Bridge monitoring data accurate multi-step prediction method based on spatio-temporal hypergraph neural network

Abstract

The application discloses a kind of bridge monitoring data accurate multi-step prediction method based on space-time hypergraph neural network, the method comprises the following steps: one, collect bridge structure space-time monitoring two-dimensional data as original data set;Two, original data set is carried out missing data filling, trend extraction, data standardization preprocessing operation;Three, space domain data is expressed as different vertex on hypergraph, time domain data is expressed as one-dimensional time series on each vertex of hypergraph, define correlation matrix;Four, design space-time hypergraph neural network model to carry out space-time correlation modeling to bridge monitoring data;Five, use the monitoring data in the initial stage of bridge operation within half a year to train space-time hypergraph neural network model;Six, the trained space-time hypergraph neural network model is applied to monitoring data after half a year.The application solves the shortcoming that data-driven response prediction method is insufficient in the degree of space-time correlation of monitoring data, realizes the multi-step accurate prediction of monitoring data.

Description

TECHNICAL FIELD

[0001] The application relates to a bridge structure health monitoring method, in particular to a bridge monitoring data accurate multi-step prediction method based on a space-time hypergraph neural network. BACKGROUND

[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 the symbol of national economy, industry and technology development. Accurate understanding of the mechanical behavior of bridge response in a period of time can timely evaluate the state and make maintenance decisions. In the past 40 years, structural health monitoring systems have been widely used in bridges, laying a solid foundation for achieving this goal. 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 the bridge.

[0003] Since all components belong to the same system, they have natural deformation constraints, and there is inherent correlation between these natural constraints, which is related to relative spatial position and influence mode. Specifically, on the one hand, their spatial positions are difficult to represent with regular grids; on the other hand, the deformation of a single component influences the deformation of multiple components, and the influence mode is not pairwise. The above analysis reflects on the structure response, that is, there is inherent non-Euclidean high-order correlation between the structure responses. Whether the correlation can be effectively mined is a prerequisite for achieving high-precision prediction results. However, existing models either ignore the non-Euclidean characteristics and use simple traditional convolution architectures for analysis, or ignore the high-order correlation characteristics 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 mode between responses can provide more accurate prediction results than traditional models, so as to enable the bridge operator to timely carry out state evaluation work, and has great significance for the scientific operation of data-driven bridge structures. SUMMARY

[0004] In order to solve the problem of low multi-step prediction accuracy of bridge structure monitoring data at present, the application provides a bridge monitoring data accurate multi-step prediction method based on a space-time hypergraph neural network. The method solves the problem of insufficient mining of time-space correlation degree of monitoring data in the response prediction method driven by data, realizes accurate multi-step prediction of monitoring data, and is suitable for scientific operation of bridge structures equipped with structural health monitoring systems.

[0005] The purpose of the application is achieved by the following technical solutions:

[0006] A bridge monitoring data accurate multi-step prediction method based on a space-time hypergraph neural network, comprising the following steps:

[0007] Step one, collecting bridge structure space-time monitoring two-dimensional data as an original data set;

[0008] Step two, performing missing data filling, trend extraction and data standardization preprocessing operations on the original data set;

[0009] Step three, representing spatial domain data as different vertices on a hypergraph, representing time domain data as a one-dimensional time sequence on each vertex of the hypergraph, and defining an association matrix based on a clustering-based static method or a dynamic method based on parameter automatic updating;

[0010] Step four, designing a space-time hypergraph neural network model to model the space-time association of bridge monitoring data;

[0011] Step five, training the space-time hypergraph neural network model using monitoring data within the first half year of bridge operation;

[0012] Step six, applying the trained space-time hypergraph neural network model to monitoring data after half a year.

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

[0014] 1. The present application can effectively solve the problem of insufficient mining of space-time association of monitoring data in data-driven response prediction methods, and realize accurate multi-step prediction of monitoring data.

[0015] 2. The present application can accurately predict monitoring data within 12 steps, and the advanced prediction accuracy is effectively proved by comparing with other classical multi-step prediction methods, which is suitable for bridge structures equipped with structural health monitoring systems and provides a scientific basis for the state evaluation and decision-making of service bridges. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The flowchart of the bridge monitoring data accurate multi-step prediction method based on the space-time hypergraph neural network of the present application;

[0017] Figure 2 The data preprocessing diagram of the embodiment step two;

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

[0019] Figure 4 The space-time hypergraph neural network structure diagram of the embodiment step four;

[0020] Figure 5This is a graph showing the decline of the loss function curve during training in step five of the embodiment;

[0021] Figure 6 This is a comparison chart of all evaluation indicators for the overall prediction effect of step 6 of the embodiment;

[0022] Figure 7 This is a comparison chart of the MAE indicators of the overall prediction effect of step 6 of the embodiment;

[0023] Figure 8 This is a scatter plot comparing the predicted value and the true value of a sensor in step 6 of the embodiment;

[0024] Figure 9 This is a timing diagram comparing the predicted value and the actual value of a sensor in step 6 of the embodiment. DETAILED DESCRIPTION

[0025] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

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

[0027] Step 1: Collect the spatiotemporal monitoring two-dimensional data of bridge structures as the original data set.

[0028] In this step, the spatiotemporal monitoring two-dimensional data is derived from data with spatiotemporal dimension 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.

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

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

[0031]

[0032] Where f(x) is the interpolation calculation result of missing data, x is the time axis coordinate of the 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.

[0033] In this step, the trend extraction preprocessing operation is realized 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 from f(x) to f(x+sl) data, and sl is the sliding step.

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

[0037]

[0038] In the formula, is the jth data standardization value of sensor i, is the jth data trend value of sensor i, μ i is the mean value of all trend data of sensor i, and σ i is the standard deviation of all trend data of sensor i.

[0039] Step three, the spatial domain data is represented as different vertices on the hypergraph, and the time domain data is represented as one-dimensional time series on each vertex of the hypergraph. The association matrix is defined by a clustering-based static method or by a dynamic method based on automatic parameter updating.

[0040] In this step, the specific method of defining the association matrix based on the clustering-based static method is: before model training, the K-means method is used to cluster the mean values of the preprocessed 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, i.e. 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] In the formula, Sc is the average profile coefficient, s(i) is the profile 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 value of sensor i and all other sensors in the different cluster, H∈R N×E is the association matrix, E is the optimal cluster (hyperedge) number, 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, and if not, then H(v, e) = 0.

[0046] In this step, the specific method for defining the association matrix based on the dynamic method of parameter automatic updating is that the association matrix is taken as a parameter to be learned during model training, 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 pre-defined, and the specific formula is:

[0047] H = ReLU(E1E2)

[0048] In the formula, and is the embedding matrix to be learned, E b is the embedding dimension.

[0049] Step four, a spatio-temporal hypergraph neural network model mainly composed of one-dimensional gated convolutional layers and hypergraph convolutional layers is designed to perform spatio-temporal association modeling on the bridge monitoring data.

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

[0051] L0 layer: full connection layer, input data size N×1×T, each dimension in the three-dimensional data represents space, feature, and time, this layer operates in the feature dimension, the input feature number is 1, and the output feature number is F hidden1 , and the output data size is N×F hidden1 ×T;

[0052] L1-1 layer: one-dimensional gated convolutional layer, connected to L0 layer, this layer operates in the time and feature dimensions, the input feature number is F hidden1 , the convolution kernel size is K, the depth is F hidden1 , the number is F hidden2 , the dilation value is 1, the output feature number is F hidden2 , and the output data size is N×F hidden2 ×(T-(K-1));

[0053] L1-2 layer: hypergraph convolutional layer, connected to L1-1 layer, this layer operates in the space and feature dimensions, the input feature number is F hidden2 , and the output feature number is Fhidden3 , the output data size is NxF hidden3 x(T-(K-1));

[0054] L1-3 layer: one-dimensional gated convolution layer, connected to L1-2 layer, operating in time and feature dimensions, input feature number is F hidden3 , convolution kernel size is K, depth is F hidden3 , number is F hidden1 , dilation value is 2, output feature number is F hidden1 , the output data size is NxF hidden1 x(T-3(K-1));

[0055] L1-4 layer: batch normalization layer, connected to L1-1 layer and L1-3 layer, no learning parameters, performing batch normalization on the accumulated output data of L1-1 layer and L1-3 layer (time dimension is truncated from back to front), the output data size is NxF hidden1 x(T-3(K-1));

[0056] L2-1 layer: one-dimensional gated convolution layer, connected to L1-4 layer, operating in time and feature dimensions, input feature number is F hidden1 , convolution kernel size is K, depth is F hidden1 , number is F hidden2 , dilation value is 1, output feature number is F hidden2 , the output data size is NxF hidden2 x(T-4(K-1));

[0057] L2-2 layer: hypergraph convolution layer, connected to L2-1 layer, operating in space and feature dimensions, input feature number is F hidden2 , output feature number is F hidden3 , the output data size is NxF hidden3 x(T-4(K-1));

[0058] L2-3 layer: one-dimensional gated convolution layer, connected to L2-2 layer, operating in time and feature dimensions, input feature number is F hidden3 , convolution kernel size is K, depth is F hidden3 , number is F hidden1 , dilation value is 2, output feature number is F hidden1 , the output data size is NxF hidden1 x(T-6(K-1));

[0059] L2-4 layer: batch normalization layer, connected to L2-1, L2-3 layer, the layer performs batch normalization after accumulating the output data of L2-1, L2-3 layer (truncated matching from back to front in time dimension), and the output data size is NxF hidden1 ×(T-6(K-1));

[0060] L3-1 layer: one-dimensional gated convolutional layer, connected to L2-4 layer, the layer operates in time and feature dimensions, the input feature number is F hidden1 , the convolution kernel size is K, the depth is F hidden1 , the number is F hidden2 , the dilation value is 1, the output feature number is F hidden2 , and the output data size is NxF hidden2 ×(T-7(K-1));

[0061] L3-2 layer: hypergraph convolutional layer, connected to L3-1 layer, the layer operates in space and feature dimensions, the input feature number is F hidden2 , the output feature number is F hidden3 , and the output data size is NxF hidden3 ×(T-7(K-1));

[0062] L3-3 layer: one-dimensional gated convolutional layer, connected to L3-2 layer, the layer operates in time and feature dimensions, the input feature number is F hidden3 , the convolution kernel size is K, the depth is F hidden3 , the number is F hidden1 , the dilation value is 2, the output feature number is F hidden1 , and the output data size is NxF hidden1 ×(T-9(K-1));

[0063] L3-4 layer: batch normalization layer, connected to L3-1 layer, L3-3 layer, the layer performs batch normalization after accumulating the output data of L3-1 layer, L3-3 layer (truncated matching from back to front in time dimension), and the output data size is NxF hidden1 ×(T-9(K-1));

[0064] L4-1 layer: one-dimensional gated convolutional layer, connected to L3-4 layer, the layer operates in time and feature dimensions, the input feature number is F hidden1 , the convolution kernel size is K, the depth is F hidden1 , the number is F hidden2 , the dilation value is 1, the output feature number is F hidden2 , and the output data size is NxF hidden2 ×(T-10(K-1));

[0065] L4-2 layer: hypergraph convolution layer, connected to L4-1 layer, which operates in spatial and feature dimensions, input feature number F hidden2 , output feature number F hidden3 , output data size NxF hidden3 x (T-10 (K-1)) ;

[0066] L4-3 layer: one-dimensional gated convolution layer, connected to L4-2 layer, which operates in time and feature dimensions, input feature number F hidden3 , convolution kernel size K, depth F hidden3 , number F hidden1 , dilation value 2, output feature number F hidden1 , output data size NxF hidden1 x1;

[0067] L4-4 layer: batch normalization layer, connected to L4-1 layer, L4-3 layer, which performs batch normalization on the output data of L4-1 layer, L4-3 layer after accumulation (truncated from back to front in time dimension), output data size NxF hidden1 x1;

[0068] L5 layer: fully connected layer, connected to L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer, which operates in feature dimension after accumulation (truncated from back to front in time dimension) of the output data of L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer, input feature number F hidden1 , output feature number F hidden4 , output data size NxF hidden4 x1;

[0069] L6 layer: fully connected layer, connected to L5 layer, which operates in feature dimension, input feature number F hidden4 , output feature number prediction length T predict , output data size N x 1 x T after transposition predict .

[0070] In this step, L0 layer has no activation function, L1-1, L1-3 layer activation function is Tanh and Sigmoid, L1-2 layer activation function is ReLU, L1-4 layer has no activation function, L2-L4 layer internal activation function is set as L1 layer, L5, L6 layer activation function is ReLU.

[0071] In this step, the formula of one-dimensional gated convolution layer is:

[0072]

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

[0074] In this step, the formula of the hypergraph convolutional layer is:

[0075]

[0076] D e = diag [δ (e1), δ (e2),..., δ (e E )]

[0077] W = diag [w (e1), w (e2),..., 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 first hypergraph convolutional layer, is the input of the first 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 the vertex v1, δ (e1) is the degree of the hyperedge e1, w (e1) is the weight of the hyperedge e1, E、 respectively represent the hyperedge set and the vertex set.

[0081] Step five, using the monitoring data within half a year in the initial stage of bridge operation to train the spatio-temporal hypergraph neural network model.

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

[0083] Step six, applying the trained spatio-temporal hypergraph neural network model to the monitoring data after half a year, and introducing other classic machine learning / deep learning models to evaluate the multi-step prediction ability and show the advancement of the present application.

[0084] In this step, the evaluation indexes are root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAE), and determination coefficient (R2 ), the specific formula is:

[0085]

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

[0087] Embodiment:

[0088] The embodiment provides a bridge monitoring data accurate multi-step prediction method based on a spatio-temporal hypergraph neural network, and the method comprises the following steps:

[0089] Step 1: Collecting spatio-temporal monitoring two-dimensional data of a bridge structure as an original data set.

[0090] In this step, the spatio-temporal monitoring two-dimensional data is generated by 42 cable force sensors of the same type installed at different positions of a certain side cable tower of a cable-stayed bridge according to a sampling frequency of 10 Hz, and the data has a spatio-temporal dimension attribute.

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

[0092] In this step, the missing data filling preprocessing operation is realized based on a cubic interpolation method, and the specific formula is:

[0093]

[0094] In the formula, f(x) is an interpolation calculation result of missing data, x is a time axis coordinate of missing data, x1 is a second nearest neighbor non-missing data coordinate on the left side of x, x2 is a nearest neighbor non-missing data coordinate on the left side of x, x3 is a nearest neighbor non-missing data coordinate on the right side of x, x4 is a second nearest neighbor non-missing data coordinate on the right side of x, f(x1) is a true data corresponding to the moment x1, and the like.

[0095] In this step, the trend extraction preprocessing operation is realized based on a moving average method, as shown in Figure 2 , and the specific formula is:

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

[0097] In the formula, f(x) trend is a trend component at the moment x, Avg(f(x):f(x+sl)) is an average value of data from f(x) to f(x+sl), and sl is a sliding step length, which is 10 min.

[0098] In this step, the data standardization preprocessing operation is realized based on the z-score method, and the specific formula is:

[0099]

[0100] In the formula, is the jth data standardization value 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.

[0101] Step three, the spatial domain data is represented as different vertices on the hypergraph, and the time domain data is represented as a one-dimensional time sequence on each vertex of the hypergraph. The association matrix is defined by a clustering-based static method or by a dynamic method based on automatic parameter updating.

[0102] In this step, the specific method of defining the association matrix based on the clustering-based static method is: before model training, the K-means method is used to cluster the mean values of the preprocessed 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, i.e., 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:

[0103]

[0104] a(i)=Avg i,j∈A,j≠i (dist(i,j))

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

[0106]

[0107] In the formula, 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 value between sensor i and all other sensors in different clusters, and H∈R 42×E is the association matrix, and E is the optimal number of clusters (hyperedges). Based on the clustering results, if sensor v is connected to hyperedge e, then H(v,e)=1, and if not, then H(v,e)=0. The average silhouette coefficient obtained is shown in Figure 3 , it can be seen that E=9. The hypergraph neural network designed based on the static method is named STHGCN(S).

[0108] In this step, the specific method of defining the association matrix based on the dynamic method of automatic parameter update is: regarding the association matrix as a parameter to be learned during model training, updating the connection relationship through parameter iteration, and updating the element value in the association matrix through parameter iteration, that is, not defining the hypergraph structure in advance, and the specific formula is:

[0109] H = ReLU (E1E2)

[0110] In the formula, and are embedding matrices to be learned, E b is the embedding dimension, which is 7. The hypergraph neural network designed based on the dynamic method is named STHGCN(D).

[0111] Step four, design a space-time hypergraph neural network model mainly composed of one-dimensional gated convolutional layer and hypergraph convolutional layer to perform space-time correlation modeling on bridge monitoring data.

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

[0113] L0 (fully connected) layer, the input data scale size is 42x1x12, and each dimension in the three-dimensional data respectively represents space, feature, and time. This layer operates in the feature dimension, the input feature number is 1, the output feature number is 32, and the output data scale size is 42x32x12;

[0114] L1-1 (one-dimensional gated convolution) layer, connected to the L0 layer, which operates in the time and feature dimensions, the input feature number is 32, the convolution kernel size is 2, the depth is 32, the number is 16, the dilation value is 1, the output feature number is 16, and the output data scale size is 42x16x11;

[0115] L1-2 (hypergraph convolution) layer, connected to the L1-1 layer, which operates in the space and feature dimensions, the input feature number is 16, the output feature number is 8, and the output data scale size is 42x8x11;

[0116] L1-3 (one-dimensional gated convolution) layer, connected to the L1-2 layer, which operates in the time and feature dimensions, the input feature number is 8, the convolution kernel size is 2, the depth is 8, the number is 32, the dilation value is 2, the output feature number is 32, and the output data scale size is 42x32x9;

[0117] L1-4 (batch normalization) layer, connected to L1-1 layer, L1-3 layer, the layer has no parameters to be learned, and the output data of the L1-1 layer and the L1-3 layer is accumulated (truncated and matched from back to front in the time dimension) and then batch normalization is performed, and the output data has a size of 42x32x9;

[0118] L2-1 (one-dimensional gated convolution) layer, connected to the L1-4 layer, the layer operates in the time and feature dimensions, the input feature number is 32, the convolution kernel size is 2, the depth is 32, the number is 16, the dilation value is 1, the output feature number is 16, and the output data has a size of 42x16x8;

[0119] L2-2 (hypergraph convolution) layer, connected to the L2-1 layer, the layer operates in the space and feature dimensions, the input feature number is 16, the output feature number is 8, and the output data has a size of 42x8x8;

[0120] L2-3 (one-dimensional gated convolution) layer, connected to the L2-2 layer, the layer operates in the time and feature dimensions, the input feature number is 8, the convolution kernel size is 2, the depth is 8, the number is 32, the dilation value is 2, the output feature number is 32, and the output data has a size of 42x32x6;

[0121] L2-4 (batch normalization) layer, connected to the L2-1 layer, L2-3 layer, the layer accumulates the output data of the L2-1 layer and the L2-3 layer (truncated and matched from back to front in the time dimension) and then performs batch normalization, and the output data has a size of 42x32x6;

[0122] L3-1 (one-dimensional gated convolution) layer, connected to the L2-4 layer, the layer operates in the time and feature dimensions, the input feature number is 32, the convolution kernel size is 2, the depth is 32, the number is 16, the dilation value is 1, the output feature number is 16, and the output data has a size of 42x16x5;

[0123] L3-2 (hypergraph convolution) layer, connected to the L3-1 layer, the layer operates in the space and feature dimensions, the input feature number is 16, the output feature number is 8, and the output data has a size of 42x8x5;

[0124] L3-3 (one-dimensional gated convolution) layer, connected to the L3-2 layer, the layer operates in the time and feature dimensions, the input feature number is 8, the convolution kernel size is 2, the depth is 8, the number is 32, the dilation value is 2, the output feature number is 32, and the output data has a size of 42x8x3;

[0125] L3-4 (batch normalization) layer, connected to L3-1 layer, L3-3 layer, the layer performs batch normalization after accumulating the output data of L3-1 layer, L3-3 layer (truncated matching from back to front in time dimension), and outputs data with a size of 42x8x3;

[0126] L4-1 (one-dimensional gated convolution) layer, connected to L3-4 layer, the layer operates in time and feature dimensions, with an input feature number of 32, a convolution kernel size of 2, a depth of 32, a number of 16, a dilation value of 1, an output feature number of 16, and an output data size of 42x16x2;

[0127] L4-2 (hypergraph convolution) layer, connected to L4-1 layer, the layer operates in space and feature dimensions, with an input feature number of 16 and an output feature number of 8, and an output data size of 42x8x2;

[0128] L4-3 (one-dimensional gated convolution) layer, connected to L4-2 layer, the layer operates in time and feature dimensions, with an input feature number of 8, a convolution kernel size of 2, a depth of 8, a number of 32, a dilation value of 2, an output feature number of 32, and an output data size of 42x32x1;

[0129] L4-4 (batch normalization) layer, connected to L4-1 layer, L4-3 layer, the layer performs batch normalization after accumulating the output data of L4-1 layer, L4-3 layer (truncated matching from back to front in time dimension), and outputs data with a size of 42x32x1;

[0130] L5 (full connection) layer, connected to L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer, the layer operates in feature dimension after accumulating the output data of L1-4 layer, L2-4 layer, L3-4 layer, L4-4 layer (truncated matching from back to front in time dimension), with an input feature number of 32, an output feature number of 64, and an output data size of 42x64x1;

[0131] L6 (full connection) layer, connected to L5 layer, the layer operates in feature dimension, with an input feature number of 64, an output feature number of prediction length 12, and an output data size of 42x1x64 after transposition;

[0132] L0 layer has no activation function, L1-1 layer and L1-3 layer have Tanh and Sigmoid activation functions, L1-2 layer has ReLU activation function, L1-4 layer has no activation function, L2-L4 layers have the same activation function settings as L1 layer, L5 layer and L6 layer have ReLU activation function;

[0133] The formula of one-dimensional gated convolution layer is:

[0134]

[0135] where Gt (l) (X (l) ) is the output of the lth one-dimensional gated convolutional layer, X (l) is the input of the lth one-dimensional gated convolutional layer, is the convolution kernel weight parameter, b and c are bias parameters, and is the Hadamard product.

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

[0137]

[0138] D e = diag [δ (e1), δ (e2),..., δ (e E )]

[0139] W = diag [w (e1), w (e2),..., w (e E )]

[0140] d (v i ) = Σ e∈E w (e) H (v i , e)

[0141]

[0142] wherein, 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 vertices, D e is the degree matrix of hyperedges, W is the weight matrix of vertices, d (v1) is the degree of vertex v1, δ (e1) is the degree of hyperedge e1, and w (e1) is the weight of hyperedge e1.

[0143] Step five, the standardized trend data from May 2006 to December 2006 is selected to train the spatio-temporal hypergraph neural network model, and the training model is realized based on the small batch gradient descent. The batch size is 64, the learning rate is 1E-3, the training round is 50, the loss function is the mean square error function, and the optimization method is the adaptive moment estimation method. As shown in the loss function in the training process, the model converges with iterations, and there is no underfitting and overfitting phenomenon. Figure 5

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

[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, and is 3295. The smaller the RMSE, MAE, MAPE, and the larger the R 2 , the better the model prediction performance. The prediction results of each model are shown in Table 1. Figures 6-9 As can be seen from Table 1, the performance of the STHGCN(S) and STHGCN(D) models based on hypergraph is significantly higher than that of the M-SVR model, the ConvLSTM model and the GWN model which are not based on hypergraph in the multi-step prediction task.

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, and represent the temporal domain data as one-dimensional time series on each vertex of the hypergraph. Define the association matrix through a static method based on clustering or a dynamic method based on automatic parameter updating. Step 4: Design a spatiotemporal hypergraph neural network model to perform spatiotemporal correlation modeling on the bridge monitoring data. The spatiotemporal 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: 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 convolution layer, connected to layer L1-1, which operates on spatial and feature dimensions, with the number of input features being 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, which operates on the time and feature dimensions, with the input feature number 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 accumulates the output data of L1-1 layer and L1-3 layer and then performs batch normalization. The output data scale 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 convolution layer, connected to layer L2-1, which operates on spatial and feature dimensions, with the input feature number 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, which operates on the time and feature dimensions, with the number of input features being 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 layers L2-1 and L2-3. This layer accumulates the output data of layers L2-1 and L2-3 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 convolution layer, connected to layer L3-1, which operates on spatial and feature dimensions, with the input feature number 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)); Layer L3-4: Batch normalization layer, connected to layers L3-1 and L3-3. This layer accumulates the output data of layers L3-1 and L3-3 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 convolution layer, connected to layer L4-1, which operates on spatial and feature dimensions, with the input feature number 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, which operates on the time and feature dimensions, with the input feature number 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 number of input features 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, and the number of input features 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 monitoring data from the initial six months of bridge operation 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 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 calculation result of missing data, x is the time axis coordinate of the 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 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: Where, is the normalized value of the j-th 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 step 3, the specific method of defining the association matrix based on the static clustering method is as follows: 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. When selecting the optimal number of clusters, the average silhouette coefficient is used as the evaluation indicator. 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 sensor v is connected to hyperedge e, then H(v,e) = 1; if not, 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 step 3, the specific method for defining the association matrix based on the dynamic method of automatic parameter update is: during model training, the association matrix is ​​used as the 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) Where, 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 to 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: Where Gt (l) (X (l) ) is the output of the l-th dimensional gated convolution 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| )] W=diag[w(e1),w(e2),...,w(e |ε| )] d(v i )mΣ e∈ε w(e)H(v i ,e) Where, 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 step five, the training of the spatiotemporal hypergraph neural network model is implemented 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.

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