Spatial-temporal feature fusion concrete arch dam deformation prediction method based on multi-scale hierarchical clustering

Abstract

The invention discloses a spatial-temporal feature fusion concrete arch dam deformation prediction method based on multi-scale hierarchical clustering, and the method comprises the following steps: decomposing a dam deformation sequence into trend, period and fluctuation items, and constructing a new multi-scale similarity distance index; adopting a hierarchical clustering method based on a Ward criterion, and utilizing the constructed multi-scale similarity distance index to perform clustering partition on the deformation measuring points with the similar deformation rule; a deep learning model TCT-CANet fused with the spatial and temporal characteristics is constructed; the deformation of the concrete arch dam is predicted by utilizing the constructed TCT-CANet model, the prediction performance of the model is evaluated through various evaluation indexes, and meanwhile, the effect of each module in the aspects of spatial-temporal feature capture and prediction precision improvement is analyzed through an ablation experiment; the TCT-CANet model is compared with various time sequence prediction methods on all measurement points, and the superiority and generalization ability of the model are verified. According to the method, the prediction model TCT-CANet based on spatial-temporal feature fusion is constructed, and accurate prediction of deformation of the concrete arch dam is realized.

Description

Technical Field

[0001] This invention pertains to methods for predicting the deformation of concrete arch dams, specifically involving a method for predicting the deformation of concrete arch dams based on the spatiotemporal feature fusion of multi-scale hierarchical clustering. Background Technology

[0002] As a crucial water conservancy project, the operational safety of concrete arch dams directly impacts flood control, water resource management, and the safety of life and property in downstream areas. Deformation monitoring is a vital tool in structural safety management, comprehensively reflecting the dam's stress response and operational status changes, and serving as a crucial basis for assessing the health status and risk level of arch dams. Therefore, constructing a stable, reliable, and highly accurate dam deformation prediction model is of great significance for improving engineering safety monitoring and early warning capabilities. Influenced by factors such as structural stress paths, material continuity, and environmental disturbances, adjacent measuring points of concrete arch dams often exhibit similar deformation patterns, while significant spatial differences exist between different regions. Currently, traditional methods often focus on modeling the temporal characteristics of individual measuring points, neglecting spatial synergistic effects. Therefore, accurately identifying and modeling these spatial distribution characteristics, effectively integrating spatiotemporal information, and constructing a prediction model with synergistic expressive capabilities have become key to improving the accuracy of deformation prediction. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the deformation of concrete arch dams based on spatiotemporal feature fusion using multi-scale hierarchical clustering. By using a hierarchical clustering method based on multi-scale similarity distance, deformation measurement points with similar deformation patterns are clustered and partitioned, and a prediction model TCT-CANet based on spatiotemporal feature fusion is constructed to achieve accurate prediction of the deformation of concrete arch dams.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for predicting the deformation of concrete arch dams based on spatiotemporal feature fusion using multi-scale hierarchical clustering includes the following steps:

[0006] S1 decomposes the dam deformation sequence into trend, periodic and random fluctuation terms to construct a new multi-scale similarity distance index;

[0007] S2 adopts a hierarchical clustering method based on the Ward criterion and uses the multi-scale similarity distance index constructed in S1 to cluster and partition deformation measurement points with similar deformation patterns.

[0008] S3, Constructing a deep learning model TCT-CANet that integrates spatiotemporal features;

[0009] S4. The deformation of concrete arch dams was predicted using the constructed TCT-CANet model. The predictive performance of the model was evaluated through various evaluation indicators. At the same time, the role of each module in capturing spatiotemporal features and improving prediction accuracy was analyzed through ablation experiments.

[0010] S5 compares the TCT-CANet model with various time series prediction methods at all measurement points to verify the model's superiority and generalization ability.

[0011] Preferably, the specific steps of S1 are as follows:

[0012] S101, the variational mode decomposition method is used to decompose the arch dam deformation sequence into trend, periodic and random fluctuation terms;

[0013] S102, Calculate the similarity distance index d for trend items. T (x, y), the calculation formula is as follows:

[0014]

[0015] Among them, S T σ represents the trend slope. T R is the standard deviation. T Let x and y be the rate of change, and let x and y be different arch dam deformation sequences;

[0016] S103, Calculate the similarity distance index d for periodic terms. p (x, y), the calculation formula is as follows:

[0017]

[0018] Among them, L p Let A be the period length. p For amplitude, Φ p As phase, x and y represent different arch dam deformation sequences;

[0019] S104, Calculate the similarity distance index d for the random fluctuation term. f (x, y), the calculation formula is as follows:

[0020]

[0021] Among them, I f For the wave intensity, W f For the fluctuation range, x and y represent different arch dam deformation sequences;

[0022] S105 integrates the similarity distances of trend, periodic, and stochastic fluctuation terms to calculate the multi-scale similarity distance index D. MSD (x, y), the calculation formula is as follows:

[0023] DMSD (x,y)=w trend ·d T (x,t)+w period ·d p (x,y)+w fluctuation ·d f (x,t)

[0024] Where, d T (x,y) is the similarity distance index for the trend terms, d p (x,y) is the similarity distance index for periodic terms, d f (x,y) is the similarity distance index for the random fluctuation term, w trend w period and w fluctuation The weights are the corresponding weights for the trend term, periodic term, and random fluctuation term.

[0025] Preferably, the specific steps of S2 are as follows:

[0026] S201, Initialization: Before starting clustering, each deformation measurement point is treated as an independent cluster;

[0027] S202, Intra-cluster error assessment: Calculate the multi-scale similarity error between each measurement point in each cluster and its cluster center, and assess the internal compactness of the current cluster accordingly;

[0028] S203, Overall Error Measurement: Under the current clustering structure, the intra-cluster errors of all clusters are summarized as an evaluation index of the overall clustering effect;

[0029] S204, Two-class merging error calculation: For any two different clusters, estimate the impact of the merged cluster structure on the overall error;

[0030] S205, Minimum Incremental Merging: Select the two clusters that result in the smallest increase in overall error and merge them. Repeat steps S203 and S204 until the preset number of clusters is reached.

[0031] Preferably, the specific steps of S3 are as follows:

[0032] S301, input the extended factor set, consisting of the environmental feature factor set and the deformation sequence of other measurement points in the partition where the target measurement point is located, into the input dataset of the model;

[0033] S302, the TCN module captures the spatial dependencies between measurement points within the same deformation partition and outputs a spatial feature representation;

[0034] S303, the Transformer module analyzes long-term dependencies and trends in time series and outputs time feature representations;

[0035] The spatial and temporal features extracted by S304, TCN and Transformer are input into the Cross-Attention mechanism for integration.

[0036] S305 uses cross-attention mechanism to fuse features, which are then processed by adaptive average pooling layer for dimensionality reduction, and finally outputs the prediction result through fully connected layer.

[0037] Preferably, in step S4, when evaluating the predictive performance of the model using multiple evaluation metrics, the evaluation metric is the coefficient of determination R. 2 Root mean square error (RMSE), mean absolute error (MAE), and maximum absolute error (AE) max The calculation formula is:

[0038]

[0039] Where n is the number of samples, y i and These are the actual and predicted values ​​of the arch dam deformation, respectively. This represents the average value of the actual deformation.

[0040] Preferably, in S4, the ablation experiment design includes multiple model configuration schemes. The specific methods for the configuration schemes are as follows: using only environmental factors as input; removing the Cross-Attention mechanism and using ordinary fully connected layers for spatiotemporal feature fusion; removing the Transformer module; and removing the TCN module.

[0041] The beneficial effects of this invention are as follows: By combining multi-scale hierarchical clustering and spatiotemporal feature fusion methods, this invention proposes a high-precision deformation prediction model for concrete arch dams, TCT-CANet. This method, through hierarchical clustering based on multi-scale similarity distance, can reasonably partition deformation measurement points with similar deformation patterns. Simultaneously, the model incorporates TCN, Transformer, and Cross-Attention mechanisms to fully exploit the spatiotemporal features in the deformation sequence, enhancing the ability to model spatiotemporal features. Compared to traditional prediction methods, it has stronger generalization ability and superior prediction performance, providing more accurate deformation predictions in various complex monitoring scenarios, and offering more effective technical support for dam safety monitoring and early warning. Attached Figure Description

[0042] Figure 1 The flowchart shows a method for predicting the deformation of concrete arch dams based on spatiotemporal feature fusion using multi-scale hierarchical clustering.

[0043] Figure 2 This is a schematic diagram of the spatial distribution of the clustering results;

[0044] Figure 3 The deformation curves of each measurement point within each cluster are shown.

[0045] Figure 4 This is a diagram illustrating the overall construction of the spatiotemporal feature fusion model TCT-CANet.

[0046] Figure 5 This is a schematic diagram of the TCN structure;

[0047] Figure 6 This is a schematic diagram of the Transformer structure;

[0048] Figure 7 This is a comparison chart of the evaluation indicators for various ablation experiment models. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0050] like Figures 1-7 As shown, a method for predicting the deformation of concrete arch dams based on spatiotemporal feature fusion using multi-scale hierarchical clustering includes the following steps:

[0051] S1 employs Variational Mode Decomposition (VMD) to decompose the dam deformation sequence into three components: trend, periodicity, and fluctuation. For each component, a corresponding metric is defined, constructing a new multi-scale similarity distance index. This index will serve as a crucial basis for evaluating the similarity of monitoring points in subsequent hierarchical clustering analysis, supporting the construction of deformation monitoring zones.

[0052] S101, using the variational mode decomposition method, with the number of modes set to 3, the arch dam deformation sequence is decomposed into three main modal components: trend term T, periodic term P, and random fluctuation term F;

[0053] S102 defines the similarity distance index for trend items, and the features selected include trend slope (S T ), standard deviation (σ) T ) and rate of change (R) T The formula for calculating trend characteristics is as follows:

[0054]

[0055] Where n is the length of the deformed sequence, t i For a point in time, and Divided into time and trend terms, the average, T1 and T n These represent the initial and final values ​​of the trend term, respectively. Based on the aforementioned trend characteristics, the similarity distance index d of the trend term is calculated. T(x, y), the calculation formula is as follows:

[0056]

[0057] Among them, S T σ represents the trend slope. T R represents the standard deviation. T Let x be the rate of change, and y be different arch dam deformation sequences.

[0058] S103, Define the similarity distance index for periodic items, with selected features including period length (L). p ), amplitude (A) p ) and phase (Φ p The formula for calculating the periodic characteristics is as follows:

[0059]

[0060] Φ p =argmax|F(p i )| Formula 7

[0061] Where R(τ) is the autocorrelation function, τ is the time delay, and p i Let F represent the periodic term value, argmax represent the Fourier transform, and argmax represent the position where the phase angle is taken. Based on the above periodic characteristics, the similarity distance index d of the periodic terms is calculated. p (x, y), the calculation formula is as follows:

[0062]

[0063] Among them, L p Let A be the period length. p For amplitude, Φ p Let x and y be the phases, and let x and y be different arch dam deformation sequences.

[0064] S104 defines a similarity distance index for random fluctuation terms, where the selected features include fluctuation intensity (I0). f ) and fluctuation range (W f The formula for calculating random fluctuation characteristics is as follows:

[0065]

[0066] W f =max(f i )-min(f i ) Formula 10

[0067] Among them, f i These are the data values ​​for the fluctuation term. This is the average value of the random fluctuation term. Based on the above characteristics of random fluctuation, the similarity distance index d of the random fluctuation term is calculated.f (x, y), the calculation formula is as follows:

[0068]

[0069] Among them, I f For the wave intensity, W f For the fluctuation range, x and y represent different arch dam deformation sequences.

[0070] S105 integrates the similarity distances of trend, periodic, and stochastic fluctuation terms to calculate the multi-scale similarity distance index D. MSD (x, y), the calculation formula is as follows:

[0071] D MSD (x,y)=w trend ·d T (x,y)+w period ·d p (x,y)+w fluctuation ·d f (x,y) Formula 12

[0072] Where, d T (x,y) is the similarity distance index for the trend terms, d p (x,y) is the similarity distance index for periodic terms, d f (x,y) is the similarity distance index for the random fluctuation term, w trend w period and w fluctuation The weights are the corresponding weights for the trend term, periodic term, and random fluctuation term.

[0073] To ensure a balanced contribution of each feature to the clustering results, an average weight allocation is adopted. This method simplifies the model's complexity while avoiding the excessive influence of a single feature on the clustering results.

[0074] S2 employs a hierarchical clustering method based on the Ward criterion, utilizing the multi-scale similarity distance index constructed in S1 to cluster and partition deformation measurement points with similar deformation patterns.

[0075] This similarity index serves as the basis for calculating the differences between measurement points, ensuring that the deformation sequences of measurement points within the same partition are highly consistent in multi-scale features, while significant differences exist between different partitions.

[0076] S201, Initialization: Before starting clustering, each deformation measurement point is treated as an independent cluster;

[0077] S202, Intra-cluster Error Assessment: Calculate the multi-scale similarity error between each measurement point in each cluster and its respective cluster center, and assess the internal compactness of the current cluster accordingly.

[0078] Calculate the sum of squared errors (ESS) within the cluster. For any cluster C containing multiple deformation measurement points of a concrete arch dam, its ESS value is calculated as follows:

[0079] ESS(C)=∑ x∈C D 2 (x,μ C ) Formula 13

[0080] Where μ(C) is the center point of cluster C, defined as the measurement point in the cluster that minimizes the sum of the multi-scale similarity indices with all other measurement points, and D is the multi-scale similarity distance index.

[0081] S203, Overall Error Measurement: Under the current clustering structure, the intra-cluster errors of all clusters are summarized as an evaluation metric for the overall clustering effect.

[0082] Calculate the total sum of squared errors (ESS). If there are currently k clusters C1, C2, ..., C... k Then the sum of ESS for all clusters is expressed as:

[0083]

[0084] Among them, ESS(C i ) represents the sum of squared errors for the i-th cluster.

[0085] S204, Two-class merging error calculation: For any two different clusters, estimate the impact of the merged cluster structure on the overall error.

[0086] Calculate the ESS increment after merging the two clusters in all cases. Considering the merged cluster C... i and C j Forming a new cluster C t In this case, the incremental value of ESS is calculated as follows:

[0087] ΔESS ij =ESS(C t )-(ESS(C i )+ESS(C j )) Formula 15

[0088] Among them, ESS(C i Let ) be the sum of squared errors of the i-th cluster, ESS(C j Let ESS(C) be the sum of squared errors of the j-th cluster. t ) represents the sum of squared errors of the cluster resulting from merging the i-th and j-th clusters.

[0089] S205, Minimum Incremental Merging: Select the two clusters that result in the smallest increase in overall error and merge them. Repeat steps S203 and S204 until the preset number of clusters is reached.

[0090] Minimize the incremental merge clustering of ESS. Choose the increment value ΔESS. ij The two smallest clusters are merged, and S203 and S204 are repeated until the predetermined target number of clusters is reached.

[0091] The optimal number of clusters was determined using the Calinski-Harabasz index and silhouette coefficient. The spatial distribution of the final clustering results is shown in the attached figure. Figure 2 As shown in the attached figure, the deformation curves of the test points within each cluster are as follows. Figure 3 As shown.

[0092] Combined with appendix Figure 2 and attached Figure 3 It can be seen that the clustering results divide the monitoring points into five spatial zones. The locations of each zone on the dam body have clear distribution characteristics, reflecting strong geographical concentration and consistency in deformation patterns.

[0093] Cluster 1 includes two measuring points, PL1-1 and PL7-1, located on the bank slopes at both ends of the arch dam. Its deformation amplitude is relatively small, exhibiting an overall stable deformation trend without significant periodic fluctuations.

[0094] Cluster 2 comprises five measuring points: PL2-1, PL3-1, PL4-1, PL5-1, and PL6-1, concentrated in the middle of the dam crest. Its deformation curves exhibit significant periodic fluctuations, with an overall upward trend in deformation.

[0095] Cluster 3 includes three measuring points: PL5-2, PL4-2, and PL3-2, mainly distributed in the central region of the arch dam. These deformation curves also exhibit obvious periodic fluctuations, but the fluctuation amplitude is significantly smaller than that of partition 2, while also showing certain trend changes.

[0096] Cluster 4 contains three measuring points: PL5-3, PL4-3, and PL3-3, located in the lower part of the arch dam. Its deformation curve shows a slow upward trend overall, accompanied by small fluctuations.

[0097] Cluster 5 includes eight measuring points: PL2-2, PL6-2, PL2-3, PL6-3, PL3-4, PL4-4, PL5-4, and PL4-5. These points are located at the bottom and sides of the arch dam. The deformation curves are generally stable with moderate periodic fluctuations.

[0098] S3. To achieve efficient prediction of concrete arch dam deformation, a deep learning model integrating spatiotemporal features, TCT-CANet, was constructed. This model combines a temporal convolutional network (TCN), a Transformer module, and a cross-attention mechanism. Its overall structure is shown in the attached figure. Figure 4 As shown.

[0099] S301, the input dataset of the model is an extended factor set consisting of the environmental feature factor set and the deformation sequence of other measurement points within the partition where the target measurement point is located.

[0100] The environmental characteristic factor set consists of environmental factors, specifically monitoring data on upstream water level and humidity. The extended factor set consists of deformation factors, specifically deformation sequences within the same region other than the predicted target.

[0101] The use of this integrated data can not only effectively capture the complex spatiotemporal relationships between measuring points, but also reveal the influence of environmental factors on deformation patterns.

[0102] The S302, TCN module is used to capture the spatial dependencies between measurement points within the same deformation partition and output a spatial feature representation.

[0103] This module consists of two TCN Blocks, each containing two layers of one-dimensional dilated convolutions (dilation factor d = 1, 2), with a kernel size of 3. The first Block outputs 8 channels of features, while the second Block expands the number of channels to 16 to extract richer high-level features.

[0104] The structural diagram of the TCN module is shown in the attached figure. Figure 5 As shown, causal convolution is the core component of the TCN model, ensuring that the model can only use current and past information when predicting future values, and will not use future information, thus avoiding the leakage of future information.

[0105] While stacked causal convolutions can expand the receptive field, they require many layers to process long sequences, which can easily lead to gradient blurring and reduced efficiency. To address this, TCN introduces dilated convolutions, using a dilation factor d=2. i (where i is the layer number), achieving exponential growth of the receptive field, significantly expanding the perceptual range without increasing the number of layers. The dilated convolution F(s) is calculated using the following formula:

[0106]

[0107] Where d is the dilation factor and k is the kernel size, which only represents the convolution of past states.

[0108] Appendix Figure 5(a) shows a schematic diagram of dilated convolution with dilation factors d = 1, 2, and 4, where d = 1 is a hidden layer, d = 2 is a hidden layer, and d = 4 is an output layer.

[0109] As network depth increases, the increase in model parameters can lead to gradient vanishing or exploding problems. Residual blocks can alleviate this issue by adding skip connections to the network, allowing gradients to propagate effectively. The output o of the residual block is calculated using the following formula:

[0110] o = Activation(x + F(x)) Formula 17

[0111] Where Activation is the activation function and F(x) is the residual information.

[0112] Appendix Figure 5 (b) illustrates the structure of the residual block, which consists of two layers of dilated causal convolutions and a Rectified Linear Unit (ReLU) function. Weight normalization layers and dropout layers are used to improve the network's generalization ability. To ensure consistency between the input and output dimensions, a 1×1 convolution is ultimately used for adjustment. (See appendix) Figure 5 (c) shows an example of residual connections in TCN.

[0113] S303, the Transformer module is used to analyze long-term dependencies and trends in time series and output time feature representations.

[0114] To meet the input dimension requirements of the Transformer, the original deformed sequence is upsampled using a 1×1 convolutional layer. This module only uses the encoder part of the Transformer, and by stacking two encoder layers, it can effectively extract temporal dimension feature information at multiple depth levels.

[0115] The Transformer mainly consists of an encoder and a decoder, and its structure is shown in the attached figure. Figure 6 As shown. The encoder is responsible for extracting feature representations of the input sequence, and the decoder generates the corresponding output based on these features. Each encoder and decoder consists of multiple stacked layers with the same structure, each layer containing two substructures: a multi-head self-attention mechanism and a feed-forward neural network (FFN). The core mechanism of the Transformer is the self-attention mechanism, which enables the model to dynamically focus on information at different positions when processing sequence data, thereby enhancing its ability to understand and model temporal features. The calculation expression of the self-attention mechanism is as follows:

[0116]

[0117] Where Attention(Q,K,V) is the self-attention mechanism, W Q W K and W V These are the weight matrices for the query, key, and value, respectively, where Q, K, and V represent the query, key, and value, respectively. k The key dimension is used, and softmax is the normalization operation. To enhance the model's expressive power, Transformer introduces a multi-head attention mechanism. MultiHead(Q,K,V) is the multi-head attention mechanism, where head... i The formula for calculating the attention mechanism for each head is as follows:

[0118] MultiHead(Q,K,V)=Concat(head1,head2,…,head h W O Formula 19

[0119]

[0120] Where i = 1, 2, ..., h, i represents the number of heads. Let Q, K, and V be the corresponding trainable weight matrix, where Q, K, and V represent the query, key, and value, respectively.

[0121] After each attention sublayer, the Transformer uses a feedforward neural network (FFN) to perform a non-linear transformation of the features. The FFN consists of two fully connected layers and an activation function. Its formula is as follows:

[0122] FFN(X)=max(0,XW1+b1)W2+b2 (Formula 21)

[0123] Here, FFN(X) is a feedforward neural network, W1 and W2 are trainable weight matrices, and b1 and b2 are bias terms. The ReLU activation function is used to introduce non-linearity and increase the expressive power of the model.

[0124] Since the Transformer model itself does not depend on the order of the input sequence, positional encoding is introduced to inject positional information. Positional encoding is generated using sine and cosine functions, and its formula is as follows:

[0125]

[0126] Where P is the position encoding matrix, p is the fixed position in the time sequence of the input sequence, i is the dimension of the sequence number, and d model The total dimension of the sequence.

[0127] In this way, positional encoding introduces positional information into the model, ensuring that the Transformer can effectively handle sequence-dependent information.

[0128] The spatial and temporal features extracted by S304, TCN, and Transformer are input side-by-side into a cross-attention mechanism for integration. The fused features are then integrated via Cross-Attention (Q-Focus). time ,K space V space The calculation formula is as follows:

[0129]

[0130] Among them, Q time K is the temporal feature extracted by the Transformer. space and V space Spatial features extracted for TCN. This structure allows the model to dynamically select the most relevant spatial information based on changes in temporal features, significantly improving its ability to handle complex spatiotemporal interaction patterns.

[0131] In S305, the features fused through the Cross-Attention mechanism undergo dimensionality reduction via an adaptive average pooling layer, and finally the prediction result is output through a fully connected layer. To ensure optimal performance of the TCT-CANet model, all hyperparameters are optimized using a random search strategy. The final optimal hyperparameter configuration for TCT-CANet is shown in Table 1.

[0132] Table 1. Parameter settings for the TCT-CANet model

[0133] Hyperparameters meaning numerical values TL TCN network layers 2 KS TCN convolution kernel size 3 DL Inflation factor {1,2} TC Number of TCN output channels [8,16] EL Transformer encoder layer 2 HD Attention dimension 64 MH Number of attention heads 2 DR Drop rate 0.2 LR Learning rate 0.001 epoch Training times 100 batch_size Training batch 32 time_step Time step 6

[0134] S4. The deformation of concrete arch dams was predicted using the constructed TCT-CANet model. The predictive performance of the model was evaluated through various evaluation indicators. At the same time, the role of each module in capturing spatiotemporal features and improving prediction accuracy was analyzed through ablation experiments.

[0135] S401 evaluates the predictive performance of the model using multiple evaluation metrics, with the coefficient of determination R being the most important metric. 2 Root mean square error (RMSE), mean absolute error (MAE), and maximum absolute error (AE) max These four indicators are used to evaluate the prediction accuracy and performance of the model at different measurement points. The calculation formulas for the above four indicators are as follows:

[0136]

[0137] Where n is the number of samples, yi and These are the actual and predicted values ​​of the arch dam deformation, respectively. This represents the average value of the actual deformation.

[0138] R 2 RMSE, MAE, and AE are used to measure the goodness of model fit; the closer the value is to 1, the better the fit. max Used to assess prediction error, the closer the value is to 0, the smaller the error.

[0139] S402 uses ablation experiments to design various model configuration schemes, analyzes the impact of each feature extraction module and feature fusion mechanism on prediction performance, and verifies the contribution of each module in spatiotemporal feature representation and accuracy improvement.

[0140] To evaluate the contribution of each module in the TCT-CANet model to the deformation prediction performance, four ablation experiments were designed. The specific model configuration is detailed in Table 2.

[0141] Table 2. Configuration scheme for ablation experiments

[0142]

[0143] The specific method of the configuration scheme is as follows: only environmental factors are used as input; the Cross-Attention mechanism is removed, and spatiotemporal feature fusion is performed using ordinary fully connected layers; the Transformer module is removed; and the TCN module is removed.

[0144] It is important to note that in the experiments where TCN or Transformer was removed, the model was left with only a single feature extraction module, and the Cross-Attention mechanism could not function. Therefore, the models corresponding to these experiments were versions that only contained TCN or Transformer structures, not "TCN-CANet" or "Transformer-CANet".

[0145] The evaluation metrics for each experimental design model are attached. Figure 7 As shown in the figure. The results show that TCT-CANet performs best in all metrics, verifying the synergistic effect of TCN, Transformer and Cross-Attention mechanisms, as well as the effectiveness of using deformed sequences as input.

[0146] S5 compares the TCT-CANet model with various time series prediction methods at all measurement points to verify the model's superiority and generalization ability.

[0147] The proposed spatiotemporal feature fusion model TCT-CANet was compared with the performance of various mainstream time series prediction methods on all measurement points. The comparison methods included deep learning models (TCN-LSTM, ConvLSTM, GRU, LSTM), machine learning models (SVM, RF), and classical statistical models (HST). The prediction performance of each model was evaluated in different clustering regions to verify the applicability and advantages of the TCT-CANet model in complex deformation scenarios.

[0148] The average prediction performance of each model in different clusters is shown in Table 3.

[0149] Table 3. Average prediction performance of different models in each cluster.

[0150]

[0151] The results show that TCT-CANet outperforms the comparison model in terms of fitting accuracy and error control, and maintains good prediction consistency and robustness under different deformation modes, fully demonstrating its wide applicability and generalization ability in complex deformation feature scenarios.

Claims

1. A spatiotemporal feature fusion concrete arch dam deformation prediction method based on multi-scale hierarchical clustering, characterized in that, The method comprises the following steps: S1, decomposing the dam deformation sequence into trend, periodic and random fluctuation items to construct a new multi-scale similarity distance index; S2, using a hierarchical clustering method based on Ward criterion, using the multi-scale similarity distance index constructed in S1, clustering and partitioning deformation measuring points with similar deformation laws; S3, constructing a deep learning model TCT-CANet that integrates spatial and temporal characteristics; S4, using the constructed TCT-CANet model to predict the deformation of the concrete arch dam, evaluating the prediction performance of the model through multiple evaluation indexes, and analyzing the role of each module in capturing spatial and temporal characteristics and improving prediction accuracy through ablation experiments; S5, comparing the TCT-CANet model with various time series prediction methods at all measuring points to verify the superiority and generalization ability of the model.

2. The multi-scale hierarchical clustering based spatio-temporal feature fusion concrete arch dam deformation prediction method according to claim 1, characterized in that, The specific steps of S1 are: S101, using a variational mode decomposition method to decompose the arch dam deformation sequence into trend, periodic and random fluctuation items; S102, calculate the similarity distance index d of the trend item T (x, y), the calculation formula is as follows: where S T is the trend slope, σ T is the standard deviation, R T is the rate of change, and x and y are different arch dam deformation sequences. S103, calculate the similarity distance index d of the period term p (x, y), the calculation formula is as follows: where L p is the period length, A p is the amplitude, Φ p is the phase, and x and y are different arch dam deformation sequences. S104, calculate the similarity distance index d of the random fluctuation term f (x, y), the calculation formula is as follows: where I f is the fluctuation intensity, W f is the fluctuation range, and x and y are different arch dam deformation sequences. S105, integrate the similarity distance of the trend item, the cycle item and the random fluctuation item, calculate the multi-scale similarity distance index D MSD (x, y), the calculation formula is as follows: D MSD (x,y) = w trend • d T (x,y) + w period • d p (x,y) + w fluctuation • d f (x,y) where d T (x, y) is the similarity distance indicator of the trend term, d p (x, y) is the similarity distance indicator of the periodic term, d f (x, y) is the similarity distance indicator of the random fluctuation term, w trend , w period , and w fluctuation are the weights corresponding to the trend term, the periodic term, and the random fluctuation term, respectively.

3. The multi-scale hierarchical clustering based spatio-temporal feature fusion concrete arch dam deformation prediction method according to claim 1, characterized in that, The specific steps of S2 are: S201, initialization: before starting clustering, each deformation measuring point is regarded as an independent cluster; S202, intra-class error evaluation: the multi-scale similarity error between each measuring point in each cluster and its cluster center is calculated, and the internal tightness of the current cluster is evaluated accordingly; S203, overall error measurement: under the current cluster structure, the intra-class error of all clusters is summarized as an evaluation index of the overall clustering effect; S204, two-class merging error calculation: for any two different clusters, estimate the influence degree of the merged cluster structure on the overall error; S205, minimum incremental merging: select the two clusters with the minimum overall error increment for merging, and repeat steps S203 and S204 until the preset number of clusters is reached.

4. The multi-scale hierarchical clustering based spatio-temporal feature fusion concrete arch dam deformation prediction method according to claim 1, characterized in that, The specific steps of S3 are: S301, inputting the environmental characteristic factor set and the deformation sequence of other measuring points in the partition where the target measuring point is located into the input data set of the model; S302, the TCN module captures the spatial dependency between measuring points in the same deformation partition, and outputs the spatial feature representation; S303, the Transformer module analyzes the long-term dependency relationship and change trend in the time series, and outputs the time feature representation; S304, the spatial and temporal features extracted by TCN and Transformer are input into the Cross-Attention mechanism for integration; S305, the features fused by the Cross-Attention mechanism are processed by the adaptive average pooling layer for dimension reduction, and finally the prediction result is output through the fully connected layer.

5. The multi-scale hierarchical clustering based spatio-temporal feature fusion concrete arch dam deformation prediction method according to claim 1, characterized in that, In the S4, when evaluating the prediction performance of the model by various evaluation indexes, the evaluation indexes are a determination coefficient R 2 , a root mean square error RMSE, a mean absolute error MAE, and a maximum absolute error AE max , and the calculation formula is: where n is the number of samples, y i and are the true and predicted values of the arch dam deformation, respectively; y is the average of the actual deformations.

6. The multi-scale hierarchical clustering based spatio-temporal feature fusion concrete arch dam deformation prediction method according to claim 1, characterized in that, In S4, the ablation experiment designs multiple model configuration schemes, and the specific method of the configuration scheme is: only using environmental factors as input; removing the Cross-Attention mechanism and using the ordinary fully connected layer for spatio-temporal feature fusion; removing the Transformer module; removing the TCN module.

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