Probabilistic Prediction Method for Typhoon Effects on Long-Span Bridges Driven by Physics-Data Collaboration
Through the physical-data collaboration-driven method, combined with bridge health monitoring data and integrated learning, the accuracy and interpretability problems of existing typhoon effect prediction are solved, efficient probability prediction and uncertainty quantification of typhoon effect of large-span bridges are realized, and the early warning capability of bridge wind engineering is improved.
Patent Information
- Application Number
- CN202510682584.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-26
- Publication Date
- 2025-08-01
- Estimated Expiration
- 2045-05-26
AI Technical Summary
The existing typhoon effect prediction methods have limited prediction accuracy, difficulty in quantifying uncertainty, unstable prediction performance and lack of interpretability, resulting in insufficient early warning technology in bridge wind engineering.
The physical-data synergistically driven method is adopted, combined with bridge structure health monitoring data, and a multi-agent model is constructed. Through integrated learning and interpretability methods, the probability of typhoon effect of large-span bridges is predicted. The bridge wind vibration equation and data-driven loss terms are used to achieve synchronous output of response mean and variance, and the feature contribution is analyzed through the improved Shapley additive interpretation method.
The prediction accuracy and uncertain quantification performance of vibration response of large-span bridges under the action of typhoons are improved, the interpretability and stability of the model are enhanced, and more comprehensive wind disaster prevention information is provided.
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Figure CN120217900B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of bridge wind engineering. By combining integrated learning and interpretability methods, real-time intelligent prediction of wind-induced vibration responses of long-span bridges with the integration of physics and data is carried out. Specifically, it relates to a physical-data collaborative-driven probabilistic prediction method for typhoon effects on long-span bridges. Background Art
[0002] Long-span bridges exhibit strong wind sensitivity due to their flexibility and slenderness. Especially for long bridges spanning mountains, valleys, rivers, lakes and seas, strong / typhoon events can endanger structural stability, thereby increasing the risk of wind-induced disasters and traffic accidents. However, the management and operation and maintenance of bridges under extreme weather conditions still largely depend on the subjective experience of maintenance personnel, and effective early warning technologies have not been fully developed. Accurately predicting wind-induced responses helps to take reasonable intervention measures in a timely manner to ensure the wind resistance safety of bridges and the stability of their service states.
[0003] Data-driven methods have opened up a new way for the intelligent prediction of typhoon effects on bridges. Especially for algorithms based on machine learning and deep learning, they only capture the non-linear mapping between inputs and outputs from a data perspective, effectively avoiding complex geometric modeling. Currently, structural health monitoring systems have been deployed on many long-span bridges, and through the collaborative acquisition of measured data by multiple devices, a reliable platform for the intelligent perception of typhoon effects is provided. However, some problems still emerge in the process of practice: data-driven models usually only rely on training datasets to learn the inline laws of wind-induced vibrations, so predictions beyond the dataset may be doubtful; most practices only focus on deterministic predictions, that is, generating single-value outputs for each independent sample point, and the uncertainty of predictions is not fully considered; when the training samples are insufficient, single models often have problems such as overfitting, resulting in unstable prediction performance and poor robustness; due to the black-box nature of the models, data-driven methods have limitations in prediction scenarios that emphasize high interpretability.
[0004] In recent years, physics-data collaborative driving has become increasingly attractive. Among them, physical laws and equations are regarded as prior knowledge and integrated into the surrogate model to guide the training and prediction processes. On this basis, the model architecture is further appropriately adjusted to achieve the synchronous output of the response mean and variance, so as to adapt to prediction uncertainty. To further enhance the physics-data fusion performance, the ensemble learning strategy integrally combines multiple surrogate models with random initializations, which has remarkable effects in improving the stability and robustness of probability prediction. Explainable artificial intelligence helps to understand why the model produces specific prediction behaviors by quantitatively visualizing the feature contributions, thus cultivating trust in the model. However, the above methods have not yet formed a systematic analysis framework in the field of bridge wind engineering. Therefore, it is urgent to carry out the probability prediction of typhoon effects on long-span bridges from the perspective of physics-data collaborative driving based on ensemble learning and explainable methods to improve the effectiveness and reliability of prediction results. Summary of the Invention
[0005] Technical Problem: Aiming at the problems of limited prediction accuracy, difficulty in quantifying uncertainty, unstable prediction performance, and lack of interpretability in existing typhoon effect prediction methods, the present invention proposes a physics-data collaborative driving-based probability prediction method for typhoon effects on long-span bridges, so as to effectively improve the prediction accuracy of the vibration response of long-span bridges under typhoon action and the uncertainty quantification performance, and at the same time take into account the marginal contribution analysis of feature variables to the prediction results to enhance the interpretability of the model.
[0006] Technical Solution: The present invention is a physics-data collaborative driving-based probability prediction method for typhoon effects on long-span bridges, and the method includes the following steps:
[0007] S1. Obtain the typhoon and its effect monitoring data recorded by the long-span bridge structural health monitoring system, and calculate the typhoon characteristic parameters and the bridge vibration response parameters;
[0008] S2. Use the typhoon characteristic parameters calculated in step S1 as the model input and the bridge vibration response parameters as the model output to construct a sample set, and divide the sample sets of multiple typhoons and their effects into a training set and a test set;
[0009] S3. Adopt a physics-data collaborative driving-based deep ensemble strategy to adjust the scalable neural network architecture to construct a typhoon effect probability prediction model that provides dynamic estimates of the response mean and variance;
[0010] S4. Based on the training set and test set divided in step S2 and the probability prediction model established in step S3, carry out model training and response prediction;
[0011] S5. Adopt an improved Shapley additive explanation method to carry out the interpretation analysis of the probability prediction model, and clarify the marginal contributions of each feature variable and its substantial impact on the final prediction result.
[0012] Among them,
[0013] In step S1, typhoon and its effect monitoring data are obtained based on an anemometer and an accelerometer at the mid-span position of the main girder; typhoon characteristic parameters include average wind speed, wind direction angle, turbulence intensity, turbulence standard deviation, turbulence integral scale, and gust factor; bridge vibration response parameters include vertical acceleration and torsional acceleration.
[0014] In step S2, the total number of the sample sets of typhoon and its effects is not less than 10, the test set contains 2 independent sample sets of typhoon and its effects, and the remaining sample sets are used as the training set.
[0015] In step S3, a physics-data co-driven deep integration strategy is adopted to adjust the scalable neural network architecture. The specific steps are as follows:
[0016] S31. The scoring rule is used as the training criterion. For a model with an input of X , an output of Y , and hyperparameters of , let its predicted distribution be , the true distribution be , and the ideal scoring rule is written as:
[0017] (1)
[0018] In the formula, is the scoring function; represents the performance score of the predicted distribution under the true distribution ; represents the theoretical optimal score of predicting the true distribution itself; when and only when , ; when maximizing the likelihood, the scoring rule that satisfies the Gibbs inequality is expressed as:
[0019] (2)
[0020] In the physics-data co-driven method, the loss function of the surrogate model needs to consider the physics-informed loss term and the data-driven loss term ; for the physics-informed loss term , the bridge wind-induced vibration equation is used as the control condition:
[0021] (3)
[0022] In the formula, M , C , Krepresent the mass, damping, and stiffness matrices respectively; ü ( x , t ), , u ( x , t ) represent the acceleration, velocity, and displacement vectors in the spatial coordinate x and time scale t respectively; F aero ( x , t ) represents the external wind load vector, which consists of the aerodynamic lift F L (t), aerodynamic drag F D (t), and aerodynamic torque F M (t). They can be expressed separately during bridge buffeting as follows:
[0023] (4)
[0024] (5)
[0025] (6)
[0026] In the formula, ρ is the air density; U ( t ) is the incoming flow wind speed; B is the width of the main girder; H is the height of the main girder; α ( t ) is the effective wind attack angle of the main girder section; C L α ( t )], C D α ( t )], C M α ( t )] are the lift coefficient, drag coefficient, and torque coefficient respectively; C L ’ α ( t )], C D ’ α ( t )], C M ’ α ( t ) are respectively the first-order derivatives of the lift coefficient, drag coefficient, and torque coefficient with respect to the wind attack angle; χ L , χ L ’ , χ D , χ D ’ , χ M , χ M ’ are the aerodynamic admittance functions; h ( t ) and v ( t ) are respectively the along-wind and vertical non-stationary fluctuating wind speeds;
[0027] On this basis, the bridge acceleration response is further expressed as:
[0028] (7)
[0029] (8)
[0030] (9)
[0031] In the formula, and respectively represent the vertical acceleration components on the left and right sides of the main girder; and respectively represent the vertical acceleration and torsional acceleration;
[0032] Accordingly, the physics-informed loss term is expressed as:
[0033] (10)
[0034] In the formula, Y v and Y t respectively represent the vertical acceleration and torsional acceleration predicted by the model output; β 1 and β 2 respectively represent the weights of the vertical acceleration residual term and the torsional acceleration residual term;
[0035] For the data-driven loss term , the Gaussian negative log-likelihood is introduced to simultaneously obtain the mean value Sum of variances , to adapt to the uncertainty of prediction:
[0036] (11)
[0037] Final loss function Consists of the above two loss terms:
[0038] (12)
[0039] In the formula, and are the weights of the physics-informed loss term and the data-driven loss term respectively; the goal of model training is to minimize the loss function ;
[0040] S33. Apply adversarial training to smooth the prediction distribution. Add adversarial perturbations in the gradient direction that may increase the loss based on the fast gradient sign method to generate pseudo-samples similar to the real samples to enhance the original dataset. This process is written as:
[0041] (13)
[0042] In the formula, X p is the generated adversarial sample; ξ is a small value to keep the maximum norm of the perturbation bounded; sign is to take the sign of the gradient; represents the gradient of the loss function in the input space;
[0043] S34. In the deep ensemble system, introduce a uniform weighted mixing strategy to approximate the Gaussian distribution. On this basis, multiple groups of predictions are integrated as:
[0044] (14)
[0045] The final output result based on ensemble learning is expressed as:
[0046] (15)
[0047] (16)
[0048] In the formula, is the uniform weighted distribution function; N and i represent the total number of models and the model number of ensemble learning respectively; is the i th prediction distribution of the model; is the i th hyperparameter of the model; and respectively represent the mean and variance of the i th model; and respectively correspond to the mean and variance of the final prediction.
[0049] In step S4, an annealing search is used to obtain a local optimal setting of the model hyperparameters, and then the Bayesian algorithm is applied to update the prior distribution to identify the global optimal setting.
[0050] In step S5, when calculating the marginal contribution of the feature variables using the improved Shapley additive explanation method, the feature interaction effect is considered, and the specific calculation method is as follows:
[0051] (17)
[0052] (18)
[0053] In the formula, r and s represent different feature terms; P and Q are respectively the finite set excluding the analyzed feature and the complete set including all features; is the predictor; is the Shapley value considering the interaction effect of features r and s ; is the Shapley value considering all combinations of the interaction effect of feature r with other feature variables; is the base value; q is the order of the combination;
[0054] The substantial impact of each feature variable on the final prediction result is quantified as follows:
[0055] (19)
[0056] (20)
[0057] In the formula, and are respectively the average absolute Shapley value of feature r and its corresponding contribution ratio; p is the number of features.
[0058] Beneficial effects: Compared with the prior art, the present invention has the following advantages:
[0059] (1) Different from pure data-driven methods, physics-data co-driven integrates physical laws and equations as prior knowledge into the surrogate model to guide model training and response prediction, effectively improving the rationality and accuracy of prediction results.
[0060] (2) Different from deterministic prediction that only provides single-value output, by introducing Gaussian negative log-likelihood, the mean and variance are synchronously obtained from the perspective of probabilistic prediction, achieving good uncertainty quantification performance and providing more comprehensive information for wind disaster prevention.
[0061] (3) An ensemble learning strategy is adopted to strategically integrate multiple independent models to obtain more reliable prediction results, effectively enhancing the stability and robustness of the surrogate model.
[0062] (4) An improved Shapley additive explanation method is used to conduct model interpretation analysis, clarifying the marginal contribution and substantial impact of feature variables on prediction results on the basis of considering feature interaction effects, and enhancing the interpretability of the surrogate model. Description of the Drawings
[0063] Figure 1 It is a technical flow chart of a probability prediction method for typhoon effects of long-span bridges driven by physics-data co-driving.
[0064] Figure 2 It is a specific classification schematic diagram of model input and model output.
[0065] Figure 3 It is a schematic diagram of the analysis framework for model training and response prediction.
[0066] Figure 4 It is a schematic diagram of hyperparameter optimization based on annealing search and Bayesian algorithm. Detailed Embodiments
[0067] Next, in combination with the drawings in the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.
[0068] The present application proposes a probability prediction method for typhoon effects of long-span bridges driven by physics-data co-driving. The main technical process of the implementation solution is specifically as follows (see Figure 1 )
[0069] S1. Obtain the typhoon and its effect monitoring data recorded by the long-span bridge structural health monitoring system, and calculate the typhoon characteristic parameters and bridge vibration response parameters.
[0070] Specifically, the monitoring data of typhoons and their effects are obtained based on the anemometers and accelerometers at the mid-span position of the main girder; the typhoon characteristic parameters include the mean wind speed, wind direction angle, turbulence intensity, turbulence standard deviation, turbulence integral scale, and gust factor; the bridge vibration response parameters include vertical acceleration and torsional acceleration.
[0071] S2, using the typhoon characteristic parameters calculated in step S1 as the model input and the bridge vibration response parameters as the model output, construct a sample set (see Figure 2 ), and divide the sample sets of multiple typhoons and their effects into a training set and a test set.
[0072] Specifically, the total number of sample sets of typhoons and their effects is not less than 10, the test set contains 2 independent sample sets of typhoons and their effects, and the remaining sample sets are used as the training set.
[0073] S3, adopt a physics-data co-driven deep integration strategy to adjust the scalable neural network architecture, and construct a typhoon effect probability prediction model that provides dynamic estimates of response mean and variance.
[0074] Specifically, the steps to adopt a physics-data co-driven deep integration strategy to adjust the scalable neural network architecture are as follows:
[0075] S31, use the scoring rule as the training criterion. For a model with input X , output Y , and hyperparameters , let its prediction distribution , the true distribution , and the ideal scoring rule is written as:
[0076] (1)
[0077] In the formula, is the scoring function; represents the performance score of the prediction distribution under the true distribution ; represents the theoretical optimal score for predicting the true distribution itself; when and only when , ; when maximizing the likelihood, the scoring rule that satisfies Gibbs inequality is expressed as:
[0078] (2)
[0079] S32, in the physics-data co-driven method, the loss function of the surrogate model needs to consider the physics-informed loss term and the data-driven loss term ; For the physically informed loss term , take the bridge aerodynamic vibration equation as the control condition:
[0080] (3)
[0081] In the formula, M , C , K represent the mass, damping, and stiffness matrices respectively; ü ( x , t ), , u ( x , t ) represent the acceleration, velocity, and displacement vectors at the spatial coordinate x and the time scale t respectively; F aero ( x , t ) represents the external wind load vector, which consists of three parts: the aerodynamic lift F L (t), the aerodynamic drag F D (t), and the aerodynamic torque F M (t). During bridge buffeting, they can be expressed as follows respectively:
[0082] (4)
[0083] (5)
[0084] (6)
[0085] In the formula, ρ is the air density; U ( t ) is the oncoming wind speed; B is the width of the main girder; H is the height of the main girder; α ( t ) is the effective wind attack angle of the main girder section; C L α ( t )], C D α ( t )], C M α ( t )] are the lift coefficient, drag coefficient, and torque coefficient respectively; C L ’ α ( t )], C D ’ α ( t )], C M ’ α ( t )] are the first-order derivatives of the lift coefficient, drag coefficient, and torque coefficient with respect to the wind attack angle, respectively; χ L , χ L ’ , χ D , χ D ’ , χ M , χ M ’ are the aerodynamic admittance functions; h ( t ) and v ( t ) are the non-stationary fluctuating wind speeds in the along-wind and vertical directions, respectively;
[0086] On this basis, the bridge acceleration response is further expressed as:
[0087] (7)
[0088] (8)
[0089] (9)
[0090] In the formula, and represent the vertical components of the acceleration on the left and right sides of the main girder, respectively; and represent the vertical acceleration and torsional acceleration, respectively;
[0091] Accordingly, the physics-informed loss term is expressed as:
[0092] (10)
[0093] In the formula, Y v and Y trespectively represent the vertical acceleration and torsional acceleration of the model prediction output; β 1 and β 2 respectively represent the weights of the vertical acceleration residual term and the torsional acceleration residual term;
[0094] For the data-driven loss term , introduce the Gaussian negative log-likelihood to simultaneously obtain the mean and variance of the independent model to adapt to the uncertainty of the prediction:
[0095] (11)
[0096] The final loss function consists of the above two parts of loss terms:
[0097] (12)
[0098] where and are respectively the weights of the physics-informed loss term and the data-driven loss term ; the goal of model training is to minimize the loss function ;
[0099] S33. Apply adversarial training to smooth the prediction distribution. Add adversarial perturbations in the gradient direction that may increase the loss based on the fast gradient sign method to generate pseudo-samples similar to the real samples to enhance the original dataset. This process is written as:
[0100] (13)
[0101] where X p is the generated adversarial sample; ξ is a small value to keep the maximum norm of the perturbation bounded; sign is to take the sign of the gradient; represents the gradient of the loss function in the input space;
[0102] S34. In the deep ensemble system, introduce a uniform weighted mixing strategy to approximate the Gaussian distribution. On this basis, multiple groups of predictions are integrated as:
[0103] (14) and
[0104] The final output result based on ensemble learning is expressed as:
[0105] (15)
[0106] (16)
[0107] In the formula, is the uniform weighted distribution function; N and i respectively represent the total number of models and the model serial number in the ensemble learning; is the i th model's prediction distribution; is the i th model's hyperparameter; and respectively represent the mean and variance of the i th model; and respectively correspond to the mean and variance of the final prediction.
[0108] S4. Based on the training set and test set divided in step S2, and the probability prediction model established in step S3, conduct model training and response prediction (see Figure 3 ).
[0109] Specifically, use annealing search to obtain the local optimal setting of the model hyperparameters, and then apply the Bayesian algorithm to update the prior distribution, so as to identify the global optimal setting (see Figure 4 ).
[0110] S5. Use the improved Shapley additive explanation method to conduct an analysis of the probability prediction model, and clarify the marginal contributions of each feature variable and its substantial impact on the final prediction result.
[0111] Specifically, when using the improved Shapley additive explanation method to calculate the marginal contributions of feature variables, the feature interaction effect is considered, and the specific calculation method is as follows:
[0112] (17)
[0113] (18)
[0114] In the formula, r and s represent different feature terms; P and Q are respectively the finite set excluding the analyzed feature and the complete set including all features; is the predictor; is the Shapley value considering the interaction effect of features r and s ; is the Shapley value considering all combinations of the interaction effect of feature r and other feature variables; is the base value; q is the order of the combination;
[0115] The substantial impact of each feature variable on the final prediction result is quantified in the following manner:
[0116] (19)
[0117] (20)
[0118] In the formula, and are respectively the average absolute Shapley value of feature r and its corresponding contribution ratio; p is the number of features.
[0119] Those of ordinary skill in the art will realize that the embodiments described herein are to assist the reader in understanding the principles of the present invention and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the scope of protection of the present invention.
Claims
1. A probability prediction method for typhoon effects of long-span bridges driven by physical-data collaboration, characterized in that, The method specifically includes the following steps: S1. Obtain the typhoon and its effect monitoring data recorded by the long-span bridge structural health monitoring system, and calculate the typhoon characteristic parameters and bridge vibration response parameters; S2. Use the typhoon characteristic parameters calculated in step S1 as the model input and the bridge vibration response parameters as the model output to construct a sample set, and divide the sample sets of multiple typhoons and their effects into a training set and a test set; S3. Adopt a physics-data collaborative-driven deep integration strategy to adjust the scalable neural network architecture, and construct a typhoon effect probability prediction model that provides dynamic estimation of response mean and variance; The specific steps of adopting a physics-data collaborative-driven deep integration strategy to adjust the scalable neural network architecture are as follows: S31. Use the scoring rule as the training criterion. For a model with input X, output Y, and hyperparameters , let its predicted distribution The true distribution τ = τ(Y|X), and the ideal scoring rule is written as: Θ(f,τ)≤Θ(τ,τ) (1) where Θ is the scoring function; Θ(f,τ) represents the performance score of the predicted distribution f under the true distribution τ; Θ(τ,τ) represents the theoretically optimal score for predicting the true distribution τ itself; if and only if then Θ(f,τ) = Θ(τ,τ); when maximizing the likelihood, the scoring rule that satisfies Gibbs' inequality is expressed as: S32. In the physical-data collaborative driving method, the loss function of the surrogate model needs to consider the physics-informed loss term and the data-driven loss term For the physics-informed loss term Taking the bridge wind-induced vibration equation as the control condition: In the formula, M, C, and K represent the mass, damping, and stiffness matrices respectively; u(x,t) represents the acceleration, velocity, and displacement vectors at the spatial coordinate x and the time scale t; F aero (x,t) represents the external wind load vector, which consists of the aerodynamic lift F L (t), the aerodynamic drag F D (t), and the aerodynamic torque F M (t), which are composed of three parts and can be expressed separately during bridge buffeting as follows: where ρ is the air density; U(t) is the incoming flow wind speed; B is the width of the main girder; H is the height of the main girder; α(t) is the effective wind attack angle of the main girder cross-section; C L [α(t)], C D [α(t)], C M [α(t)] are the lift coefficient, drag coefficient, and torque coefficient, respectively; C’ L [α(t)], C’ D [α(t)], C’ M [α(t)] are the first-order derivatives of the lift coefficient, drag coefficient, and torque coefficient with respect to the wind attack angle; χ L , χ’ L , χ D , χ’ D , χ M , χ’ M is the aerodynamic admittance function; h(t) and v(t) are the non-stationary pulsating wind speeds in the along-wind and vertical directions, respectively; On this basis, the bridge acceleration response a is further expressed as: wherein, a1 and a2 respectively represent the vertical components of the acceleration on the left and right sides of the main beam; a v and a t respectively represent the vertical acceleration and the torsional acceleration; Accordingly, the physics-informed loss term is expressed as: where Y v and Y t respectively represent the vertical acceleration and torsional acceleration of the model prediction output; β1 and β2 respectively represent the weights of the vertical acceleration residual term and the torsional acceleration residual term; For the data-driven loss term introduce Gaussian negative log-likelihood to synchronously obtain the mean and variance to accommodate the uncertainty in prediction: Final loss function It consists of the above two loss terms: where δ1 and δ2 are the weights of the physics-informed loss term and the data-driven loss term respectively; the goal of model training is to minimize the loss function S33. Apply adversarial training to smooth the prediction distribution, add adversarial perturbations in the gradient direction that may increase the loss based on the fast gradient sign method, and generate pseudo-samples similar to the real samples to enhance the original data set. This process is written as: where X p is the generated adversarial sample; ξ is a small value that keeps the maximum norm of the perturbation bounded; sign is the sign of taking the gradient; represents the gradient of the loss function in the input space; S34. In the deep integration system, introduce a uniform weighted mixing strategy to approximate the Gaussian distribution. On this basis, multiple groups of predictions are integrated as: The final output result based on ensemble learning is expressed as: In the formula, is the uniform weighted distribution function; N and i respectively represent the total number of models in the ensemble learning and the model serial number; is the prediction distribution of the i-th model; is the hyperparameter of the i-th model; and respectively represent the mean and variance of the i-th model; and respectively correspond to the mean and variance of the final prediction; S4. Based on the training set and test set divided in step S2 and the probability prediction model established in step S3, carry out model training and response prediction; S5. Adopt an improved Shapley additive explanation method to carry out the explanation analysis of the probability prediction model, and clarify the marginal contribution of each characteristic variable and its substantial impact on the final prediction result; When calculating the marginal contribution of characteristic variables by adopting the improved Shapley additive explanation method, the characteristic interaction effect is considered. The specific calculation method is as follows: where r and s represent different feature terms; P and Q are respectively a finite set excluding the analysis features and a complete set including all features; f p is the predictor; φ r,s is the Shapley value considering the interaction effect of features r and s; φ r,sum is the Shapley value considering all combinations of the interaction effects of feature r and other feature variables; φ0 is the base value; q is the order of the combination; The substantial impact of each characteristic variable on the final prediction result is quantified by the following method: where Ψ r and are the average absolute Shapley value of feature r and its corresponding contribution ratio, respectively; p is the number of features.
2. The probability prediction method for typhoon effects of long-span bridges driven by physical-data collaboration according to claim 1, wherein In step S1, obtain the typhoon and its effect monitoring data based on the anemometer and accelerometer at the mid-span position of the main girder; The typhoon characteristic parameters include average wind speed, wind direction angle, turbulence intensity, turbulence standard deviation, turbulence integral scale, and gust factor; the bridge vibration response parameters include vertical acceleration and torsional acceleration.
3. The probability prediction method for typhoon effects of long-span bridges driven by physical-data collaboration according to claim 1, characterized in that In step S2, the total number of sample sets of typhoons and their effects is not less than 10, the test set contains 2 independent sample sets of typhoons and their effects, and the remaining sample sets are used as the training set.
4. The physical-data collaborative-driven probabilistic prediction method for typhoon effects of long-span bridges according to claim 1, wherein In step S4, adopt annealing search to obtain the local optimal setting of the model hyperparameters, and then apply the Bayesian algorithm to update the prior distribution to identify the global optimal setting.
Citation Information
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