiency and high-precision prediction method for bridge section flutter includes the following steps: S1. Based on the wind speed data and frequency data of the bridge section operation, collect the flutter data of the bridge section under the low wind speed subcritical condition; The flutter data in step S1 include flutter derivative aerodynamic data of different amplitudes and different wind speeds , flutter derivative aerodynamic data Including two flutter derivatives of the torsional degree of freedom , And the remaining degrees of freedom are defined according to classical theory; the wind speed data are different dimensionless wind speeds before flutter ; Frequency data is forced vibration or free response amplitude .

[0018] S2, based on the chatter data, construct a chatter single-valued function using the symbolic regression method; Step S2 includes the following steps: S2-1. Select flutter derivative aerodynamic data that meets the first screening condition , wind speed data and frequency data ; The first screening condition is to screen flutter derivative aerodynamic data, wind speed data and frequency data that are not less than the overall threshold, less than the amplitude vibration threshold and far away from the corresponding flutter critical point; among them, the overall threshold needs to be set by considering factors such as whether the data covers all expected operating conditions and environmental variables, whether the corresponding data set is large enough, and whether the data quality is high. It can be set according to the vibration amplitude of the corresponding historical data, and the amplitude vibration threshold can be comprehensively formulated taking into account different working conditions and situations.

[0019] The amplitude and vibration thresholds are formulated according to actual needs. For example, the formulation of comprehensive thresholds needs to consider S2-2, select the initial symbolic expression based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model; S2-3. Based on the initial symbolic expression, the selected wind speed data and the selected frequency data, a symbolic regression method is used to construct multiple candidate expressions of the candidate association parameters. ;in, represents the candidate association parameter, Represents an initial symbolic expression; the expression forms include but are not limited to addition, subtraction, multiplication, division, quadratic and cubic; S2-4, taking the candidate correlation parameters as independent variables and the selected flutter derivative aerodynamic data as dependent variables, the polynomial fitting method is used to construct the polynomial fitting function corresponding to each candidate expression ; S2-5, constructing a dimensionality reduction loss function based on multiple polynomial fitting functions and the selected flutter derivative aerodynamic data, and solving it to obtain the fitness corresponding to each candidate expression; Dimensionality reduction loss function is the two-norm error between the calculation result of the polynomial fitting function and the flutter derivative training data, and the corresponding formula is:

[0020] in, represents the norm 2.

[0021] S2-6, based on each fitness, performing inheritance, mutation, and crossover processing on each candidate expression to obtain a processed candidate expression; S2-7. Repeat steps S2-3 to S2-6 until the number of iterations or the accuracy meets the requirements, and filter all processed candidate expressions based on the second filtering condition to obtain the best expression, that is, the chatter single-valued function.

[0022] The second screening condition is: satisfying the minimum dimensionality reduction loss function, taking the expression as the independent variable and the flutter derivative as the dependent variable, so that the flutter derivative is expressed as a single-valued function, and the corresponding expression satisfies the principle of simplicity.

[0023] S3. Based on the flutter single-valued function, a cross-section flutter prediction model is constructed using the symbolic regression method; The cross-section flutter prediction model in step S3 adopts the classic flutter derivative Scanlan model.

[0024] Step S3 includes the following steps: S3-1. Determine the associated parameters corresponding to the chatter single-valued function of step S2 and flutter derivative aerodynamic data ; S3-2. Select the initial modeling symbolic expression for flutter derivative modeling based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model ;in, Function representing the flutter derivative prediction model; S3-3, based on the initial modeling symbolic expression, the associated parameters of step S3-1 and the flutter derivative aerodynamic data, a modeling candidate expression of the flutter derivative dimensionality reduction space is constructed using a symbolic regression method, that is, an initial cross-section flutter prediction model is constructed; S3-4, calculating the bi-norm error between the calculation result of the flutter derivative prediction model and the flutter derivative training data, that is, calculating the modeling loss function, and obtaining the fitness of the corresponding modeling candidate expression; Modeling loss function The formula is:

[0025] S3-5, based on each fitness, performing genetic, mutation, and crossover processing on each modeling candidate expression to obtain a processed modeling candidate expression; S3-6. Repeat steps S3-3 to S3-5 until the number of iterations or the accuracy meets the requirements, and filter all processed modeling candidate expressions based on the third filtering condition to obtain the best modeling candidate expression, that is, the cross-section flutter prediction model.

[0026] The third screening condition is: the modeling loss function is minimized, that is, the established flutter derivative prediction model can have a high prediction accuracy for the training data, and the corresponding expression meets the principle of simplicity. The principle of simplicity refers to selecting the expression with the simplest expression structure, the least number of parameters, and the lowest computational complexity.

[0027] S4. Couple the structural motion equations, solve the cross-section flutter prediction model, and obtain the flutter response, i.e. the prediction result.

[0028] The formula after coupling the structural motion equation in step S4 with the cross-section flutter prediction model obtained in step S3 is:

[0029] in,, , , denote the torsional vibration angle, angular velocity and angular acceleration respectively, represents the torsional structure damping ratio, represents the circular frequency of the torsion structure, represents the mass moment of inertia, represents the incoming flow density, represents the reduction frequency, represents the half chord length of the section, Indicates the incoming flow velocity, , The flutter derivatives of two torsional degrees of freedom are represented by the established flutter derivative prediction model, and the stable flutter amplitude is obtained by the classical frequency domain solution method.

[0030] In one embodiment of the present invention, Figure 2 As shown in the figure, the flutter derivative of the single degree of freedom torsion of the bridge deck at a certain location is selected for associated parameter identification, and a flutter derivative model is established to predict the flutter characteristics of the section. The method is as follows: Based on the existing torsional flutter derivative wind tunnel test data of the section, and The distribution law of Figure 3 and Figure 4 The flutter derivatives of the wind speed experiment include the wind speed , torsional vibration amplitude .

[0031] collection The flutter derivative under the condition of , and the sampling amplitude is all torsional amplitudes under this wind speed range, which is used to test the flutter prediction ability of this method for building models with different training data.

[0032] Based on the flutter derivatives under the sampled partial wind speeds, the symbolic regression method is used, the dimension reduction projection error is used as the loss function, and the gradient descent optimization algorithm is used to iteratively optimize until the loss function converges to extract and The associated parameters and .like Figure 5 and Figure 6 As shown, using the associated parameters and The flutter derivatives affected by multiple variables are projected and reduced in dimension to a single-valued function.

[0033] Based on the flutter derivative correlation parameters obtained by S2, the symbolic regression method is used to correlate the parameters and is the flutter derivative prediction model with the flutter derivative as the independent variable and the dependent variable. and The modeling is performed with different loss functions for gradient optimization .

[0034] like Figure 7 As shown in the figure, after the optimization converges, the flutter derivative prediction model is obtained, and the model can better extrapolate and predict the flutter derivatives under different wind speeds and amplitudes. The flutter characteristics obtained by the present invention using only a small amount of experimental data for training are in good agreement with the experimental results. However, the classic flutter derivative method will incorrectly predict the flutter characteristics without complete unsteady flutter derivative data, and does not have the modeling capability of small samples and low wind speeds.

[0035] collection The flutter derivative under the condition is tested, and the corresponding results are as follows Figure 8 , Fig. 9 and Fig.10 As shown, This further verifies that the present invention uses small sample modeling of flutter characteristics using associated parameters, which can not only achieve nonlinear dimensionality reduction of high-dimensional state space, but also accurately establish a new flutter derivative model of the bridge section through small samples, greatly reducing the number of samples required for flutter prediction.

[0036] In summary, the present invention constructs an efficient and low-cost prediction method for the flutter characteristics of bridge sections. Only about 1 / 5 of the wind tunnel test trains of the classic flutter derivative model interpolation prediction method are needed to achieve accurate prediction of the flutter characteristics of the section; a prediction method for the flutter characteristics of bridge sections is constructed that relies only on experimental data under low wind speed and subcritical conditions to achieve safer modeling, and only test samples are taken from pre-flutter, small vibration or even no vibration experiments to extract physical information of unsteady aerodynamic forces; the two symbolic regression methods are used to realize the process of first dimensionality reduction and then modeling. Dimensionality reduction enables the symbolic regression method to reduce the risk of overfitting, enhance the robustness of the modeling method, and improve the prediction accuracy by an order of magnitude.

Claims

1. An efficient and high-precision prediction method for bridge section flutter, characterized by: The following steps are involved: S1. Based on the wind speed data and frequency data of the bridge section operation, collect the flutter data of the bridge section under the low wind speed subcritical condition; S2, based on the chatter data, construct a chatter single-valued function using the symbolic regression method; S3. Based on the flutter single-valued function, a cross-section flutter prediction model is constructed using the symbolic regression method; S4. Couple the structural motion equations, solve the cross-section flutter prediction model, and obtain the flutter response, i.e. the prediction result.

2. The efficient and high-precision prediction method for bridge section flutter according to claim 1 is characterized by: The flutter data in step S1 include flutter derivative aerodynamic data of different amplitudes and different wind speeds; the wind speed data are different dimensionless wind speeds in the pre-flutter state; and the frequency data are forced vibration or free response amplitudes.

3. The efficient and high-precision prediction method for bridge section flutter according to claim 2 is characterized by: The step S2 comprises the following steps: S2-1, selecting flutter derivative aerodynamic data, wind speed data and frequency data that meet the first screening condition; S2-2, select the initial symbolic expression based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model; S2-3, constructing multiple candidate expressions of candidate association parameters using a symbolic regression method based on the initial symbolic expression, the selected wind speed data, and the selected frequency data; S2-4, taking the candidate correlation parameters as independent variables and the selected flutter derivative aerodynamic data as dependent variables, and constructing the polynomial fitting functions corresponding to each candidate expression by using the polynomial fitting method; S2-5, constructing a dimensionality reduction loss function based on multiple polynomial fitting functions and the selected flutter derivative aerodynamic data, and solving it to obtain the fitness corresponding to each candidate expression; S2-6, based on each fitness, performing inheritance, mutation, and crossover processing on each candidate expression to obtain a processed candidate expression; S2-7. Repeat steps S2-3 to S2-6 until the number of iterations or the accuracy meets the requirements, and filter all processed candidate expressions based on the second filtering condition to obtain the best expression, that is, the chatter single-valued function.

4. The high-efficiency and high-precision prediction method for bridge section flutter according to claim 3 is characterized by: The first screening condition is: screening flutter derivative aerodynamic data, wind speed data and frequency data that are not less than the overall threshold, less than the amplitude vibration threshold and far away from the corresponding flutter critical point; The second screening condition is: satisfying the minimum dimensionality reduction loss function, that is, taking the expression as the independent variable and the flutter derivative as the dependent variable, so that the flutter derivative is expressed as a single-valued function, and the corresponding expression satisfies the principle of simplicity.

5. The efficient and high-precision prediction method for bridge section flutter according to claim 2 is characterized by: The cross-section flutter prediction model in step S3 adopts the classic flutter derivative Scanlan model.

6. The high-efficiency and high-precision prediction method for bridge section flutter according to claim 5 is characterized by: The step S3 comprises the following steps: S3-1, determining the associated parameters and flutter derivative aerodynamic data corresponding to the flutter single-valued function of step S2; S3-2, based on the principle of simplicity and the Scanlan theory of bridge flutter and the van der Bohr model, select the initial modeling symbolic expression for flutter derivative modeling; S3-3, based on the initial modeling symbolic expression, the associated parameters of step S3-1 and the flutter derivative aerodynamic data, a modeling candidate expression of the flutter derivative dimensionality reduction space is constructed using a symbolic regression method, that is, an initial cross-section flutter prediction model is constructed; S3-4, calculating the bi-norm error between the calculation result of the flutter derivative prediction model and the flutter derivative training data, that is, calculating the modeling loss function, and obtaining the fitness of the corresponding modeling candidate expression; S3-5, based on each fitness, performing genetic, mutation, and crossover processing on each modeling candidate expression to obtain a processed modeling candidate expression; S3-6. Repeat steps S3-3 to S3-5 until the number of iterations or the accuracy meets the requirements, and filter all processed modeling candidate expressions based on the third filtering condition to obtain the best modeling candidate expression, that is, the cross-section flutter prediction model.

7. The high-efficiency and high-precision prediction method for bridge section flutter according to claim 6 is characterized by: The third screening condition is: the modeling loss function is minimized and the corresponding expression satisfies the principle of simplicity.

8. The high-efficiency and high-precision prediction method for bridge section flutter according to claim 2 is characterized by: The formula after coupling the structural motion equation in step S4 with the cross-section flutter prediction model obtained in step S3 is: in, , , denote the torsional vibration angle, angular velocity and angular acceleration respectively, represents the torsional structure damping ratio, represents the circular frequency of the torsion structure, represents the mass moment of inertia, represents the incoming flow density, represents the reduction frequency, , represents the flutter derivatives of the two torsional degrees of freedom, represents the half chord length of the section, Indicates the incoming flow velocity.

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