A method for hyperparameter optimization prediction of flood discharge vibration response of hydraulic structures

Abstract

The invention belongs to the technical field of water conservancy engineering, and relates to a method for hyperparameter optimization prediction of flood discharge vibration response of a hydraulic structure, comprising the following steps: collecting flood discharge vibration data of different spatial parts of the hydraulic structure, and dividing output features and input features; using a method of calculating a Pearson correlation coefficient and a maximum information coefficient to sort and screen the importance of input features, and screening out the most irrelevant input features; normalizing and preprocessing the screened input features in a sliding window iterative prediction mode; establishing a BO‑CNN‑BiLSTM‑CA parallel network model, inputting the preprocessed data into the network model, optimizing hyperparameters and predicting vibration responses; using partial dependence theory to provide an explanation for the rationality of Bayesian hyperparameter optimization; the invention can effectively improve the prediction performance of a vibration prediction model and the credibility of a hyperparameter optimization process.

Description

Technical Field

[0001] The invention belongs to the technical field of water conservancy projects, and in particular relates to a method for optimizing and predicting hyperparameters of flood discharge vibration responses of hydraulic structures. Background Art

[0002] In recent years, as hydraulic structures have developed towards high head, large flow and lightweight structure, the problem of structural vibration induced by discharge has become increasingly prominent. When the amplitude exceeds the allowable value specified for the structure, the continuous strong vibration is very likely to cause fatigue damage to the structure. Cases of dams, guide walls and gantry beams failing due to flow-induced vibration are common at home and abroad. The research on the prediction of vibration response of hydraulic structures during flood discharge has important practical significance for ensuring the safe operation of water conservancy hubs.

[0003] Traditional hydraulic structure vibration prediction methods have a series of defects: physically driven numerical models usually rely on idealized assumptions and simplified model structures and cannot fully capture the complex environment of actual engineering applications; although data-driven models based on deep learning present efficient and accurate results in time series prediction, the optimization selection of numerous hyperparameters directly affects the model prediction accuracy; the complexity of data-driven models and the complex logic behind the decisions often make the optimization process present a "black box" characteristic, and the opaque hyperparameter optimization process affects the credibility of the prediction model. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for optimizing the hyperparameters of the vibration response of a hydraulic structure during flood discharge, thereby providing an important reference for vibration control and design optimization of flood discharge structures in water conservancy projects.

[0005] In order to achieve the purpose of the present invention, the present invention adopts the following technical solutions.

[0006] A method for optimizing and predicting hyperparameters of flood discharge vibration response of a hydraulic structure comprises the following steps:

[0007] S1. Collect the flood discharge vibration data of different spatial parts of the hydraulic structure, use the flood discharge vibration extreme point data of the important spatial parts of the structure as the output feature, and use the flood discharge vibration data of other spatial parts as the input feature;

[0008] S2. Use the method of calculating the Pearson correlation coefficient and the maximum information coefficient to sort and screen the importance of the input features and filter out the least relevant input features;

[0009] S3, preprocessing the filtered input features using normalization and sliding window iterative prediction mode to obtain time series data;

[0010] S4. Input the time series data into the BO-CNN-BiLSTM-CA parallel network model to optimize the hyperparameters and predict the vibration response; wherein:

[0011] The BO-CNN-BiLSTM-CA parallel network model includes a convolutional neural network module, a bidirectional long short-term memory network module, a channel attention module and a Bayesian optimization module, wherein the convolutional neural network module is integrated with the channel attention module and is designed in parallel with the bidirectional long short-term memory network module; the Bayesian optimization module is used to optimize hyperparameters, and the hyperparameters include the number of network layers and units of the convolutional neural network module, the number of hidden layers and units of the bidirectional long short-term memory network module, the number of neurons in the dense connection layer, the learning rate, the selection of the activation function and the size of the batch processing; the optimization process of the hyperparameters includes the following steps:

[0012] S41. Definition of hyperparameter space: set the value range of each hyperparameter;

[0013] S42, selection of initial samples: selecting a set of initial samples in the given hyperparameter space as the starting point;

[0014] S43, construction of Gaussian process proxy model: based on the results of the initial sample set, a Gaussian process proxy model is constructed to approximately simulate the target function;

[0015] S44, calculation of acquisition function: based on the Gaussian process proxy model, the acquisition function is comprehensively calculated according to the lower confidence bound, the expected improvement amount and the improvement probability;

[0016] S45, selection of the next evaluation point: based on the evaluation result of the acquisition function, guide the identification of the hyperparameter configuration that is expected to achieve the most significant improvement in the performance of the objective function;

[0017] S46, Objective function evaluation: Apply the identified hyperparameter configuration to the actual objective function evaluation to provide empirical data support for the refinement of the Gaussian process surrogate model;

[0018] S47, Update of Gaussian process proxy model: taking the newly evaluated points into consideration, and updating the Gaussian process proxy model;

[0019] S48, evaluation of convergence criteria: monitor the optimization process to evaluate whether it has converged, and the convergence criterion is to reach a preset number of iterations: if the convergence criterion is not met, jump to execute S44; if the convergence criterion is met, execute S49;

[0020] S49. Output of optimized hyperparameters: output optimized hyperparameters.

[0021] As a preferred embodiment of the present invention, the rational explanation of the hyperparameter optimization is provided by the partial dependence theory, and the process of the rational explanation is to divide the set of predictor variables z into disjoint subsets z s and z c , that is, z=(z s , z c ), then the subset z c The partial dependence function is:

[0022] ;

[0023] In the formula, f(z S , z C ) is the response function of a given sample, P(z C ) is z C The probability distribution of .

[0024] As a preferred embodiment of the present invention, the Pearson correlation coefficient is used to quantify the strength and direction of the linear relationship between two continuous variables. For n-dimensional input features x and y, the Pearson correlation coefficient is calculated by the following formula:

[0025] ;

[0026] Where P xy is the Pearson correlation coefficient, and are the means of the two input features respectively; P xy The larger the value, the greater the similarity between the input features, and vice versa.

[0027] As a preferred solution of the present invention, the maximum information coefficient is based on mutual information to calculate the correlation between variables. Assuming input features X and Y, for the sample {(x i , y i ), i=1, 2, …, N}, is divided into a segments along the x-axis and b segments along the y-axis on a two-dimensional plane, and a×b grid G ​​is obtained. Let D|G represent the probability distribution of points in set D falling on grid G, and denote I(D|G, a, b) as the corresponding X and Y mutual information estimation value under this partitioning situation; for different partitioning grids G, different mutual information I(D|G, a, b) values ​​can be estimated, and I*(D, a,b) is denote as the maximum mutual information value under all different partitioning grids G, that is:

[0028]

[0029] The maximum information coefficient calculation formula is:

[0030]

[0031] Where N is the number of samples, B(N) is a function of the samples, indicating that the total number of small cells in the grid a×b satisfies to be less than B(N); the MIC value range is [0, 1]. When the MIC value between two variables is closer to 1, the correlation between the two variables is stronger. Conversely, when the MIC value is closer to 0, the correlation between the two variables is weaker.

[0032] As a preferred embodiment of the present invention, the normalization is batch normalization, and the formula is:

[0033]

[0034] In the formula, x * Represents x i The value after batch normalization, μ represents the mean of the input data, σ represents the standard deviation, γ and β are learnable parameters, and ε is a minimum value to prevent division by zero.

[0035] As a preferred solution of the present invention, the sliding window iterative prediction mode, that is, a sliding window with a length of m is selected, and the data is processed as a window sliding with a length of m, the data of the first m time points are used as features, and the data of the next time point are used as labels, the feature data are brought into the model to obtain the vibration prediction value at the next moment, and then the window slides backward by one time point, the prediction value is added to this window, and a new window of the same sequence length is generated, and this process is repeated until a number of continuous sub-time series data are obtained.

[0036] As a preferred solution of the present invention, the m is obtained through comparative tests, wherein: the comparative test is to take sliding windows of different lengths for m, calculate the prediction accuracy of the predicted value, and the length with the highest prediction accuracy obtained by comparison is m.

[0037] As a preferred solution of the present invention, the convolutional neural network module utilizes its nonlinear feature extraction capability to capture the spatiotemporal characteristics of the signal through convolution operations, activation functions and maximum pooling operations, while reducing model parameters through downsampling to avoid feature loss.

[0038] As a preferred solution of the present invention, the bidirectional long short-term memory network module can effectively capture the dynamic characteristics and long-term dependencies in time series data through a bidirectional information processing mechanism.

[0039] As a preferred solution of the present invention, the working mechanism of the channel attention module is to first aggregate the information of each channel through global average pooling and global maximum pooling to obtain the global feature representation of each channel to reduce the spatial dimension of the feature map while retaining the information of the channel dimension; then, the aggregated global information is input into the multi-layer perceptron for feature learning; finally, the learned weight is multiplied by the original feature map for weighted processing.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention proposes a BO-CNN-BiLSTM-CA parallel network model, which combines the ability of CNN in capturing the spatial characteristics of input data, the advantages of BiLSTM in capturing sequence-sequence correlation and bidirectional long-term and short-term dependencies, and the deep learning ability of CA in mining the nonlinear and temporal characteristics of vibration data. It gives full play to the advantages of each model and achieves stronger prediction performance than a single model. The BO technology further improves the prediction accuracy of the model and provides an efficient optimization strategy for the high-dimensional hyperparameters of the deep learning model.

[0042] By integrating PD analysis into the Bayesian optimization framework, the present invention not only optimizes the hyperparameters of the neural network, but also deeply understands how specific configurations improve model performance, reveals the complex relationship between a single hyperparameter and the overall model behavior, and provides a more transparent and explainable optimization path for complex applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flowchart of a method for optimizing and predicting hyperparameters of a hydraulic structure flood discharge vibration response according to the present invention;

[0044] Figure 2 It is a schematic diagram of the structure of the BO-CNN-BiLSTM-CA parallel network model in the present invention;

[0045] Figure 3 Schematic diagram of the structure of the channel attention module in the present invention;

[0046] Figure 4 is a flow chart of the hyperparameter optimization process in the present invention;

[0047] Figure 5 It is a partial dependence diagram of any two-dimensional parameter space and a partial dependence diagram of a single parameter in the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0049] As an embodiment of the present invention, Figures 1 to 4 As shown, a method for optimizing and predicting hyperparameters of flood discharge vibration response of a hydraulic structure comprises the following steps:

[0050] (1) Collect flood discharge vibration data at different spatial locations of the hydraulic structure. In this example, the vibration extreme point data (BZ51_Z) of the dam crest beam during flood discharge is used as the output feature, and the vibration data of other spatial points (BZ51_X, BZ51_Y, BZ52_Z, BZ52_X, BZ52_Y, BZ53_Z, BZ53_X, BZ53_Y) are used as the input features.

[0051] (2) Combining the Pearson correlation coefficient and the maximum information coefficient (MIC) method, the importance of input features is ranked and screened, and the least relevant input features are screened out to ensure that the model can focus on the feature subset with the most predictive value.

[0052] For n-dimensional input features x and y, their Pearson correlation coefficient can be calculated as follows:

[0053] ;

[0054] Where P xy is the Pearson correlation coefficient, and are the means of the two input features respectively; P xy The larger the value, the greater the similarity between the input features; otherwise, the similarity is smaller.

[0055] Furthermore, the maximum information coefficient (MIC) is based on mutual information to calculate the correlation between variables. Suppose input features X and Y, for the sample {(x i , y i ), i=1, 2, …, N}, is divided into a segment along the x-axis and b segments along the y-axis on a two-dimensional plane, and a×b grid G ​​is obtained. Let D|G represent the probability distribution of points in set D falling on grid G, and denote I(D|G, a, b) as the corresponding X and Y mutual information estimation value under this partitioning situation. For different partitioning grids G, different mutual information I(D|G, a, b) values ​​can be estimated, and I*(D, a, b) is denoted as the maximum mutual information under all different partitions G, that is:

[0056] ;

[0057] The maximum information coefficient calculation formula is:

[0058] ;

[0059] Where N is the number of samples, B(N) is a function of the samples, indicating that the total number of small cells in the grid a×b satisfies less than B(N). The MIC value range is [0, 1]. The larger the MIC value between the two variables, the stronger the correlation. Conversely, the smaller the MIC value, the smaller the correlation between the two variables.

[0060] (3) The filtered input features (BZ52_X, BZ53_Z, BZ53_X) are normalized and preprocessed in the sliding window iterative prediction mode. Batch normalization is used, and the formula is:

[0061] ;

[0062] In the formula, x * Represents x i The value after batch normalization, μ represents the mean of the input data, σ represents the standard deviation, γ and β are learnable parameters, and ε is a minimum value to prevent division by zero.

[0063] The sliding window iterative prediction mode is to select a sliding window with a length of 6, perform window sliding processing on the data with a length of 6, use the data of the first 6 time points as features, and the data of the next time point as labels, bring the feature data into the model to obtain the vibration prediction value at the next moment, then slide the window back one time point, add the prediction value to this window, generate a new window with the same sequence length, and repeat this process until a number of continuous sub-time series data are obtained. Among them, the length value of 6 is obtained through comparative tests, wherein: the comparative test is that m takes sliding windows of lengths of 3, 6, 9 and 12 respectively, calculates the prediction accuracy of the prediction value, and the length with the highest prediction accuracy obtained by comparison is 6.

[0064] (4) Establish a BO-CNN-BiLSTM-CA parallel network model, whose structure is as follows Figure 2 As shown in Figure 1, the model combines different layer architectures of convolutional neural network (CNN) and bidirectional long short-term memory network (BiLSTM), in which the CNN module further integrates channel attention (CA). The structure of the CA module is shown in Figure 1. Figure 3 First, the information of each channel is aggregated through global average pooling and global maximum pooling to obtain the global feature representation of each channel to reduce the spatial dimension of the feature map while retaining the information of the channel dimension; then, the aggregated global information is input into the two-layer neural network structure for feature learning; finally, the two features are added together and the weight coefficient is obtained through the Sigmoid activation function.

[0065] As an embodiment of the present invention, Figure 4 As shown, the process of hyperparameter optimization includes the following steps:

[0066] 1) Definition of hyperparameter space. The initial stage of Bayesian optimization is to define the boundaries of the hyperparameter space. The present invention selects batch size, learning rate, number of CNN unit layers, activation function, number of BiLSTM units and unit layers, and number of Dense units, as shown in Table 1, and sets the possible value range for each hyperparameter.

[0067] 2) Selection of initial samples: This process starts with selecting a set of initial samples in a given hyperparameter space.

[0068] 3) Construction of Gaussian process surrogate model: Based on the results of the initial sample set, a Gaussian process (GP) surrogate model is constructed to approximately simulate the objective function.

[0069] 4) Calculation of acquisition function: Based on the establishment of the GP agent model, the acquisition function is calculated comprehensively according to the lower confidence bound (LCB), expected improvement (EI) and improvement probability (PI).

[0070] 5) Select the next evaluation point. Obtaining the evaluation results of the function will guide the identification of a hyperparameter configuration that is expected to achieve the most significant improvement in the performance of the objective function.

[0071] 6) Objective function evaluation. Subsequently, the selected hyperparameter configuration will be applied to the actual objective function evaluation to provide empirical data support for the refinement of the surrogate model.

[0072] 7) Update of GP proxy model: Taking the newly evaluated points into consideration, update the GP proxy model.

[0073] 8) Evaluation of convergence criteria: Monitor the optimization process to evaluate whether it has converged. The convergence criterion is to reach the preset number of iterations. If the convergence criterion is not met, jump to 4); if the convergence criterion is met, execute 9);

[0074] 9) Output of optimized hyperparameters: Output optimized hyperparameters.

[0075] Table 1 Bayesian optimization hyperparameters and their search space

[0076]

[0077] (5) The partial dependence (PD) theory is used to explain the rationality of BO hyperparameter optimization. The set of predictors z is divided into non-overlapping subsets z s and z c , that is, z=(z s , z c ). Then the subset z c The partial dependence function is:

[0078]

[0079] In the formula, f(z S , z C ) is the response function of a given sample, P(z C ) is z C The probability distribution of .

[0080] like Figure 5 As shown in the figure, a two-dimensional cross-sectional diagram of the optimization process of the Bayesian optimization algorithm in any two parameter dimensions in the process of predicting the vertical vibration trend of the BZ51 measuring point is visualized. It can be found that changing the number of BiLSTM layers, the number of units, and the number of Dense units has little effect on the prediction results, while changing the number of CNN stacking layers, learning rate, Batch size, and activation function has a greater impact. The Bayesian optimization algorithm has a denser distribution of sampling points near the five-star mark in the dark area, and a sparse distribution of sampling points in the area with lower proxy function values, indicating that the Bayesian optimization algorithm does not waste too much computer resources on hopeless parameter combinations, but effectively obtains high-fidelity prior information from limited historical searches, and iterates accordingly to quickly locate the optimal parameter configuration.

[0081] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures, characterized in that: The steps include: S1. Collect the flood discharge vibration data of different spatial parts of the hydraulic structure, use the flood discharge vibration extreme point data of the important spatial parts of the structure as the output feature, and use the flood discharge vibration data of other spatial parts as the input feature; S2. Use the method of calculating the Pearson correlation coefficient and the maximum information coefficient to sort and screen the importance of the input features and filter out the least relevant input features; S3, preprocessing the filtered input features using normalization and sliding window iterative prediction mode to obtain time series data; S4. Input the time series data into the BO-CNN-BiLSTM-CA parallel network model to optimize the hyperparameters and predict the vibration response; wherein: The BO-CNN-BiLSTM-CA parallel network model includes a convolutional neural network module, a bidirectional long short-term memory network module, a channel attention module and a Bayesian optimization module, wherein the convolutional neural network module is integrated with the channel attention module and is designed in parallel with the bidirectional long short-term memory network module; the Bayesian optimization module is used to optimize hyperparameters, and the hyperparameters include the number of network layers and units of the convolutional neural network module, the number of hidden layers and units of the bidirectional long short-term memory network module, the number of neurons in the dense connection layer, the learning rate, the selection of the activation function and the size of the batch processing; wherein the optimization process of the hyperparameters includes the following steps: S41. Definition of hyperparameter space: set the value range of each hyperparameter; S42, selection of initial samples: selecting a set of initial samples in the given hyperparameter space as the starting point; S43, construction of Gaussian process proxy model: based on the results of the initial sample set, a Gaussian process proxy model is constructed to approximately simulate the target function; S44, calculation of acquisition function: based on the Gaussian process proxy model, the acquisition function is comprehensively calculated according to the lower confidence bound, the expected improvement amount and the improvement probability; S45, selection of the next evaluation point: based on the evaluation result of the acquisition function, guide the identification of the hyperparameter configuration that is expected to achieve the most significant improvement in the performance of the objective function; S46, Objective function evaluation: Apply the identified hyperparameter configuration to the actual objective function evaluation to provide empirical data support for the refinement of the Gaussian process surrogate model; S47, Update of Gaussian process proxy model: taking the newly evaluated points into consideration, and updating the Gaussian process proxy model; S48, evaluation of convergence criteria: monitor the optimization process to evaluate whether it has converged, and the convergence criterion is to reach a preset number of iterations: if the convergence criterion is not met, jump to execute S44; if the convergence criterion is met, execute S49; S49. Output of optimized hyperparameters: output optimized hyperparameters.

2. The method for optimizing and predicting hyperparameters of the vibration response of a hydraulic structure to discharge flood according to claim 1, characterized in that: The rationale for the hyperparameter optimization is provided by partial dependence theory, which involves dividing the set of predictors z into disjoint subsets z s and z c , that is, z=(z s , z c ), then the subset z c The partial dependence function is: ； In the formula, f(z S , z C ) is the response function of a given sample, P(z C ) is z C The probability distribution of .

3. The method for optimizing and predicting hyperparameters of the vibration response of a hydraulic structure to discharge flood according to claim 1, characterized in that: The Pearson correlation coefficient is used to quantify the strength and direction of the linear relationship between two continuous variables. For n-dimensional input features x and y, the Pearson correlation coefficient is calculated by the following formula: ； Where P xy is the Pearson correlation coefficient, and are the means of the two input features respectively; P xy It is used to indicate the similarity between input features.

4. The method for optimizing and predicting hyperparameters of the flood discharge vibration response of a hydraulic structure according to claim 1, characterized in that: The maximum information coefficient is based on mutual information to calculate the correlation between variables. Suppose input features X and Y are given. For the sample {(x i , y i ), i=1, 2, …, N}, is divided into a segments along the x-axis and b segments along the y-axis on a two-dimensional plane, and a×b grid G ​​is obtained. Let D|G represent the probability distribution of points in set D falling on grid G, and denote I(D|G, a, b) as the corresponding X and Y mutual information estimation value under this segmentation. For different partitioning grids G, different mutual information I(D|G, a, b) values ​​can be estimated, and I*(D, a, b) is denoted as the maximum mutual information value under all different partitioning grids G, that is: ； The maximum information coefficient calculation formula is: ； Where N is the number of samples, B(N) is a function of the samples, indicating that the total number of small cells in the grid a×b satisfies to be less than B(N); the MIC value range is [0, 1]. When the MIC value between two variables is closer to 1, the correlation between the two variables is stronger. Conversely, when the MIC value is closer to 0, the correlation between the two variables is weaker.

5. The method for optimizing and predicting hyperparameters of the vibration response of a hydraulic structure to discharge flood according to claim 1, characterized in that: The normalization is batch normalization, and the formula is: ； In the formula, x * Represents x i The value after batch normalization, μ represents the mean of the input data, σ represents the standard deviation, γ and β are learnable parameters, and ε is a minimum value to prevent division by zero.

6. The method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures according to claim 1, characterized in that: The sliding window iterative prediction mode, that is, a sliding window with a length of m is selected, and the data is processed as a window sliding with a length of m, the data of the first m time points are used as features, and the data of the next time point are used as labels, the feature data is brought into the model to obtain the vibration prediction value at the next moment, and then the window slides backward for one time point, the prediction value is added to this window, and a new window with the same sequence length is generated. This process is repeated until a number of continuous sub-time series data are obtained.

7. The method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures according to claim 6, characterized in that: The m is obtained through comparative tests, wherein: the comparative test is to take sliding windows with different lengths respectively, calculate the prediction accuracy of the predicted value, and the length with the highest prediction accuracy obtained through comparison is m.

8. The method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures according to claim 1, characterized in that: The convolutional neural network module uses its nonlinear feature extraction capability to capture the spatiotemporal characteristics of the signal through convolution operations, activation functions and maximum pooling operations, while reducing model parameters through downsampling to avoid feature loss.

9. The method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures according to claim 1, characterized in that: The bidirectional long short-term memory network module can effectively capture the dynamic characteristics and long-term dependencies in time series data through a bidirectional information processing mechanism.

10. The method for optimizing and predicting hyperparameters of flood discharge vibration response of hydraulic structures according to claim 1, characterized in that: The working mechanism of the channel attention module includes the following steps: S101, aggregating the information of each channel through global average pooling and global maximum pooling to obtain a global feature representation of each channel, so as to reduce the spatial dimension of the feature map while retaining the information of the channel dimension; S102, inputting the aggregated global information into a multi-layer perceptron to perform feature learning; S103: multiply the learned weights by the original feature map to perform weighted processing.

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