Wind-induced vibration prediction method based on clustering and stage-adaptive multi-output surrogate model

Abstract

The application discloses a wind vibration prediction method based on clustering and phased adaptive multi-output proxy model, and belongs to the technical field of structural wind resistance design and proxy model, and comprises the following steps: constructing an input feature vector and a multi-output target vector to form a multi-output candidate pool; performing K-means clustering on all sample points in the multi-output candidate pool, and selecting sample points corresponding to the minimum Euclidean distance for each cluster center to form an initial training set; constructing a plurality of Gaussian process proxy models; dividing the Gaussian process proxy models into two training stages, i.e., a global exploration stage and a local refining stage, and using different acquisition functions to iteratively train the Gaussian process proxy models; and performing wind vibration prediction based on the trained Gaussian process proxy models. The method improves the accuracy of wind vibration prediction, has good universality, is suitable for prediction tasks of different structural forms and different wind vibration response quantities, and provides a new technical means with both efficiency and precision for structural wind resistance design.

Description

Technical Field

[0001] This application relates to the field of structural wind-resistant design and surrogate model technology, and in particular to a wind vibration prediction method based on clustering and a phased adaptive multi-output surrogate model. Background Technology

[0002] In wind-resistant design of building structures, obtaining the wind-induced vibration response under equivalent static wind loads is a core step. When using wind tunnel tests or high-fidelity numerical simulations as data sources, traditional methods often employ a "load case traversal" strategy. This involves combining parameters such as wind direction angle, basic wind pressure, and damping ratio, conducting tests or calculations one by one to create a full matrix load case table covering all parameter combinations. Subsequently, each load case undergoes time-consuming high-precision solutions or physical tests, ultimately yielding a full-space response database from which design control values ​​are extracted. While this method ensures complete results, it has significant drawbacks in engineering practice. Taking a medium-scale wind-induced vibration test or parametric analysis as an example, if it includes dozens of wind direction angles, multiple basic wind pressure levels, and several damping ratio levels, the combined load cases can easily reach thousands. Each test or calculation requires independent use of site, equipment, or computing resources, with an overall time consumption of several days, severely slowing down the design iteration pace. Furthermore, the response values ​​corresponding to a large number of load cases are only used as trend references in subsequent designs, resulting in an extremely low return on investment.

[0003] To address this issue, existing research has attempted to employ surrogate model techniques, which train a mathematical model using a small number of high-cost samples to predict the responses of other points. Gaussian process (GP) models, due to their ability to simultaneously provide the prediction mean and uncertainty, are often combined with active learning / adaptive point addition strategies to reduce the required number of samples. Specifically, Existing technology 1 (CN118940602A) uses a deep Gaussian process combined with Bayesian optimization for point addition; Existing technology 2 (CN117057194A) also uses a GP surrogate model with Bayesian optimization; Existing technology 3 (CN112749495A) combines GP with efficient global optimization (EGO), using an expectation improvement function for adaptive point addition; Existing technology 4 (CN117952021A) discloses clustering of detection samples and incorporates the hypersphere formed by the clusters as a constraint into the sampling criterion to avoid duplicate sampling; Existing technology 5 utilizes a sparse Gaussian process for dynamic prediction of wind-induced vibration response.

[0004] The above schemes generally have the following limitations: (1) They are mostly focused on single output response prediction and do not fully consider that the actual wind vibration response is a vector composed of multiple directional components; (2) The point addition strategy is mostly based on a single uncertainty index and lacks awareness of the geometric complexity of the response surface in the parameter space. It is easy to undersample in highly nonlinear regions and waste samples in flat regions; (3) The selection of initial training points is mostly random sampling or simple Latin hypercube, resulting in poor model initial accuracy and convergence stability; (4) A few schemes involving clustering exclude the clustering regions of existing samples as redundant regions instead of using clustering to design initial sampling.

[0005] In summary, there is a lack of a surrogate model method specifically designed for wind vibration testing scenarios, capable of simultaneously and efficiently handling multi-directional response prediction, and able to proactively adjust the sampling strategy according to the test accuracy requirements. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this application provides a wind vibration prediction method based on clustering and a phased adaptive multi-output surrogate model. This method solves the problems in existing wind vibration test surrogate model methods, such as the strong randomness in the selection of initial sampling points leading to poor initial model accuracy, the single point addition strategy failing to balance global exploration and local refinement, and the lack of collaborative prediction capability for multi-directional response components, resulting in insufficient efficiency and stability in constructing a high-precision surrogate model with a small number of samples.

[0007] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application provides a wind-induced vibration prediction method based on clustering and a staged adaptive multi-output surrogate model, including: S1: Construct a multi-output candidate pool that includes an input feature vector and multiple output target vectors. The input feature vector includes key parameters that affect wind-induced vibration response. The multiple output target vectors include response components generated under wind load. S2: Perform K-means clustering on all sample points in the multi-output candidate pool, and select the sample points corresponding to the minimum Euclidean distance for each cluster center to form the initial training set; S3: Construct multiple Gaussian process surrogate models based on input feature vectors and multiple output target vectors; S4: Based on the comparison between the accuracy of the Gaussian process surrogate model and the preset threshold, the training is divided into two phases: the global exploration phase and the local refinement phase. Different acquisition functions are used to iteratively train the Gaussian process surrogate model during the training phase. S5: Predict wind-induced vibrations based on a trained Gaussian process surrogate model.

[0008] Further, S1 includes: The key parameters affecting wind-induced vibration response are determined, and the wind direction angle among the key parameters is subjected to sine and cosine transformations. An input feature vector is formed based on the key parameters, which include damping ratio, basic wind pressure, and wind direction angle. The input features are standardized, and the working conditions to be analyzed are mapped to the standardized feature space to form a candidate sample pool. For each candidate working condition in the candidate sample pool, the corresponding response components in multiple directions are organized into a multi-output target vector, wherein the response components include horizontal two-way force components and vertical force components; The candidate sample pool is associated with and stored with the corresponding multi-output target vector to form a multi-output candidate pool.

[0009] Furthermore, the Gaussian process surrogate model adopts a kernel function combination form, and its expression is:

[0010] In the formula, For Gaussian process surrogate model, For constant kernel, It is the radial basis function kernel. It uses the Matern5 / 2 core. It is a white noise kernel. This is the input feature vector.

[0011] Further, S4 includes: S401: When the average relative root mean square error of the response components in the initial training set is higher than a preset threshold, the Gaussian process surrogate model is determined to be in the global exploration phase; otherwise, the Gaussian process surrogate model is determined to be in the local refinement phase. S402: Different acquisition functions are used for calculations during the two training phases: the global exploration phase and the local refinement phase. S403: Select the candidate point that maximizes the current stage acquisition function value as the new test sample, calculate the true response value corresponding to the new test sample, and add it to the initial training set for updating; S404: Iteratively train the Gaussian process surrogate model based on the updated training set. Evaluate the average relative root mean square error of all candidate working condition spatial response components every fixed number of steps. If the relative decrease of the average relative root mean square error is lower than the set threshold in multiple consecutive evaluation periods, terminate the iteration and output the current Gaussian process surrogate model; otherwise, proceed to S401 to update the training set.

[0012] Furthermore, the calculation formula for the acquisition function during the global exploration period is as follows:

[0013] In the formula, This is the data acquisition function during the global exploration phase. , and Let the standard deviations of the candidate point predictions be given by the three Gaussian process surrogate models. Let be the minimum Euclidean distance from the candidate point to the current training set. This is the distance weighting index for the global exploration period.

[0014] Furthermore, the calculation formula for the acquisition function during the local refining period is as follows:

[0015] In the formula, This is the acquisition function for the local refining period. This is the curvature gain coefficient. This refers to the normalized local curvature calculated using a Gaussian process surrogate model after applying small perturbations near the candidate points. This is the distance weighting index for the local refining period.

[0016] The beneficial effects of this application are: This application proposes a wind vibration prediction method based on clustering and a phased adaptive multi-output surrogate model. By training multiple Gaussian process surrogate models in two phases—a global exploration phase and a local refinement phase—it can simultaneously and accurately predict multiple directional components, avoiding the problem of single-output models failing to address all aspects. Furthermore, the two-stage acquisition function automatically switches through an error threshold. In the early stage, it rapidly expands the sample based on diversity, while in the middle and later stages, it accurately targets high-error regions by combining uncertainty and curvature perception, thereby improving the model's prediction accuracy. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0018] Figure 1 This is a flowchart illustrating a wind vibration prediction method based on clustering and a phased adaptive multi-output surrogate model, provided as an embodiment of this application.

[0019] Figure 2 This is a schematic diagram illustrating the relationship between surrogate model error and computational quantity, provided as an embodiment of this application. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0021] Example 1: This application provides a wind-induced vibration prediction method based on clustering and a staged adaptive multi-output surrogate model. This method can be found in [reference needed]. Figure 1 ,include: S1: Construct the input feature vector and multiple output target vectors to form a multiple output candidate pool.

[0022] In one embodiment of this application, key parameters affecting wind-induced vibration response (such as damping ratio, basic wind pressure, and wind direction angle) are used to construct an input feature vector. The wind direction angle is then subjected to sine and cosine transformations to eliminate periodic jumps. After standardization, all input features are mapped to the standardized feature space, forming a candidate sample pool. At this stage, the candidate pool only represents parameter combinations and has not yet undergone any experiments or calculations. For each working condition, its response components in three directions (such as horizontal components FX and FY, and vertical component FZ) are recorded simultaneously, forming a multi-output target vector. The candidate sample pool is associated with and stored with the corresponding multi-output target vector to form a multi-output candidate pool.

[0023] S2: Selection of the initial training set based on K-means clustering.

[0024] In one embodiment of this application, an initial number of samples (e.g., 50) is set to be much smaller than the total number of samples in the candidate pool. K-means clustering is performed on all points in the candidate pool, and the number of clusters is equal to the initial number of samples. For each cluster center, the unique sample point with the closest Euclidean distance to it is selected from the candidate pool to form the initial training set. Unlike the prior art approach of judging whether existing samples overlap and rejecting them based on clustering, this embodiment actively selects points near the cluster centers from the unlabeled candidate pool as initial samples, thereby ensuring that the initial training points have essentially uniform coverage in the parameter space, providing a good training starting point for the surrogate model.

[0025] S3: Construct multiple Gaussian process proxy models based on input feature vectors and multiple output target vectors.

[0026] In one embodiment of this application, an independent Gaussian process regression model is established for each output component, but all models share the same set of sampling points to ensure that response information from different directions can synergistically influence the point selection process. The kernel function of the Gaussian process adopts a combined form: constant kernel × (radial basis function kernel + Matérn5 / 2 kernel) + white noise kernel. This combination can simultaneously capture the overall smooth trend and local irregular changes of the response surface, and the calculation formula is as follows:

[0027] In the formula, For Gaussian process surrogate model, For constant kernel, It is the radial basis function kernel. It uses the Matern5 / 2 core. It is a white noise kernel. This is the input feature vector.

[0028] S4: Based on the comparison between the accuracy of the Gaussian process surrogate model and the preset threshold, the training is divided into two phases: a global exploration phase and a local refinement phase. Different acquisition functions are used in the two training phases to iteratively train the Gaussian process surrogate model.

[0029] S5: Predict wind-induced vibrations based on a trained Gaussian process surrogate model.

[0030] In one embodiment of this application, when the average relative root mean square error of the responses in the three directions exceeds a preset threshold (e.g., 2%), the model is determined to be in an underfitting state, i.e., the global exploration period. At this time, the acquisition function is dominated by spatial exploration, using the formula:

[0031] In the formula, This is the data acquisition function during the global exploration phase. , and The standard deviation of the candidate point predictions by the three Gaussian process surrogate models is used, and the maximum value is taken as the comprehensive uncertainty index. The minimum Euclidean distance from the candidate point to the current training set. This is the distance weighting index for the global exploration phase, ranging from 0.6 to 1.0. A larger value indicates a higher weighting. The value forces new sample points to fill the sparse regions in the parameter space first, thus enabling the model to quickly capture response trends over a wide range in the early stages.

[0032] Once the average relative root mean square error drops below a preset threshold, the system automatically switches to the local refinement stage. At this point, the model has grasped the basic contours of the response, and the focus shifts to local refinement of highly nonlinear or high-error regions. The acquisition function during the refinement phase integrates information from three factors: uncertainty, spatial distance, and local curvature. The formula is:

[0033] In the formula, This is the acquisition function for the local refining period. This is the curvature gain coefficient, which can be set to 0.8. This refers to the normalized local curvature calculated using a Gaussian process surrogate model after applying small perturbations near the candidate points. The distance weighting index for the local refinement phase is set to 0.2~0.5, which is smaller than that for the global exploration phase. Value, preferred Take 0.4, A value of 0.8 is chosen to appropriately weaken the spatial distance constraint and concentrate more sampling resources in regions with high uncertainty and strong nonlinearity. In each iteration, the candidate point that maximizes the current stage's acquisition function value is selected as a new experimental sample. The experimental or calculation program is called to obtain the true values ​​of the responses in the three directions, which are then added to the training set and all Gaussian process surrogate models are updated. Subsequently, the stage switching conditions are re-evaluated.

[0034] An early stopping mechanism is implemented during the iteration process: the average relative root mean square error of all candidate working conditions is evaluated at fixed intervals. If the relative decrease in error is lower than a set threshold within multiple consecutive evaluation periods, the iteration is terminated early. The threshold is set between 0.02 and 0.05, and can be set to 0.03. The early stopping mechanism effectively avoids resource waste caused by oversampling. After the iteration converges, the trained multi-output Gaussian process surrogate model and feature normalization processor are output. Subsequently, for any parameter point in the experimental matrix that has not yet been actually tested, simply inputting the parameters into this model will provide high-precision response predictions in three directions simultaneously within seconds, without occupying high-performance computing resources, and allowing the occupation of the experimental site to end early.

[0035] In one embodiment of this application, such as Figure 2As shown, in 1260 wind vibration response verification cases covering all operating conditions, the embodiments of this application demonstrate outstanding efficiency advantages. Specifically: by the 45th iteration (95 samples in the training set, accounting for approximately 7.5% of the entire space), the average relative root mean square error of the three-dimensional response had decreased to 1.61%. After entering the refinement stage, the model increased the sampling density in key regions. By the 60th iteration (110 samples in the training set, accounting for approximately 8.7% of the entire space), the average relative root mean square error of the three-dimensional response further decreased to 1.46%. At this point, the errors of the horizontal two-dimensional force components FX and FY and the vertical force component FZ were 1.29%, 1.81%, and 1.29%, respectively. By the 150th iteration (200 samples in the training set, accounting for approximately 15.9% of the entire space), the average error of the three-dimensional response broke through the 1% mark and decreased to 0.95%. FX, FY, and FZ reached excellent levels of 0.96%, 0.84%, and 1.05%, respectively. Subsequently, the model triggered the early stopping mechanism to automatically terminate the iteration. This means that, with a relative error of 1.5% as an acceptable threshold, this application only requires approximately 110 iterations (less than 9% of all operating conditions) to meet the standard, a reduction of more than an order of magnitude compared to the traditional approach that requires traversing all 1260 operating conditions. Even with a more stringent target of 1% error, only about 200 iterations are needed (approximately 16% of the total space), still far less than a full-coverage test. This efficiency improvement can directly shorten the testing cycle by several times, significantly reduce the time spent on site and equipment, and free designers from lengthy testing waits.

[0036] Unlike existing technologies that generally focus on proxy modeling of a single response quantity, this application establishes a multi-output shared sampling mechanism based on the inherently vector characteristics of wind vibration response. It uses the maximum standard deviation in each direction as the joint point selection criterion, ensuring that abrupt changes in response in a certain direction under different wind angles are prioritized for refinement. The final model can simultaneously predict multiple directional components with high accuracy, avoiding the problem of single-output models neglecting certain aspects. Furthermore, its unique two-stage acquisition function automatically switches error thresholds. In the early stages, it rapidly expands samples based on diversity, while in the mid-to-late stages, it accurately targets high-error regions using uncertainty and curvature perception. This customized strategy achieves the target accuracy earlier than fixed-weight methods with the same number of trials and significantly outperforms the fitting effect on "steep" regions of the response surface. In addition, while existing technologies often use clustering to detect the clustering of existing samples to avoid repeated sampling in dense areas (exclusive use), this application creatively uses clustering for the active selection of the initial training set, extracting the most spatially representative sample combinations from the unlabeled candidate space, significantly improving the model's initial accuracy and convergence stability. The entire method requires no manual parameter tuning and can automatically complete the entire process from initial point selection and stage discrimination to encryption and termination. The output surrogate model can provide the predicted mean, which facilitates the evaluation of results by engineers throughout the experiment.

[0037] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model, characterized in that, include: S1: Construct a multi-output candidate pool that includes an input feature vector and multiple output target vectors. The input feature vector includes key parameters that affect wind-induced vibration response. The multiple output target vectors include response components generated under wind load. S2: Perform K-means clustering on all sample points in the multi-output candidate pool, and select the sample points corresponding to the minimum Euclidean distance for each cluster center to form the initial training set; S3: Construct multiple Gaussian process proxy models based on input feature vectors and multiple output target vectors; S4: Based on the comparison between the accuracy of the Gaussian process surrogate model and the preset threshold, the training is divided into two phases: the global exploration phase and the local refinement phase. Different acquisition functions are used to iteratively train the Gaussian process surrogate model during the training phase. S5: Predict wind-induced vibrations based on a trained Gaussian process surrogate model.

2. The wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model according to claim 1, characterized in that, S1 includes: The key parameters affecting wind-induced vibration response are determined, and the wind direction angle among the key parameters is subjected to sine and cosine transformations. An input feature vector is formed based on the key parameters, which include damping ratio, basic wind pressure, and wind direction angle. The input features are standardized, and the working conditions to be analyzed are mapped to the standardized feature space to form a candidate sample pool. For each candidate working condition in the candidate sample pool, the corresponding response components in multiple directions are organized into a multi-output target vector, wherein the response components include horizontal two-way force components and vertical force components; The candidate sample pool is associated with and stored with the corresponding multi-output target vector to form a multi-output candidate pool.

3. The wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model according to claim 1, characterized in that, The Gaussian process surrogate model adopts a kernel function combination form, and its expression is: In the formula, For Gaussian process surrogate model, For constant kernel, It is the radial basis function kernel. It uses the Matern5 / 2 core. It is a white noise kernel. This is the input feature vector.

4. The wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model according to claim 2, characterized in that, The S4 includes: S401: When the average relative root mean square error of the response components in the initial training set is higher than a preset threshold, the Gaussian process surrogate model is determined to be in the global exploration phase; otherwise, the Gaussian process surrogate model is determined to be in the local refinement phase. S402: Different acquisition functions are used for calculations during the two training phases: the global exploration phase and the local refinement phase. S403: Select the candidate point that maximizes the current stage acquisition function value as the new test sample, calculate the true response value corresponding to the new test sample, and add it to the initial training set for updating; S404: Iteratively train the Gaussian process surrogate model based on the updated training set. Evaluate the average relative root mean square error of all candidate working condition spatial response components every fixed number of steps. If the relative decrease of the average relative root mean square error is lower than the set threshold in multiple consecutive evaluation periods, terminate the iteration and output the current Gaussian process surrogate model; otherwise, proceed to S401 to update the training set.

5. The wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model according to claim 4, characterized in that, The formula for calculating the acquisition function during the global exploration period is: In the formula, This is the data acquisition function during the global exploration phase. , and Let the standard deviations of the candidate point predictions be given by the three Gaussian process surrogate models. Let be the minimum Euclidean distance from the candidate point to the current training set. This is the distance weighting index for the global exploration period.

6. The wind-induced vibration prediction method based on clustering and a phased adaptive multi-output surrogate model according to claim 4, characterized in that, The calculation formula for the acquisition function during the local refining period is as follows: In the formula, This is the acquisition function for the local refining period. This is the curvature gain coefficient. This refers to the normalized local curvature calculated using a Gaussian process surrogate model after applying small perturbations near the candidate points. This is the distance weighting index for the local refining period.

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