Precise multi-step prediction method for bridge monitoring data based on space-time hypergraph neural network

Abstract

The invention discloses a bridge monitoring data accurate multi-step prediction method based on a space-time hypergraph neural network. The method comprises the following steps: 1, collecting space-time monitoring two-dimensional data of a bridge structure as an original data set; 2, performing missing data filling, trend extraction and data standardization preprocessing operation on the original data set; 3, representing the spatial domain data as different vertexes on the hypergraph, representing the time domain data as one-dimensional time sequences on the vertexes of the hypergraph, and defining an incidence matrix; 4, designing a space-time hypergraph neural network model to carry out space-time correlation modeling on the bridge monitoring data; 5, training the space-time hypergraph neural network model by using monitoring data within half a year at the initial stage of bridge operation; and 6, applying the trained space-time hypergraph neural network model to monitoring data after half a year. According to the method, the defect that a data-driven response prediction method is insufficient in mining of the monitoring data space-time correlation degree is overcome, and multi-step accurate prediction of the monitoring data is achieved.

Description

Technical Field

[0001] The present invention relates to a method for bridge structure health monitoring, and more particularly to a method for accurate multi-step prediction of bridge monitoring data based on spatio-temporal hypergraph neural network. Background Art

[0002] In modern society, bridges have become a microcosm of social development. As one of the important social assets, bridges are not only the lifeline of transportation, but also a symbol of the development of the national economy, industry and technology. Accurately grasping the mechanical behavior of bridge responses over a period of time can enable timely condition assessment and maintenance decision-making. In the past 40 years, structural health monitoring systems have been widely applied in bridges, laying a solid foundation for achieving this goal by continuously recording monitoring data. An important function of the structural health monitoring system is to predict future responses based on historical and current data and issue possible safety warnings before they become reality. Therefore, establishing a model with high prediction accuracy in the multi-step prediction task is crucial for the operation of bridges.

[0003] Since all components belong to the same system, there are natural deformation constraints among them, and there are inherent correlations among these natural constraints, which are related to the relative spatial position and influence mode. Specifically, on the one hand, it is difficult to represent their spatial positions with regular grids; on the other hand, the deformation of a single component affects the deformation of multiple components, and this influence mode is not pairwise. The above analysis is reflected in the structural responses, that is, there are inherent non-Euclidean high-order correlations among the structural responses. Whether such correlations can be deeply and effectively mined is a prerequisite for achieving high-precision prediction results. However, most of the existing models either ignore the non-Euclidean features and use simple traditional convolutional architectures for analysis, or ignore the high-order correlation features and use graph neural networks based on simple graphs for analysis. Therefore, designing a multi-step prediction neural network model that can mine the non-Euclidean high-order correlation patterns among responses can provide more accurate prediction results than traditional models, so that bridge operators can carry out condition assessment work in a timely manner, which is of great significance for the scientific operation of data-driven bridge structures. Summary of the Invention

[0004] In order to solve the problem of low accuracy in multi-step prediction of current bridge structure monitoring data, the present invention provides a method for accurate multi-step prediction of bridge monitoring data based on spatio-temporal hypergraph neural network. This method solves the shortcoming of insufficient mining of the spatio-temporal correlation degree of monitoring data by data-driven response prediction methods, realizes multi-step accurate prediction of monitoring data, and is applicable to the scientific operation of bridge structures equipped with structural health monitoring systems.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] An accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network includes the following steps:

[0007] Step 1: Collect the spatiotemporal monitoring two-dimensional data of bridge structures as the original data set;

[0008] Step 2: Perform missing data filling, trend extraction, and data standardization preprocessing operations on the original data set;

[0009] Step 3: Represent the spatial domain data as different vertices on the hypergraph, represent the time domain data as one-dimensional time series on each vertex of the hypergraph, and define the association matrix through a static method based on clustering or a dynamic method based on automatic parameter update;

[0010] Step 4: Design a spatiotemporal hypergraph neural network model to model the spatiotemporal correlation of bridge monitoring data;

[0011] Step 5: Use the monitoring data from the initial half-year operation phase of the bridge to train the spatiotemporal hypergraph neural network model;

[0012] Step 6: Apply the trained spatiotemporal hypergraph neural network model to the monitoring data six months later.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] 1. The present invention performs multi-step prediction of data by mining high-order correlations between monitoring data, effectively solving the shortcoming of data-driven response prediction methods that the temporal and spatial correlations of monitoring data are insufficiently mined, and realizes multi-step accurate prediction of monitoring data.

[0015] 2. The present invention can make high-precision predictions of monitoring data within the next 12 steps, and effectively proves the advanced nature of prediction accuracy by introducing other classic multi-step prediction methods for comparison. It is suitable for the operation of bridge structures equipped with structural health monitoring systems, and provides a scientific basis for status assessment and decision-making of serving bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic flow chart of the accurate multi-step prediction method of bridge monitoring data based on spatiotemporal hypergraph neural network of the present invention;

[0017] Figure 2 This is a data preprocessing diagram for step 2 of the embodiment;

[0018] Figure 3 This is the clustering result diagram of step three of the embodiment;

[0019] Figure 4 This is the structure diagram of the spatiotemporal hypergraph neural network in step 4 of the embodiment;

[0020] Figure 5The loss function curve decline graph during the training in Step Five of the embodiment;

[0021] Figure 6 The comparison graph of all evaluation indexes of the overall prediction effect in Step Six of the embodiment;

[0022] Figure 7 The comparison graph of the MAE index of the overall prediction effect in Step Six of the embodiment;

[0023] Figure 8 The scatter plot of the predicted value and the true value of a certain sensor in Step Six of the embodiment;

[0024] Figure 9 The time series graph of the predicted value and the true value of a certain sensor in Step Six of the embodiment. Specific implementation mode

[0025] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0026] The present invention provides an accurate multi-step prediction method for bridge monitoring data based on a spatio-temporal hypergraph neural network, as Figure 1 shown, the method includes the following steps:

[0027] Step 1: Collect two-dimensional spatio-temporal monitoring data of the bridge structure as the original data set.

[0028] In this step, the two-dimensional spatio-temporal monitoring data is data with spatio-temporal dimension attributes generated by the same type of N cable force sensors installed at different positions on a certain side tower and a certain side of the cable-stayed bridge at the same sampling frequency.

[0029] Step 2: Perform preprocessing operations on the original data set, including missing data filling, trend extraction, and data standardization.

[0030] In this step, the missing data filling preprocessing operation is implemented based on the cubic interpolation method, and the specific formula is:

[0031]

[0032] In the formula, f(x) is the interpolation calculation result of the missing data, x is the time axis coordinate of the missing data, x 1 is the second nearest neighbor non-missing data coordinate on the left side of x, x 2 is the nearest neighbor non-missing data coordinate on the left side of x, x 3 is the nearest neighbor non-missing data coordinate on the right side of x, x 4 is the second nearest neighbor non-missing data coordinate on the right side of x, f(x 1 ) is x1 The moment corresponds to the real data, f(x 2 ) is x 2 The moment corresponds to the real data, f(x 3 ) is x 3 The moment corresponds to the real data, f(x 4 ) is x 4 The moment corresponds to the real data.

[0033] In this step, the trend extraction preprocessing operation is implemented based on the moving average method, and the specific formula is:

[0034] f(x) trend = Avg(f(x):f(x + sl))

[0035] In the formula, f(x trend is the trend component at time x, Avg(f(x):f(x + sl)) is the average value of the data from f(x) to f(x + sl), and sl is the moving step size.

[0036] In this step, the data normalization preprocessing operation is implemented based on the z-score method, and the specific formula is:

[0037]

[0038] In the formula, is the normalized value of the j-th data of sensor i, is the trend value of the j-th data of sensor i, μ i is the mean of all trend data of sensor i, and σ i is the standard deviation of all trend data of sensor i.

[0039] Step 3: Represent the spatial domain data as different vertices on the hypergraph, represent the time domain data as one-dimensional time series on each vertex of the hypergraph, and define the adjacency matrix through a static method based on clustering or through a dynamic method based on automatic parameter update.

[0040] In this step, the specific method for defining the adjacency matrix by the static method based on clustering is: Before model training, cluster the mean values of the preprocessed data of each sensor by the K-means method to define the adjacency matrix. All vertices within the same cluster are connected by hyperedges, and vertices in different clusters are not connected, that is, the hypergraph structure is predefined. When selecting the optimal number of clusters (hyperedges), the average silhouette coefficient is used as the evaluation index, and the specific formula is:

[0041]

[0042] a(i) = Avg i,j∈A,j≠i (dist(i,j))

[0043] b(i) = min B≠A (average i∈A,j∈B (dist(i, j)))

[0044]

[0045] where Sc is the average silhouette coefficient, s(i) is the silhouette coefficient of sensor i, a(i) is the average distance between sensor i and all other sensors in the same cluster as it, b(i) is the minimum average value between sensor i and all other sensors in different clusters from it, H ∈ R N×E is the incidence matrix, E is the number of optimal clusters (hyperedges), and N is the number of cable force sensors. Based on the clustering result, if sensor v is connected to hyperedge e, then H(v, e) = 1; if not, then H(v, e) = 0.

[0046] In this step, the specific method for defining the incidence matrix based on the dynamic method of automatic parameter update is as follows: During model training, the incidence matrix is regarded as a parameter to be learned. The connection relationship is updated iteratively through parameters, and the element values in the incidence matrix are updated iteratively through parameters, that is, the hypergraph structure is not predefined in advance. The specific formula is:

[0047] H = ReLU(E 1 E 2 )

[0048] where and are embedding matrices to be learned, and E b is the embedding dimension.

[0049] Step 4: Design a spatio-temporal hypergraph neural network model mainly composed of a one-dimensional gated convolutional layer and a hypergraph convolutional layer to perform spatio-temporal correlation modeling on bridge monitoring data.

[0050] In this step, the spatio-temporal hypergraph neural network model includes a fully connected layer, a hypergraph convolutional layer, a one-dimensional gated convolutional layer, and a batch normalization layer. The specific structure is as follows:

[0051] Layer L0: Fully connected layer. The input data scale size is N × 1 × T. Each dimension in the three-dimensional data represents space, feature, and time respectively. This layer operates on the feature dimension. The number of input features is 1, and the number of output features is F hidden1 , and the output data scale size is N × F hidden1 × T;

[0052] Layer L1-1: One-dimensional gated convolutional layer, connected to layer L0 above. This layer operates on the time and feature dimensions. The number of input features is F hidden1 , the convolutional kernel size is K, the depth is F hidden1 , and the number is F hidden2, the dilation value is 1, and the number of output features is F hidden2 , the output data scale size is N×F hidden2 ×(T-(K-1));

[0053] Layer L1-2: Hypergraph convolutional layer, connected to Layer L1-1 above. This layer operates in the spatial and feature dimensions, and the number of input features is F hidden2 , the number of output features is F hidden3 , the output data scale size is N×F hidden3 ×(T-(K-1));

[0054] Layer L1-3: One-dimensional gated convolutional layer, connected to Layer L1-2 above. This layer operates in the time and feature dimensions, and the number of input features is F hidden3 , the convolutional kernel size is K, and the depth is F hidden3 , the quantity is F hidden1 , the dilation value is 2, and the number of output features is F hidden1 , the output data scale size is N×F hidden1 ×(T-3(K-1));

[0055] Layer L1-4: Batch normalization layer, connected to Layer L1-1 and Layer L1-3 above. This layer has no parameters to be learned. After accumulating the output data of Layer L1-1 and Layer L1-3 (truncating and matching backward in the time dimension), batch normalization is performed, and the output data scale size is N×F hidden1 ×(T-3(K-1));

[0056] Layer L2-1: One-dimensional gated convolutional layer, connected to Layer L1-4 above. This layer operates in the time and feature dimensions, and the number of input features is F hidden1 , the convolutional kernel size is K, and the depth is F hidden1 , the quantity is F hidden2 , the dilation value is 1, and the number of output features is F hidden2 , the output data scale size is N×F hidden2 ×(T-4(K-1));

[0057] Layer L2-2: Hypergraph convolutional layer, connected to Layer L2-1 above. This layer operates in the spatial and feature dimensions, and the number of input features is F hidden2 , the number of output features is F hidden3 , the output data scale size is N×F hidden3 ×(T-4(K-1));

[0058] Layer L2-3: One-dimensional gated convolutional layer, connected to Layer L2-2 above. This layer operates in the time and feature dimensions, and the number of input features is F hidden3 , the convolutional kernel size is K, and the depth is F hidden3 , the quantity is Fhidden1 , with a dilation value of 2 and the number of output features being F hidden1 , and the output data scale size being N×F hidden1 ×(T - 6(K - 1));

[0059] Layer L2-4: Batch normalization layer, connected to L2-1 and L2-3 layers above. This layer accumulates the output data of L2-1 and L2-3 layers (truncating and matching from the back in the time dimension) and then performs batch normalization. The output data scale size is N×F hidden1 ×(T - 6(K - 1));

[0060] Layer L3-1: 1D gated convolutional layer, connected to L2-4 layer above. This layer operates in both time and feature dimensions, with the number of input features being F hidden1 , with a convolutional kernel size of K and a depth of F hidden1 , and the number being F hidden2 , with a dilation value of 1 and the number of output features being F hidden2 , and the output data scale size being N×F hidden2 ×(T - 7(K - 1));

[0061] Layer L3-2: Hypergraph convolutional layer, connected to L3-1 layer above. This layer operates in both spatial and feature dimensions, with the number of input features being F hidden2 , with the number of output features being F hidden3 , and the output data scale size being N×F hidden3 ×(T - 7(K - 1));

[0062] Layer L3-3: 1D gated convolutional layer, connected to L3-2 layer above. This layer operates in both time and feature dimensions, with the number of input features being F hidden3 , with a convolutional kernel size of K and a depth of F hidden3 , and the number being F hidden1 , with a dilation value of 2 and the number of output features being F hidden1 , and the output data scale size being N×F hidden1 ×(T - 9(K - 1));

[0063] Layer L3-4: Batch normalization layer, connected to L3-1 and L3-3 layers above. This layer accumulates the output data of L3-1 and L3-3 layers (truncating and matching from the back in the time dimension) and then performs batch normalization. The output data scale size is N×F hidden1 ×(T - 9(K - 1));

[0064] Layer L4-1: 1D gated convolutional layer, connected to L3-4 layer above. This layer operates in both time and feature dimensions, with the number of input features being F hidden1 , with a convolutional kernel size of K and a depth of F hidden1 , and the number being Fhidden2 with a dilation value of 1 and the number of output features being F hidden2 and the output data scale size being N×F hidden2 ×(T - 10(K - 1));

[0065] Layer L4-2: Hypergraph convolutional layer, connected to layer L4-1 above. This layer operates in the spatial and feature dimensions, with the number of input features being F hidden2 and the number of output features being F hidden3 and the output data scale size being N×F hidden3 ×(T - 10(K - 1));

[0066] Layer L4-3: 1D gated convolutional layer, connected to layer L4-2 above. This layer operates in the time and feature dimensions, with the number of input features being F hidden3 with the convolutional kernel size being K and the depth being F hidden3 and the number being F hidden1 with a dilation value of 2 and the number of output features being F hidden1 and the output data scale size being N×F hidden1 ×1;

[0067] Layer L4-4: Batch normalization layer, connected to layers L4-1 and L4-3 above. This layer performs batch normalization after accumulating the output data of layers L4-1 and L4-3 (truncating and matching in the time dimension from back to front), and the output data scale size is N×F hidden1 ×1;

[0068] Layer L5: Fully connected layer, connected to layers L1-4, L2-4, L3-4, and L4-4 above. This layer operates in the feature dimension after accumulating the output data of layers L1-4, L2-4, L3-4, and L4-4 (truncating and matching in the time dimension from back to front), with the number of input features being F hidden1 and the number of output features being F hidden4 and the output data scale size being N×F hidden4 ×1;

[0069] Layer L6: Fully connected layer, connected to layer L5 above. This layer operates in the feature dimension, with the number of input features being F hidden4 and the number of output features being the prediction length T predict and after transposition, the output data scale size is N×1×T predict .

[0070] In this step, there is no activation function in layer L0, the activation functions in layers L1-1 and L1-3 are Tanh and Sigmoid, the activation function in layer L1-2 is ReLU, there is no activation function in layer L1-4, the internal activation functions in layers L2-L4 are set the same as those in layer L1, and the activation functions in layers L5 and L6 are ReLU.

[0071] In this step, the formula for the one-dimensional gated convolutional layer is as follows:

[0072]

[0073] In the formula, Gt (l) (X (l) ) is the output of the l-th one-dimensional gated convolutional layer, and X (l) is the input of the l-th one-dimensional gated convolutional layer. is the convolutional kernel weight parameter, b and c are bias parameters, and ⊙ represents the Hadamard product.

[0074] In this step, the formula for the hypergraph convolutional layer is as follows:

[0075]

[0076] D e = diag[δ(e 1 ), δ(e 2 ),..., δ(e E )]

[0077] W = diag[w(e 1 ), w(e 2 ),..., w(e E )]

[0078] d(v i ) = Σ e∈E w(e)H(v i , e)

[0079]

[0080] In the formula, is the output of the l-th hypergraph convolutional layer, is the input of the l-th hypergraph convolutional layer, D v is the degree matrix of vertices, D e is the degree matrix of hyperedges, W is the weight matrix of vertices, d(v 1 ) is the degree of vertex v 1 , δ(e 1 ) is the degree of hyperedge e 1 , w(e 1 ) is the weight of hyperedge e 1 , and E, respectively represent the hyperedge set and the vertex set.

[0081] Step 5: Use the monitoring data within the first six months of the initial operation stage of the bridge to train the spatio-temporal hypergraph neural network model.

[0082] In this step, the training of the spatiotemporal hypergraph neural network model is based on mini-batch gradient descent, where the batch size is bt, the learning rate is lr, the number of training rounds is ne, the loss function is the mean square error function, and the optimization method is the adaptive moment estimation method.

[0083] Step 6: Apply the trained spatiotemporal hypergraph neural network model to the monitoring data six months later, and introduce and apply other classic machine learning / deep learning models to evaluate their multi-step prediction capabilities and demonstrate the advancement of the present invention.

[0084] In this step, the evaluation indicators are root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAE), determination coefficient (R 2 ), the specific formula is:

[0085]

[0086] In the formula, y i is the true value of the data, is the data prediction value, and S is the number of test set instances. The smaller the RMSE, MAE, and MAPE, the better the R 2 The larger it is, the better the model prediction performance is.

[0087] Example:

[0088] This embodiment provides a method for accurate multi-step prediction of bridge monitoring data based on a spatiotemporal hypergraph neural network, the method comprising the following steps:

[0089] Step 1: Collect the spatiotemporal monitoring two-dimensional data of bridge structures as the original data set.

[0090] In this step, the two-dimensional spatiotemporal monitoring data is derived from 42 cable tension sensors of the same type installed at different positions on a certain side of a cable tower on a cable-stayed bridge, which are generated at a sampling frequency of 10 Hz and have spatiotemporal dimensional attributes.

[0091] Step 2: Perform missing data filling, trend extraction, and data standardization preprocessing operations on the original data set, including:

[0092] In this step, the missing data filling preprocessing operation is implemented based on the cubic interpolation method. The specific formula is:

[0093]

[0094] Where f(x) is the interpolation result of missing data, x is the time axis coordinate of missing data, and x 1 is the coordinate of the next nearest non-missing data to the left of x, x 2 is the coordinate of the nearest non-missing data to the left of x, 3is the coordinate of the nearest non-missing data to the right of x, x 4 is the coordinate of the second nearest non-missing data to the right of x, f(x 1 ) is x 1 corresponds to the real data at the moment, and so on.

[0095] In this step, the trend extraction preprocessing operation is implemented based on the moving average method, as Figure 2 shown. The specific formula is:

[0096] f(x) trend = Avg(f(x):f(x + sl))

[0097] In the formula, f(x) trend is the trend component at time x, Avg(f(x):f(x + sl)) is the average value of the data from f(x) to f(x + sl), and sl is the moving step size, taking 10 min.

[0098] In this step, the data normalization preprocessing operation is implemented based on the z-score method. The specific formula is:

[0099]

[0100] In the formula, is the normalized value of the j-th data of sensor i, is the trend value of the j-th data of sensor i, μ i is the mean of all trend data of sensor i, and σ i is the standard deviation of all trend data of sensor i.

[0101] Step 3: Represent the spatial domain data as different vertices on a hypergraph, represent the time domain data as a one-dimensional time series on each vertex of the hypergraph, and define the adjacency matrix through a static method based on clustering or through a dynamic method with automatic parameter update.

[0102] In this step, the specific method for defining the adjacency matrix by the static method based on clustering is as follows: Before model training, cluster the means of the preprocessed data of each sensor by the K-means method to define the adjacency matrix. All vertices within the same cluster are connected by hyperedges, and vertices in different clusters are not connected. That is, the hypergraph structure is predefined. When selecting the optimal number of clusters (hyperedges), the average silhouette coefficient is used as the evaluation index. The specific formula is:

[0103]

[0104] a(i) = Avg i,j∈A,j≠i (dist(i,j))

[0105] b(i) = min B≠A (averagei∈A,j∈B (dist(i,j)))

[0106]

[0107] Where Sc is the average silhouette coefficient, s(i) is the silhouette coefficient of sensor i, a(i) is the average distance between sensor i and all other sensors in its same cluster, b(i) is the minimum average value between sensor i and all other sensors in its different clusters, and H ∈ R 42×E is the incidence matrix, and E is the number of optimal clusters (hyperedges). Based on the clustering result, if sensor v is connected to hyperedge e, then H(v,e) = 1; if not, then H(v,e) = 0. The obtained average silhouette coefficient is as Figure 3 shown, and it can be seen that E = 9. Name the hypergraph neural network designed based on the static method as STHGCN(S).

[0108] In this step, the specific method for defining the incidence matrix based on the dynamic method with automatic parameter update is as follows: During model training, the incidence matrix is regarded as a parameter to be learned, the connection relationship is updated iteratively through parameters, and the element values in the incidence matrix are updated iteratively through parameters, that is, the hypergraph structure is not predefined. The specific formula is:

[0109] H = ReLU(E 1 E 2 )

[0110] Where and are embedding matrices to be learned, and E b is the embedding dimension, taking 7. Name the hypergraph neural network designed based on the dynamic method as STHGCN(D).

[0111] Step 4: Design a spatio-temporal hypergraph neural network model mainly composed of a one-dimensional gated convolutional layer and a hypergraph convolutional layer to perform spatio-temporal correlation modeling on bridge monitoring data.

[0112] As Figure 4 shown, the designed spatio-temporal hypergraph neural network model includes a fully connected layer, a hypergraph convolutional layer, a one-dimensional gated convolutional layer, and a batch normalization layer, where:

[0113] The L0 (fully connected) layer, the input data scale size is 42×1×12. Each dimension in the three-dimensional data represents space, feature, and time respectively. This layer operates on the feature dimension, the number of input features is 1, the number of output features is 32, and the output data scale size is 42×32×12;

[0114] The L1-1 (1D gated convolution) layer, connected to the L0 layer above, operates in the time and feature dimensions. It has 32 input features, a convolution kernel size of 2, a depth of 32, a quantity of 16, a dilation value of 1, 16 output features, and an output data scale size of 42×16×11;

[0115] The L1-2 (hypergraph convolution) layer, connected to the L1-1 layer above, operates in the spatial and feature dimensions. It has 16 input features, 8 output features, and an output data scale size of 42×8×11;

[0116] The L1-3 (1D gated convolution) layer, connected to the L1-2 layer above, operates in the time and feature dimensions. It has 8 input features, a convolution kernel size of 2, a depth of 8, a quantity of 32, a dilation value of 2, 32 output features, and an output data scale size of 42×32×9;

[0117] The L1-4 (batch normalization) layer, connected to the L1-1 layer and L1-3 layer above, has no parameters to be learned. It performs batch normalization after accumulating the output data of the L1-1 layer and L1-3 layer (truncating and matching in the backward direction in the time dimension), and the output data scale size is 42×32×9;

[0118] The L2-1 (1D gated convolution) layer, connected to the L1-4 layer above, operates in the time and feature dimensions. It has 32 input features, a convolution kernel size of 2, a depth of 32, a quantity of 16, a dilation value of 1, 16 output features, and an output data scale size of 42×16×8;

[0119] The L2-2 (hypergraph convolution) layer, connected to the L2-1 layer above, operates in the spatial and feature dimensions. It has 16 input features, 8 output features, and an output data scale size of 42×8×8;

[0120] The L2-3 (1D gated convolution) layer, connected to the L2-2 layer above, operates in the time and feature dimensions. It has 8 input features, a convolution kernel size of 2, a depth of 8, a quantity of 32, a dilation value of 2, 32 output features, and an output data scale size of 42×32×6;

[0121] The L2-4 (batch normalization) layer, connected to the L2-1 layer and L2-3 layer above, performs batch normalization after accumulating the output data of the L2-1 layer and L2-3 layer (truncating and matching in the backward direction in the time dimension), and the output data scale size is 42×32×6;

[0122] The L3-1 (1D gated convolution) layer, connected to the L2-4 layer above, operates in the time and feature dimensions. The number of input features is 32, the convolution kernel size is 2, the depth is 32, the number is 16, the dilation value is 1, the number of output features is 16, and the output data scale size is 42×16×5;

[0123] The L3-2 (hypergraph convolution) layer, connected to the L3-1 layer above, operates in the spatial and feature dimensions. The number of input features is 16, the number of output features is 8, and the output data scale size is 42×8×5;

[0124] The L3-3 (1D gated convolution) layer, connected to the L3-2 layer above, operates in the time and feature dimensions. The number of input features is 8, the convolution kernel size is 2, the depth is 8, the number is 32, the dilation value is 2, the number of output features is 32, and the output data scale size is 42×8×3;

[0125] The L3-4 (batch normalization) layer, connected to the L3-1 layer and L3-3 layer above, performs batch normalization after accumulating the output data of the L3-1 layer and L3-3 layer (truncating and matching from back to front in the time dimension), and the output data scale size is 42×8×3;

[0126] The L4-1 (1D gated convolution) layer, connected to the L3-4 layer above, operates in the time and feature dimensions. The number of input features is 32, the convolution kernel size is 2, the depth is 32, the number is 16, the dilation value is 1, the number of output features is 16, and the output data scale size is 42×16×2;

[0127] The L4-2 (hypergraph convolution) layer, connected to the L4-1 layer above, operates in the spatial and feature dimensions. The number of input features is 16, the number of output features is 8, and the output data scale size is 42×8×2;

[0128] The L4-3 (1D gated convolution) layer, connected to the L4-2 layer above, operates in the time and feature dimensions. The number of input features is 8, the convolution kernel size is 2, the depth is 8, the number is 32, the dilation value is 2, the number of output features is 32, and the output data scale size is 42×32×1;

[0129] The L4-4 (batch normalization) layer, connected to the L4-1 layer and L4-3 layer above, performs batch normalization after accumulating the output data of the L4-1 layer and L4-3 layer (truncating and matching from back to front in the time dimension), and the output data scale size is 42×32×1;

[0130] The L5 (fully connected) layer is connected to the L1-4 layer, L2-4 layer, L3-4 layer, and L4-4 layer. This layer accumulates the output data of the L1-4 layer, L2-4 layer, L3-4 layer, and L4-4 layer (truncating and matching from the back to the front in the time dimension) and then operates in the feature dimension. The number of input features is 32, the number of output features is 64, and the scale size of the output data is 42×64×1;

[0131] The L6 (fully connected) layer is connected to the L5 layer. This layer operates in the feature dimension. The number of input features is 64, the number of output features is the predicted length 12, and after transposition, the scale size of the output data is 42×1×64;

[0132] There is no activation function in the L0 layer, the activation functions in the L1-1 layer and L1-3 layer are Tanh and Sigmoid, the activation function in the L1-2 layer is ReLU, there is no activation function in the L1-4 layer, the internal activation functions in the L2-L4 layers are set the same as those in the L1 layer, and the activation functions in the L5 layer and L6 layer are ReLU;

[0133] The formula for the one-dimensional gated convolutional layer is:

[0134]

[0135] In the formula, Gt (l) (X (l) ) is the output of the l-th one-dimensional gated convolutional layer, X (l) is the input of the l-th one-dimensional gated convolutional layer, is the convolutional kernel weight parameter, b and c are bias parameters, and ⊙ is the Hadamard product;

[0136] The formula for the hypergraph convolutional layer is:

[0137]

[0138] D e =diag[δ(e 1 ),δ(e 2 ),...,δ(e E )]

[0139] W=diag[w(e 1 ),w(e 2 ),...,w(e E )]

[0140] d(v i )=Σ e∈E w(e)H(v i ,e)

[0141]

[0142] In the formula, is the output of the l-th hypergraph convolutional layer, is the input of the l-th hypergraph convolutional layer, D v is the degree matrix of vertices, D e is the degree matrix of hyperedges, W is the weight matrix of vertices, d(v 1 ) is the degree of vertex v 1 of, δ(e 1 ) is the hyperedge e 1 of, w(e 1 ) is the hyperedge e 1 of the weight.

[0143] Step 5: Select the standardized trend data from May 2006 to December 2006 to train the spatio-temporal hypergraph neural network model. The training model is implemented based on mini-batch gradient descent. The batch size is 64, the learning rate is 1E-3, the number of training epochs is 50, the loss function is the mean square error function, the optimization method is the adaptive moment estimation method, and the loss function decreases during training as Figure 5 shown. It can be seen that the model converges with iterations during training, without underfitting and overfitting phenomena.

[0144] Step 6: Select the data in February 2007 for testing, and introduce the classical machine learning M-SVR model, the classical deep learning ConvLSTM model and the GWN model for comparison. The multiple prediction tasks are 1-step prediction, 2-step prediction, 3-step prediction, 6-step prediction and 12-step prediction. The evaluation metrics are root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), coefficient of determination (R 2 ), and the specific formulas are:

[0145]

[0146] In the formula, y i is the true value of the data, is the predicted value of the data, S is the number of test set instances, which is 3295. The smaller the RMSE, MAE, and MAPE, and the larger the R 2 , the better the model prediction performance. The prediction results of each model are as Figures 6 to 9 shown. It can be seen that the hypergraph-based STHGCN(S) and STHGCN(D) models perform significantly better than the non-hypergraph-based M-SVR model, ConvLSTM model and GWN model in multi-step prediction tasks.

Claims

1. An accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network, characterized by The method comprises the following steps: Step 1: Collect the spatiotemporal monitoring two-dimensional data of bridge structures as the original data set; Step 2: Perform missing data filling, trend extraction, and data standardization preprocessing operations on the original data set; Step 3: Represent the spatial domain data as different vertices on the hypergraph, represent the time domain data as one-dimensional time series on each vertex of the hypergraph, and define the association matrix through a static method based on clustering or a dynamic method based on automatic parameter update; Step 4: Design a spatiotemporal hypergraph neural network model to perform spatiotemporal correlation modeling on bridge monitoring data. The spatiotemporal hypergraph neural network model includes a fully connected layer, a hypergraph convolution layer, a one-dimensional gated convolution layer, and a batch normalization layer. The specific structure is as follows: L0 layer: fully connected layer, the input data scale is N×1×T, each dimension in the three-dimensional data represents space, feature, and time. This layer operates on the feature dimension, the input feature number is 1, and the output feature number is F hidden1 , the output data scale is N×F hidden1 ×T; Layer L1-1: One-dimensional gated convolution layer, connected to layer L0, this layer operates on the time and feature dimensions, and the number of input features is F hidden1 , the convolution kernel size is K and the depth is F hidden1 , the quantity is F hidden2 , the dilation value is 1, and the output feature number is F hidden2 , the output data scale is N×F hidden2 ×(T-(K-1)); Layer L1-2: Hypergraph convolutional layer, connected to layer L1-1, this layer operates on the spatial and feature dimensions, and the number of input features is F hidden2 , the output feature number is F hidden3 , the output data scale is N×F hidden3 ×(T-(K-1)); Layer L1-3: One-dimensional gated convolution layer, connected to layer L1-2, this layer operates on the time and feature dimensions, and the number of input features is F hidden3 , the convolution kernel size is K and the depth is F hidden3 , the quantity is F hidden1 , the dilation value is 2, and the output feature number is F hidden1 , the output data scale is N×F hidden1 ×(T-3(K-1)); L1-4 layer: Batch normalization layer, connected to L1-1 layer and L1-3 layer. This layer has no parameters to be learned. It performs batch normalization after accumulating the output data of L1-1 layer and L1-3 layer. The scale of the output data is N×F hidden1 ×(T-3(K-1)); Layer L2-1: One-dimensional gated convolution layer, connected to layer L1-4, this layer operates on the time and feature dimensions, and the number of input features is F hidden1 , the convolution kernel size is K and the depth is F hidden1 , the quantity is F hidden2 , the dilation value is 1, and the output feature number is F hidden2 , the output data scale is N×F hidden2 ×(T-4(K-1)); Layer L2-2: Hypergraph convolutional layer, connected to layer L2-1, this layer operates on the spatial and feature dimensions, and the number of input features is F hidden2 , the output feature number is F hidden3 , the output data scale is N×F hidden3 ×(T-4(K-1)); Layer L2-3: One-dimensional gated convolution layer, connected to layer L2-2, this layer operates on the time and feature dimensions, and the number of input features is F hidden3 , the convolution kernel size is K and the depth is F hidden3 , the quantity is F hidden1 , the dilation value is 2, and the output feature number is F hidden1 , the output data scale is N×F hidden1 ×(T-6(K-1)); Layer L2-4: Batch normalization layer, connected to L2-1 and L2-3 layers. This layer accumulates the output data of L2-1 and L2-3 layers and performs batch normalization. The output data scale is N×F hidden1 ×(T-6(K-1)); Layer L3-1: One-dimensional gated convolution layer, connected to layer L2-4, this layer operates on the time and feature dimensions, and the number of input features is F hidden1 , the convolution kernel size is K and the depth is F hidden1 , the quantity is F hidden2 , the dilation value is 1, and the output feature number is F hidden2 , the output data scale is N×F hidden2 ×(T-7(K-1)); Layer L3-2: Hypergraph convolutional layer, connected to layer L3-1, this layer operates on the spatial and feature dimensions, and the number of input features is F hidden2 , the output feature number is F hidden3 , the output data scale is N×F hidden3 ×(T-7(K-1)); Layer L3-3: One-dimensional gated convolution layer, connected to layer L3-2, this layer operates on the time and feature dimensions, and the number of input features is F hidden3 , the convolution kernel size is K and the depth is F hidden3 , the quantity is F hidden1 , the dilation value is 2, and the output feature number is F hidden1 , the output data scale is N×F hidden1 ×(T-9(K-1)); L3-4 layer: Batch normalization layer, connected to L3-1 layer and L3-3 layer. This layer accumulates the output data of L3-1 layer and L3-3 layer and performs batch normalization. The output data scale is N×F hidden1 ×(T-9(K-1)); Layer L4-1: One-dimensional gated convolution layer, connected to layer L3-4, this layer operates on the time and feature dimensions, and the number of input features is F hidden1 , the convolution kernel size is K and the depth is F hidden1 , the quantity is F hidden2 , the dilation value is 1, and the output feature number is F hidden2 , the output data scale is N×F hidden2 ×(T-10(K-1)); Layer L4-2: Hypergraph convolutional layer, connected to layer L4-1, this layer operates on the spatial and feature dimensions, and the number of input features is F hidden2 , the output feature number is F hidden3 , the output data scale is N×F hidden3 ×(T-10(K-1)); Layer L4-3: One-dimensional gated convolution layer, connected to layer L4-2, this layer operates on the time and feature dimensions, and the number of input features is F hidden3 , the convolution kernel size is K and the depth is F hidden3 , the quantity is F hidden1 , the dilation value is 2, and the output feature number is F hidden1 , the output data scale is N×F hidden1 ×1; L4-4 layer: Batch normalization layer, connected to L4-1 layer and L4-3 layer. This layer accumulates the output data of L4-1 layer and L4-3 layer and performs batch normalization. The output data scale is N×F hidden1 ×1; L5 layer: fully connected layer, connected to L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer. This layer accumulates the output data of L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer and operates on the feature dimension. The input feature number is F hidden1 , the output feature number is F hidden4 , the output data scale is N×F hidden4 ×1; L6 layer: fully connected layer, connected to L5 layer, this layer operates on the feature dimension, the input feature number is F hidden4 , the output feature number is the prediction length T predict , after transposition, the output data scale is N×1×T predict ; Step 5: Use the monitoring data from the initial half-year operation phase of the bridge to train the spatiotemporal hypergraph neural network model; Step 6: Apply the trained spatiotemporal hypergraph neural network model to the monitoring data six months later.

2. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 1, the two-dimensional spatiotemporal monitoring data is derived from data with spatiotemporal dimensional attributes generated by N cable tension sensors of the same type installed at different positions on a certain side of a cable tower on a cable-stayed bridge at the same sampling frequency.

3. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 2, the missing data filling preprocessing operation is implemented based on the cubic interpolation method, and the specific formula is: Where f(x) is the interpolation result of missing data, x is the time axis coordinate of missing data, x1 is the coordinate of the next nearest neighbor non-missing data on the left side of x, x2 is the coordinate of the nearest neighbor non-missing data on the left side of x, x3 is the coordinate of the nearest neighbor non-missing data on the right side of x, x4 is the coordinate of the next nearest neighbor non-missing data on the right side of x, f(x1) is the real data corresponding to time x1, f(x2) is the real data corresponding to time x2, f(x3) is the real data corresponding to time x3, and f(x4) is the real data corresponding to time x4.

4. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 2, the trend extraction preprocessing operation is implemented based on the sliding average method, and the specific formula is: f(x) trend =Avg(f(x):f(x+sl)) Where f(x) trend is the trend component at time x, Avg(f(x):f(x+sl)) is the average value of the data from f(x) to f(x+sl), and sl is the sliding step size.

5. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In step 2, the data standardization preprocessing operation is implemented based on the z-score method, and the specific formula is: In the formula, is the normalized value of the jth data of sensor i, is the jth data trend value of sensor i, μ i is the mean of all trend data of sensor i, σ i is the standard deviation of all trend data of sensor i.

6. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 3, the specific method of defining the association matrix based on the static method of clustering is: before model training, the K-means method is used to cluster the mean values ​​of the pre-processed sensor data to define the association matrix, all vertices in the same cluster are connected by hyperedges, and vertices in different clusters are not connected, that is, the hypergraph structure is pre-defined, and when selecting the optimal number of clusters, the average silhouette coefficient is used as an evaluation index, and the specific formula is: a(i)=Avg i,j∈A,j≠i (dist(i,j)) b(i)=min B≠A (average i∈A,j∈B (dist(i,j))) Where Sc is the average silhouette coefficient, s(i) is the silhouette coefficient of sensor i, a(i) is the average distance between sensor i and all other sensors in the same cluster, b(i) is the minimum average distance between sensor i and all other sensors in different clusters, and H∈R N×E is the correlation matrix, E is the optimal number of clusters, and N is the number of cable force sensors; Based on the clustering results, if the sensor v is connected to the hyperedge e, then H(v, e) = 1, if not connected, then H(v, e) = 0.

7. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 3, the specific method of defining the association matrix based on the dynamic method of automatic parameter update is: during model training, the association matrix is ​​used as a parameter to be learned, the connection relationship is updated through parameter iteration, and the element value in the association matrix is ​​updated through parameter iteration, that is, the hypergraph structure is not predefined. The specific formula is: H = ReLU(E1E2) In the formula, and is the embedding matrix to be learned, E b is the embedding dimension, H∈R N×E is the correlation matrix, and E is the optimal number of clusters.

8. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 4, the L0 layer has no activation function, the activation functions of the L1-1 layer and the L1-3 layer are Tanh and Sigmoid, the activation function of the L1-2 layer is ReLU, the L1-4 layer has no activation function, the internal activation function of the L2-L4 layer is set the same as the L1 layer, and the activation function of the L5 layer and the L6 layer is ReLU.

9. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In step 4, the formula of the one-dimensional gated convolutional layer is: In the formula, Gt (l) (X (l) ) is the output of the l-th dimensional gated convolutional layer, X (l) is the input of the l-th dimensional gated convolutional layer, is the convolution kernel weight parameter, b and c are bias parameters, and ⊙ is the Hadamard product. The formula of the hypergraph convolutional layer is: D e =diag[δ(e1),δ(e2),...,δ(e |ε| )] <h2 style=";text-align:left;direction:ltr">W = diag[w(e1),w(e2),...,w(e<h2 style=";text-align:left;direction:ltr"> |ε| <h2 style=";text-align:left;direction:ltr"> )] d(v i )mΣ e∈ε w(e)H(v i ,e) In the formula, is the output of the lth hypergraph convolutional layer, is the input of the lth hypergraph convolutional layer, D v is the degree matrix of the vertex, D e is the degree matrix of the hyperedge, W is the weight matrix of the vertex, d(v1) is the degree of vertex v1, δ(e1) is the degree of hyperedge e1, w(e1) is the weight of hyperedge e1, ε, Represent the hyperedge set and vertex set respectively.

10. The accurate multi-step prediction method for bridge monitoring data based on spatiotemporal hypergraph neural network according to claim 1 is characterized in that In the step 5, the training of the spatiotemporal hypergraph neural network model is implemented based on mini-batch gradient descent, wherein: the batch size is bt, the learning rate is lr, the number of training rounds is ne, the loss function is the mean square error function, and the optimization method is the adaptive moment estimation method.

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