A concrete dam crack opening prediction method, system, device and medium

Abstract

The application discloses a concrete dam crack opening prediction method, system, equipment and medium, the concrete dam crack opening prediction method first obtains the time sequence of crack opening and the time sequence of each environmental variable; then the time sequence of crack opening is decomposed once through IEMD; then the intrinsic mode function with similarity is reconstructed into trend component, periodic component and random component based on the mode reconstruction method of SPMFE and t-SNE; the random component with the highest complexity is decomposed twice by using SVMD; finally, the components are predicted by using the space-time attention mechanism of Crossformer, and the final prediction result is obtained by superimposing the prediction results of the components. The application can effectively reduce the complexity of the dam crack opening time sequence, thereby being conducive to learning deeper space-time correlation features from simple components, and improving the accuracy and robustness of non-stationary sequence prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of concrete structure safety monitoring, in particular to a concrete dam crack opening prediction method, system, device and medium. BACKGROUND

[0002] Affected by factors such as geological conditions, environmental loads and material aging, structural cracks are prone to occur in the dam body of a concrete dam. These cracks can weaken the strength and stiffness of the dam, significantly reduce the durability of the dam, and cause diseases such as leakage and corrosion, which seriously threaten the safety of the dam structure and the downstream ecology and public safety. Crack opening is an intuitive indicator of dam deformation and a key indicator for assessing the safety of the dam structure. Therefore, it is of great scientific significance and engineering value to establish a precise and efficient crack opening prediction model based on concrete dam monitoring data for diagnosing crack evolution and evaluating the operating state of the dam and guiding engineering safety decisions.

[0003] Existing crack opening prediction models can be mainly divided into three categories, including traditional models based on a single algorithm, combined models that fuse multiple algorithms, and hybrid models that use signal decomposition and reconstruction techniques. Both traditional models and combined models construct prediction models on the entire time series, so they cannot effectively distinguish between the trend component driven by environmental loads and the non-trend component caused by random disturbances in the dam crack opening, resulting in poor prediction results. Modal decomposition techniques can effectively reduce the complexity of the crack opening time series, but the high-frequency components obtained from a single decomposition still contain significant random components, and their non-stationary characteristics and irregularities still constrain the further improvement of prediction accuracy. SUMMARY

[0004] The first object of the present application is to provide a concrete dam crack opening prediction method with high prediction accuracy. The second object of the present application is to provide a concrete dam crack opening prediction system. The third object of the present application is to provide a concrete dam crack opening prediction device. The fourth object of the present application is to provide a computer-readable storage medium.

[0005] Technical solution: A concrete dam crack opening prediction method according to the present application comprises:

[0006] S1: Collecting crack opening and environmental variables affecting its change to obtain crack opening time series and time series of each environmental variable;

[0007] S2: Decomposing the crack opening time series into a plurality of intrinsic mode functions by an improved empirical mode decomposition algorithm IEMD;

[0008] S3: The multi-scale entropy feature vectors of each intrinsic mode function are calculated by the spatial post-multi-scale fusion entropy algorithm SPMFE. The dimensionality of the multi-scale entropy feature vectors of each intrinsic mode function is reduced by the t-distributed random neighborhood embedding algorithm t-SNE. Intrinsic mode functions with similar entropy features are superimposed and reconstructed into trend components, periodic components and random components.

[0009] S4: The random components are decomposed twice using the Continuous Variational Mode Decomposition (SVMD) algorithm to obtain several random component subsequences;

[0010] S5: Using the monitoring data of each environmental variable as input factors, and taking the trend component, periodic component and each random component subsequence as prediction targets respectively, multiple Crossformer models are constructed to perform component-level prediction. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

[0011] Furthermore, in step S1, the environmental variables include reservoir water level, temperature, and rainfall.

[0012] Further, step S3 includes: dividing each intrinsic mode function into equal parts. Each segment is calculated using the Spatial Post-Multi-Scale Fusion Entropy (SPMFE) algorithm. Entropy values ​​at different scales form The entropy-valued eigenvector is calculated using the following formula:

[0013]

[0014] in, For intrinsic mode functions, , This represents the number of sampling points; grayscale matrix various gray levels The probability of;

[0015] The t-distributed random neighborhood embedding algorithm t-SNE is used to... The entropy value eigenvector is projected into a two-dimensional eigenvector, and the intrinsic mode functions with similar two-dimensional features are superimposed and reconstructed into trend components, periodic components and random components.

[0016] Further, step S4 includes:

[0017] Assuming random components For the first Modality With remaining signals The sum of:

[0018]

[0019] Remaining signal Divided into the sum of extracted modes and unprocessed signal :

[0020]

[0021] in, For the extracted first One mode;

[0022] SVMD defines its optimization problem using the following four criteria:

[0023] Rule 1 Spectral compactness: Each mode has maximum spectral compactness near its center frequency.

[0024]

[0025] in, For the partial derivative with respect to time; It is the Dirac function; The imaginary unit; for The center frequency; This is a convolution operation;

[0026] Guideline 2 The spectral exclusivity of modes and residual signals, minimizing modes. With remaining signals Overlap in the spectrum:

[0027]

[0028] in, To revolve around the center frequency of the current mode to be extracted Constructed frequency domain penalty function; Angular frequency; for The impulse response; This is a penalty factor used to control spectral compactness and mode separation.

[0029] Guideline 3 Spectral distinguishability between modes to prevent overlap between the spectra of new modes and those of already extracted modes:

[0030]

[0031] in, To revolve around the extracted first A frequency domain penalty function constructed from the center frequencies of each mode; for The impulse response; For the extracted number The center frequency of each mode;

[0032] Guideline 4 Signal reconstruction constraints ensure complete signal reconstruction:

[0033]

[0034] Based on the above four criteria, the SVMD optimization problem can be categorized into the following constrained optimization model:

[0035]

[0036] SVMD solves the above optimization problem iteratively using the alternating direction multiplier method, and the final modal update formula is:

[0037]

[0038] in, For the first In the next iteration The frequency domain update value; This refers to the frequency domain representation of the signal. For the first During the next iteration The estimated center frequency; This is the frequency domain representation of the Lagrange multiplier.

[0039] Furthermore, in step S5, the Crossformer model includes a segmented embedding module, a two-stage attention layer, and a hierarchical encoder-decoder.

[0040] Crossformer embedding vectors are used to represent time series of each environment variable over fixed-length time intervals. Divide the data into several segments; perform linear projection on each segment to generate a vector. Combine it with location information Combine them to generate a two-dimensional vector group;

[0041] The two-stage attention layer consists of a first temporal attention layer and a second spatial attention layer, which are used to capture the temporal and spatial correlations of the input, respectively. The temporal attention layer uses a multi-head self-attention mechanism (MSA) to capture the temporal correlations within environmental variables.

[0042] The spatial attention layer comprises a router mechanism and two MSA layers. In the first MSA, the router is used as the query within the MSA, aggregating messages for all environment variables using all environment variable vectors as keys and values. In the second MSA, the opposite of the first MSA, the router uses environment variable vectors as queries, aggregating messages as keys and values, and transmitting received messages between vectors. This establishes... Full pairwise full connections between environmental variables enable the extraction of spatial features among environmental variables;

[0043] A scale fusion mechanism is introduced into the hierarchical encoder-decoder architecture. In the encoder, except for the first layer, each layer merges two adjacent vectors to obtain vectors with a larger time scale; using... The layer decoder performs predictions by linearly projecting the output of each layer to obtain the prediction result for that layer. The prediction results for each layer are summed to obtain the final prediction result. .

[0044] Furthermore, in step S5, the hyperparameters of each Crossformer model are optimized using the Snow Ablation Optimization Algorithm (SAO).

[0045] Furthermore, the hyperparameters include time periods. Number of routers , number of attention Number of encoder and decoder layers Training rounds and hidden layer dimension In the initial stage of SAO, the randomly generated hyperparameter set samples are modeled as a... The matrix, Indicates the size of the group. The dimension of the solution space is represented; the root mean square error is used as the fitness function; in the exploration phase of SAO, Brownian motion is used to simulate the random motion of water vapor in the parameter space; in the development phase of SAO, the degree-day method is used to simulate the snow melting process; a dual-population mechanism is used to achieve a balance between exploration and development.

[0046] Based on the same inventive concept, the present invention provides a concrete dam crack aperture prediction system, comprising:

[0047] The data acquisition module is used to collect crack aperture and environmental variables that affect its changes, and to obtain the time series of crack aperture and the time series of each environmental variable.

[0048] A primary decomposition module is used to decompose the crack aperture time series into several intrinsic mode functions using the improved empirical mode decomposition algorithm (IEMD).

[0049] The reconstruction module is used to calculate the multi-scale entropy feature vector of each intrinsic mode function through the spatial post-multi-scale fusion entropy algorithm SPMFE, reduce the dimensionality of the multi-scale entropy feature vector of each intrinsic mode function through the t-distributed random neighborhood embedding algorithm t-SNE, and superimpose and reconstruct intrinsic mode functions with similar entropy features into trend components, periodic components and random components.

[0050] The secondary decomposition module is used to perform secondary decomposition on the random components using the Continuous Variational Mode Decomposition (SVMD) algorithm to obtain several random component subsequences.

[0051] The prediction module uses monitoring data of various environmental variables as input factors and constructs multiple Crossformer models to perform component-level predictions, using trend components, periodic components, and random component subsequences as prediction targets. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

[0052] Based on the same inventive concept, the present invention provides a concrete dam crack opening prediction device, comprising a processor and a memory, wherein the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the concrete dam crack opening prediction device implements the steps of the concrete dam crack opening prediction method.

[0053] Based on the same inventive concept, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the concrete dam crack opening prediction method.

[0054] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: This invention proposes a multi-layer signal decomposition method: IEMD is used to decompose the crack aperture time series once; to further reduce the complexity of the prediction task and thus more fully extract deep spatiotemporal feature correlations in the time-frequency domain, significantly improving the model's prediction performance, SVMD is used to perform a secondary decomposition on the most complex random component. To reduce computational scale and error accumulation, this invention proposes a modal reconstruction method based on SPMFE and t-SNE, reconstructing similar intrinsic mode functions into trend components, periodic components, and random components. To fully extract spatiotemporal features, the Crossformer spatiotemporal attention mechanism is used to predict each component. This invention can effectively reduce the complexity of the dam crack aperture time series, thereby facilitating the learning of deeper spatiotemporal correlation features from simpler components, improving the accuracy and robustness of non-stationary sequence prediction, and providing a scientific basis for judging crack evolution patterns and guiding engineering safety decisions. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of a method for predicting the crack opening of a concrete dam according to an embodiment of the present invention;

[0056] Figure 2 This is a plan view of the dam hub and the joint gauge in an embodiment of the present invention;

[0057] Figure 3This is a diagram showing the layout of the joint measuring instrument and thermometer measuring points in dam section 18 of this invention.

[0058] Figure 4 This is a process line graph of monitoring data for reservoir water level, rainfall, crack opening and temperature in section 18 of the dam in this embodiment of the invention;

[0059] Figure 5 This is a comparison of the predicted and measured values ​​of each model at the J1 measurement point in the embodiments of the present invention, along with a magnified view of the local area.

[0060] Figure 6 This is a comparison of the predicted and measured values ​​of each model at the J9 measurement point in the embodiments of the present invention, along with a magnified view of a portion thereof.

[0061] Figure 7 This is a comparison of the predicted and measured values ​​of each model at the J10 measurement point in the embodiments of the present invention, along with a magnified view of a portion thereof.

[0062] Figure 8 This is a comparison of the predicted and measured values ​​of each model at the J13 measurement point in the embodiments of the present invention, along with a magnified view of a portion thereof.

[0063] Figure 9 This is a radar chart of different evaluation indicators for each model in the embodiments of the present invention, where (a) is... (b) is MAE, (c) is RMSE, and (d) is SMAPE.

[0064] Figure 10 These are residual violin plots of each model at different measurement points in the embodiments of the present invention, where (a) is measurement point J1, (b) is measurement point J9, (c) is measurement point J10, and (d) is measurement point J13. Detailed Implementation

[0065] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art will understand that the objectives and advantages achievable with the present invention are not limited to those specifically described above, and that the above and other objectives achievable by the present invention will become clearer from the following detailed description.

[0066] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application, design, and conditions of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0067] In this invention, the term "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0068] Example 1: See Figure 1 , Figure 1 This is a schematic flowchart of a method for predicting the crack opening of a concrete dam, as disclosed in an embodiment of the present invention. The method for predicting the crack opening of a concrete dam may include the following operations:

[0069] S1: Collect data on crack aperture and the environmental variables affecting its changes to obtain the time series of crack aperture and each environmental variable. Environmental variables include reservoir water level, temperature, and rainfall. As is known to those skilled in the art, crack aperture can be detected by a crack gauge, reservoir water level can be detected by a reservoir water level gauge, temperature can be detected by a thermometer, and rainfall can be detected by a rain gauge.

[0070] S2: The crack aperture time series is decomposed into several intrinsic mode functions (IMFs) by the improved empirical mode decomposition (IEMD) algorithm.

[0071] Traditional EMD is prone to mode aliasing, usually because the selection stopping criterion requires prior expert knowledge and is difficult to adaptively determine the number of iterations. IEMD proposes an improved soft stopping selection criterion by defining an objective function. Furthermore, an adaptive heuristic mechanism is adopted to automatically optimize the selection of the number of iterations, effectively solving the modal aliasing problem.

[0072] IEMD has a nested loop structure, with an inner loop existing within an outer loop. The outer loop uses the same architecture as EMD to extract the IMF from the raw signal. The inner loop is powered by a soft-stop screening criterion to extract a single IMF from the residual signal. The specific steps are as follows:

[0073] S201: Calculate the crack aperture time series upper envelope and lower envelope Determine the first Mean envelope of the next iteration .

[0074] S202: Update the sequence and perform filtering operations:

[0075]

[0076] in, For the first The sequence after the second sieve iteration.

[0077] S203: According to the objective function An adaptive heuristic mechanism is used to determine whether the filtering has reached its optimal state. If so, the filtering process stops and returns to the previous state. The decomposition results are shown in the following formula:

[0078]

[0079]

[0080] in, It is the root mean square; For local pulse characteristic overpeak; This represents the number of sampling points; for The mean; This represents the number of extreme points. The number of points crossing zero.

[0081] If not satisfied, let Return to step S201 to continue iterative filtering; if the maximum number of iterations is reached, force stop and take the current filtering result as... and update the residual sequence. The final IMFs obtained are:

[0082] .

[0083] S3: The multi-scale entropy feature vectors of each intrinsic mode function are calculated using the Spatial Post-Multiscale Fusion Entropy (SPMFE) algorithm. The dimensionality of the multi-scale entropy feature vectors of each intrinsic mode function is reduced using the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm. Intrinsic mode functions with similar entropy features are superimposed and reconstructed into trend components, periodic components, and random components.

[0084] Hybrid models employing mode decomposition significantly improve performance across all evaluation metrics; however, the computational complexity and time overhead of hybrid models increase with the number of decomposition layers. To achieve the optimal balance between prediction accuracy and time efficiency, this invention proposes a mode reconstruction method based on SPMFE and t-SNE. Specifically, SPMFE is first used to calculate the multi-scale entropy feature vectors of the intrinsic mode functions (IMFs) after IEMD decomposition, quantifying their complexity; a higher entropy value indicates higher complexity. Then, t-SNE is used to map the multi-dimensional entropy feature vectors to a two-dimensional space, calculating the similarity of the IMFs, thereby grouping them into different categories. The specific steps are as follows:

[0085] S301: Perform a short-time Fourier transform on the intrinsic mode functions (IMFs) after IEMD decomposition to obtain the time-spectrum matrix. :

[0086]

[0087] in, Indicates at time and frequency The short-time Fourier transform at the point; The number of discrete frequencies; For window functions; .

[0088] Time-frequency matrix The corresponding logarithmic spectrum matrix for:

[0089]

[0090] in, for The modulus.

[0091] S302: Yes Perform spatial multi-scale processing and construct a spatial multi-scale matrix. :

[0092]

[0093] in, Scale factor; For the spatial multiscale matrix, the first... line, number Column elements.

[0094] S303: Yes Normalize:

[0095]

[0096] in, For normalized spatial multi-scale matrices; and These are spatial multi-scale matrices. The minimum and maximum values.

[0097] S304: Using grayscale mapping to... Convert to grayscale matrix :

[0098]

[0099] in, This is the rounding function.

[0100] S305: Calculate the grayscale matrix various gray levels probability Then, the multi-scale fusion entropy after defining the space is:

[0101] .

[0102] S306: Divide each intrinsic mode function (IMF) into equal parts. Each segment is calculated using the Spatial Post-Multi-Scale Fusion Entropy (SPMFE) algorithm. Entropy values ​​at different scales form The dimensional entropy feature vector is transformed using the t-distributed random neighborhood embedding algorithm t-SNE. The entropy value eigenvector is projected into a two-dimensional eigenvector, and the intrinsic mode functions (IMFs) with similar two-dimensional features are superimposed and reconstructed into trend components, periodic components, and random components.

[0103] S4: The random components (which have the strongest volatility and nonlinearity) are decomposed twice by the Successive Variational Mode Decomposition (SVMD) algorithm to further reduce the complexity of the data and obtain several random component subsequences SDIMFs.

[0104] SVMD is a novel signal decomposition method that improves upon traditional VMD, overcoming the limitation of VMD requiring a pre-determined number of modes. The core idea of ​​SVMD is to extract modes from the signal sequentially, extracting a single mode at each step and removing it from the signal before extracting the next mode, until a specified termination condition is met, such as the reconstruction error reaching a threshold or all modes having been extracted. Furthermore, the SVMD algorithm incorporates constraints to avoid spectral overlap between newly extracted modes and previously extracted modes, thereby effectively improving mode discrimination and algorithm robustness.

[0105] SVMD is used to perform a secondary decomposition on the random component with the highest complexity (i.e., the highest entropy). Assume the random component... For the first Modality With remaining signals The sum of:

[0106]

[0107] Remaining signal It can also be divided into the sum of extracted modes and the unprocessed signal. :

[0108]

[0109] in, For the extracted first One modality.

[0110] SVMD defines its optimization problem using the following four criteria:

[0111] Rule 1 Spectral compactness: Each mode has maximum spectral compactness near its center frequency.

[0112]

[0113] in, For the partial derivative with respect to time; It is the Dirac function; The imaginary unit; for The center frequency; This is a convolution operation.

[0114] Guideline 2 The spectral exclusivity of modes and residual signals, minimizing modes. With remaining signals Overlap in the spectrum:

[0115]

[0116] in, To revolve around the center frequency of the current mode to be extracted Constructed frequency domain penalty function; Angular frequency; for The impulse response; This is a penalty factor used to control spectral compactness and mode separation.

[0117] Guideline 3 Spectral distinguishability between modes to prevent overlap between the spectra of new modes and those of already extracted modes:

[0118]

[0119] in, To revolve around the extracted first A frequency domain penalty function constructed from the center frequencies of each mode; for The impulse response; For the extracted number The center frequency of each mode.

[0120] Guideline 4 Signal reconstruction constraints ensure complete signal reconstruction:

[0121] .

[0122] Based on the above four criteria, the SVMD optimization problem can be categorized into the following constrained optimization model:

[0123] .

[0124] SVMD solves the above optimization problem iteratively using the alternating direction multiplier method, and the final modal update formula is:

[0125]

[0126] in, For the first In the next iteration The frequency domain update value; This refers to the frequency domain representation of the signal. For the first During the next iteration The estimated center frequency; This is the frequency domain representation of the Lagrange multiplier.

[0127] S5: Using the monitoring data of various environmental variables as input factors, and taking the trend component, periodic component and each random component subsequence as prediction targets, multiple Crossformer models are constructed for component-level prediction. The hyperparameters of each Crossformer model are optimized by the Snow Ablation Optimizer (SAO) algorithm. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

[0128] The Crossformer model is a variant of the Transformer model. It mainly includes modules such as segmented embedding, a two-stage attention layer, and a hierarchical encoder-decoder. These modules enable the model to extract the spatiotemporal features of environmental variable monitoring data such as dam reservoir water level, temperature, and rainfall, and improve modeling performance.

[0129] Crossformer embedding vectors are used to represent time series of each environment variable over fixed-length time intervals. The system is divided into several segments. A linear projection is performed on each segment to generate a vector. to position By combining these elements, a two-dimensional vector set is generated, thus preserving both temporal and spatial information.

[0130]

[0131] in, After adding position encoding, the first The first environment variable Data for a specific time period; The projection matrix is ​​learnable; For position The learnable position embedding matrix; For all A set; The number of environment variables. This refers to the window size.

[0132] The extraction of spatiotemporal features from monitoring data primarily relies on a two-stage attention layer. The first stage is a temporal attention layer, and the second stage is a spatial attention layer, used to capture the temporal and spatial correlations of the input, respectively. The temporal attention layer employs a multi-head self-attention (MSA) mechanism to capture the temporal correlations within environmental variables, as shown in the following formula:

[0133]

[0134]

[0135] In the formula: For the first All time steps of each environment variable; LayerNorm is layer normalization; MLP is a multilayer feedforward network; This is the output of MSA; This is the output of the MLP. It can capture the temporal dependencies of a single vector and use it as input to a spatial attention layer to capture spatial dependencies between environmental variables.

[0136] The spatial attention layer comprises a router mechanism and two MSA layers. In the first MSA, the router is used as the query within the MSA, aggregating messages for all environment variables using all environment variable vectors as keys and values. In the second MSA, in contrast to the first MSA, the router uses the environment variable vectors as queries, transmitting received messages between vectors using the aggregated messages as keys and values. This establishes... Full pairwise full joins between environmental variables enable the extraction of spatial features among these variables.

[0137]

[0138]

[0139] in, For the first All environment variables at each time step; This is a learnable vector array for the router; An aggregate message for all environment variables; This is the output of the router; This represents the number of segments.

[0140] A scale fusion mechanism is introduced into the hierarchical encoder-decoder architecture. Since data at different time scales contain dependencies at different levels, scale fusion allows the model to integrate information across multiple scales, thereby better capturing long-term and short-term dependencies and improving prediction accuracy. Therefore, in the encoder, except for the first layer, each layer merges two adjacent vectors to obtain a vector with a larger time scale. Layer decoder (both encoder and decoder have multiple layers) To make predictions, a linear projection is performed on the output of each layer to obtain the prediction result for that layer. The prediction results for each layer are summed to obtain the final prediction result. .

[0141] To further improve the performance of the Crossformer model in predicting dam deformation and enhance its generalization ability, the hyperparameters of the Crossformer model are optimized, including the time period. Number of routers , number of attention Number of encoder and decoder layers Training rounds and hidden layer dimension The SAO algorithm effectively balances exploration and exploitation of the hyperparameter solution space by simulating the sublimation and melting processes of snow. During sublimation, snow transforms into water vapor, and the diffusion of water vapor is highly random, which is beneficial for efficient exploration of the search space. On the other hand, the melting process transforms snow into liquid water, thus exhibiting exploitation characteristics. The SAO algorithm utilizes a dual-population mechanism to achieve a balance between exploration and exploitation, thereby achieving efficient optimization.

[0142] In the initial stage of SAO, the randomly generated hyperparameter set samples are modeled as a The matrix is ​​shown in the following formula:

[0143]

[0144] in, This represents the lower bound of the solution space; This represents the upper bound of the solution space; Represents a random number in the range [0,1]. Indicates the size of the group; This represents the dimension of the solution space.

[0145] The root mean square error (RMSE) is used as the fitness function, and its expression is as follows:

[0146]

[0147] in, For training sample size; For the first Measured deformation values ​​at any given time; For the first The predicted deformation value at time.

[0148] During the exploration phase of SAO, Brownian motion was used to simulate the random motion of water vapor in the parameter space:

[0149]

[0150] in, To obey The random variable represents the random perturbation step size used for parameter updates; Let be the probability density function of Brownian motion.

[0151] The position update expression is as follows:

[0152]

[0153] in, For the first The iteration of the ... Individual; An individual is randomly selected from a group of elites; the individuals with the highest fitness values ​​in the top 50% are called elites. It is a vector containing random numbers based on a Gaussian distribution; This is a term-by-term multiplication; A random number in the range [0,1]. For the first The optimal solution in the next iteration; This is the centroid position of the entire group; , These are the second and third most elite individuals in the current group, ranked by fitness value. It is the central position for the elite group; The number of elites.

[0154] During the development phase of SAO, the degree-day method was used to simulate the snow melting process, as shown in the following expression:

[0155]

[0156] in, Snowmelt rate; For daily living factors; This represents the maximum number of iterations.

[0157] The position update equation is as follows:

[0158]

[0159] in, for Random numbers in the array.

[0160] A dual-population mechanism is employed to achieve a balance between exploration and exploitation. In the initial phase of iteration, the entire population... They were randomly divided into two subpopulations of equal size. , ,in Responsible for exploration, Responsible for development. Population. , and The population sizes are respectively , and As the iterations proceed, Gradually decrease, The corresponding increase allows for a smooth transition from exploration-driven to development-driven optimization. This dynamic adjustment mechanism effectively balances resource allocation between global search and local development, preventing premature convergence and improving the algorithm's convergence accuracy and robustness.

[0161] Here is a specific example.

[0162] like Figure 2 As shown, a certain dam is a concrete gravity arch dam with a crest elevation of 126.30. The maximum dam height is 76.30 meters. The dam crest arc length is 419. The dam crest width is 8 There are 28 dam sections from left to right. The design flood level is 122.20. The checked flood level is 124.60. The reservoir is designed for multi-year regulation, with a total capacity of 2.825 billion cubic meters. The dam was constructed in three phases. Due to the short intervals between pouring layers during the second-phase concrete pouring, the shrinkage deformation of the second-phase concrete was strongly constrained by the first-phase concrete, resulting in uneven shrinkage at the top of the first-phase concrete (105m). Cracks appeared near the elevation, extending from dam block #5 to dam block #28, with a length of 300 meters. 5 meters deep The above factors have impacted the overall integrity of the dam. Therefore, 14 automated crack gauges were installed in sections 8 through 28 to monitor the changes in crack opening in a timely manner. Figure 2 In the diagram, J1 to J14 are the seam measuring instrument numbers. to Number the dam section.

[0163] Figure 3 This is a layout diagram of the joint gauge and thermometer measuring points for section 18 of the dam. Figure 4 This is a timeline graph of monitoring data for reservoir water level, rainfall, crack opening, and temperature in section 18 of the dam. The monitoring sequences for crack opening and environmental variables are 1810 observations from January 1, 2009 to December 31, 2013, divided into training, validation, and test sets in an 8:1:1 ratio.

[0164] To verify the advancement of this invention, a series of comparative models were introduced: RF, LSTM, Transformer, CNN+Transformer, Crossformer, SAO+Crossformer, IEMD+Crossformer, IEMD+Crossformer+SAO, SVMD+Crossformer, and SVMD+Crossformer+SAO. All comparative models used environmental variable monitoring data as input for prediction. Crack opening monitoring data from four typical measuring points (J1, J9, J10, and J13) in dam sections 8#, 18#, and 26# were selected for analysis.

[0165] Figures 5 to 8 This section presents a comparison of the predicted and measured values ​​of each model at different measurement points, along with magnified details of specific locations.Figures 5 to 8 It can be seen that the model proposed in this invention is the most accurate in predicting the trend, peak and valley positions, and amplitude at each measurement point, with the smallest error and the most synchronized phase. In contrast, the machine learning model RF has obvious prediction bias at multiple measurement points, especially exhibiting segmented discontinuities in abrupt change segments. Deep learning models LSTM, Transformer, and CNN+Transformer show phase lag or over-smoothing issues in some segments. Although the Crossformer model performs well overall, it still has some bias in rapidly changing phases. The hybrid model that incorporates time series decomposition significantly improves the fitting ability for complex non-stationary components, with fitting accuracy significantly better than single models and combined models, verifying the effectiveness of the frequency band decoupling and frequency division modeling strategy in complex time series prediction.

[0166] Figure 9 The radar chart comprehensively compared the predictive performance of each model at four typical measurement points using four evaluation metrics. Figure 9 As can be seen, the model proposed in this invention outperforms other comparative models in all metrics, verifying the necessity and effectiveness of introducing IEMD primary decomposition, SPMFE and t-SNE clustering, SVMD secondary decomposition, and Crossformer and SAO prediction. Specifically, the prediction accuracy of the machine learning model RF is generally low, especially at the J10 measurement point. The value is 0.688, significantly lower than the model proposed in this invention. Deep learning models such as LSTM, Transformer, and CNN+Transformer... The scores were generally below 0.93, with significantly larger errors in MAE, RMSE, and SMAPE, indicating insufficient fitting of non-stationary signals. The Crossformer model comprehensively outperformed the combined CNN+Transformer model, demonstrating its stronger ability to extract spatiotemporal features from monitoring data. At the J9 measurement point, the Crossformer's MAE, RMSE, and SMAPE were 0.059, 0.088, and 0.032, respectively, lower than the CNN+Transformer's 0.089, 0.107, and 0.053, representing reductions of 33.7%, 17.8%, and 39.6%, respectively. The accuracy is 0.958, higher than 0.948 for CNN+Transformer. SAO further improves the accuracy of the Crossformer model. A hybrid model combining IEMD and SVMD with Crossformer... The error index was generally improved to the range of 0.94–0.98 at all measurement points, showing a significant decrease, indicating that multi-scale decomposition plays an important role in reducing signal complexity; however, their performance was still lower than that of the model proposed in this invention, indicating that clustering and quadratic decomposition are particularly crucial for the accurate modeling of complex random components. The model proposed in this invention... The values ​​were generally higher than 0.97, reaching 0.992 and 0.991 at measurement points J9 and J13, respectively. MAE, RMSE, and SMAPE remained at the minimum values ​​at all measurement points, significantly outperforming all comparative models. Delving into the theoretical basis, this difference arises because the crack aperture time series after secondary decomposition more clearly shows its variation pattern, which is beneficial for the model to obtain the correlation between input factors and the crack aperture time series, thereby improving prediction performance. These results fully demonstrate that the layer-by-layer strategy of "decomposition-clustering-re-decomposition-modeling" can effectively reduce the complexity of non-stationary sequences, thus exhibiting excellent accuracy and robustness in prediction.

[0167] Calculate the residuals between each model's predicted values ​​and observed values, and visualize them using a violin plot to more intuitively compare the predictive performance of each model. Figure 10 As shown. By Figure 10 As can be seen, the residuals of the model proposed in this invention exhibit the most compact and symmetrical distribution characteristics across all measurement points, with a median close to zero, the smallest interquartile range (IQR), and a significantly contracted tail extension. This indicates that the model can effectively suppress systematic bias and random errors, and the predicted results are highly consistent with the measured values. In contrast, the residual distributions of RF, MLP, and LSTM are generally more dispersed, with longer tail extensions and medians deviating from zero, especially at measurement points J1 and J10, reflecting strong bias accumulation and instability. Transformer and CNN+Transformer outperform machine learning methods at most measurement points, but still exhibit relatively large residual dispersion. Crossformer and its hybrid models combined with time series decomposition show higher concentration and stability in residual distribution; however, these models still lag behind the model proposed in this invention in terms of residual amplitude control and overall robustness. In summary, the residual distribution analysis further verifies the accuracy advantage and wide adaptability of the model proposed in this invention in predicting complex non-stationary sequences.

[0168] Example 2: Example 2 provides a concrete dam crack opening prediction system, including a data acquisition module, a primary decomposition module, a reconstruction module, a secondary decomposition module, and a prediction module.

[0169] The data acquisition module is used to collect the crack aperture and the environmental variables that affect its changes, obtaining the time series of crack aperture and the time series of each environmental variable. The environmental variables include reservoir water level, temperature, and rainfall.

[0170] The primary decomposition module is used to decompose the crack aperture time series into several intrinsic mode functions (IMFs) using the improved empirical mode decomposition (IEMD) algorithm.

[0171] The reconstruction module is used to calculate the multi-scale entropy feature vectors of each intrinsic mode function using the Spatial Post-Multiscale Fusion Entropy (SPMFE) algorithm, reduce the dimensionality of the multi-scale entropy feature vectors of each intrinsic mode function using the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm, and reconstruct the intrinsic mode functions with similar entropy features by superimposing them into trend components, periodic components, and random components.

[0172] The secondary decomposition module is used to perform secondary decomposition on random components (which have the strongest volatility and nonlinearity) using the Successive Variational Mode Decomposition (SVMD) algorithm, further reducing the complexity of the data and obtaining several random component subsequences SDIMFs.

[0173] The prediction module uses monitoring data of various environmental variables as input factors and constructs multiple Crossformer models for component-level prediction using trend components, periodic components, and random component subsequences as prediction targets. The hyperparameters of each Crossformer model are optimized using the Snow Ablation Optimizer (SAO) algorithm. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

[0174] Example 3: Example 3 provides a concrete dam crack opening prediction device, including a processor and a memory. The memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the concrete dam crack opening prediction device implements the steps of the concrete dam crack opening prediction method described in Example 1, and can achieve the same technical effect.

[0175] The memory may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the memory may be used to read and write non-removable, non-volatile magnetic media (commonly referred to as a "hard disk drive"). A program / utility having a set (at least one) of program modules may be stored in, for example, memory. Such program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The program modules typically perform the functions and / or methods described in the embodiments of the present invention.

[0176] The processor executes various functional applications and data processing by running programs stored in memory, such as the concrete dam crack opening prediction method provided in Embodiment 1 of the present invention.

[0177] Example 4: Example 4 provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the steps of the concrete dam crack opening prediction method as described in Example 1, and achieves the same technical effect.

[0178] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0179] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0180] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0181] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0182] Of course, the computer-executable instructions provided in the embodiments of the present invention are not limited to the above-described method operations, but can also perform related operations in the methods provided in any embodiment of the present invention.

[0183] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the crack opening of a concrete dam, characterized in that, include: S1: Collect crack aperture and environmental variables that affect its changes to obtain crack aperture time series and time series of each environmental variable; S2: The crack aperture time series is decomposed into several intrinsic mode functions by the improved empirical mode decomposition algorithm IEMD; S3: The multi-scale entropy feature vectors of each intrinsic mode function are calculated by the spatial post-multi-scale fusion entropy algorithm SPMFE. The dimensionality of the multi-scale entropy feature vectors of each intrinsic mode function is reduced by the t-distributed random neighborhood embedding algorithm t-SNE. Intrinsic mode functions with similar entropy features are superimposed and reconstructed into trend components, periodic components and random components. Step S3 includes: dividing each intrinsic mode function into equal parts. Each segment is calculated using the Spatial Post-Multi-Scale Fusion Entropy (SPMFE) algorithm. Entropy values ​​at different scales form The entropy-valued eigenvector is calculated using the following formula: in, For intrinsic mode functions, , This represents the number of sampling points; grayscale matrix various gray levels The probability of; The t-distributed random neighborhood embedding algorithm t-SNE is used to... The entropy value eigenvector is projected into a two-dimensional eigenvector, and the intrinsic mode functions with similar two-dimensional features are superimposed and reconstructed into trend components, periodic components and random components; S4: The random components are decomposed twice using the Continuous Variational Mode Decomposition (SVMD) algorithm to obtain several random component subsequences; S5: Using the monitoring data of each environmental variable as input factors, and taking the trend component, periodic component and each random component subsequence as prediction targets respectively, multiple Crossformer models are constructed to perform component-level prediction. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

2. The method for predicting the crack opening of a concrete dam according to claim 1, characterized in that, In step S1, the environmental variables include reservoir water level, temperature, and rainfall.

3. The method for predicting the crack opening of a concrete dam according to claim 1, characterized in that, Step S4 includes: Assuming random components For the first Modality With remaining signals The sum of: Remaining signal Divided into the sum of extracted modes and unprocessed signal : in, For the extracted first One mode; SVMD defines its optimization problem using the following four criteria: Rule 1 Spectral compactness: Each mode has maximum spectral compactness near its center frequency. in, For the partial derivative with respect to time; It is the Dirac function; The imaginary unit; for The center frequency; This is a convolution operation; Guideline 2 The spectral exclusivity of modes and residual signals, minimizing modes. With remaining signals Overlap in the spectrum: in, To revolve around the center frequency of the current mode to be extracted Constructed frequency domain penalty function; Angular frequency; for The impulse response; This is a penalty factor used to control spectral compactness and mode separation. Guideline 3 Spectral distinguishability between modes to prevent overlap between the spectra of new modes and those of already extracted modes: in, To revolve around the extracted first A frequency domain penalty function constructed from the center frequencies of each mode; for The impulse response; For the extracted number The center frequency of each mode; Guideline 4 Signal reconstruction constraints ensure complete signal reconstruction: Based on the above four criteria, the SVMD optimization problem can be categorized into the following constrained optimization model: SVMD solves the above optimization problem iteratively using the alternating direction multiplier method, and the final modal update formula is: in, For the first In the next iteration The frequency domain update value; This refers to the frequency domain representation of the signal. For the first During the next iteration The estimated center frequency; This is the frequency domain representation of the Lagrange multiplier.

4. The method for predicting the crack opening of a concrete dam according to claim 1, characterized in that, In step S5, the Crossformer model includes a segmented embedding module, a two-stage attention layer, and a hierarchical encoder-decoder. Crossformer embedding vectors are used to represent time series of each environment variable over fixed-length time intervals. Divide the data into several segments; perform linear projection on each segment to generate a vector. Combine it with location information Combine them to generate a two-dimensional vector group; The two-stage attention layer consists of a first temporal attention layer and a second spatial attention layer, which are used to capture the temporal and spatial correlations of the input, respectively. The temporal attention layer uses a multi-head self-attention mechanism (MSA) to capture the temporal correlations within environmental variables. The spatial attention layer comprises a router mechanism and two MSA layers. In the first MSA, the router is used as the query within the MSA, aggregating messages for all environment variables using all environment variable vectors as keys and values. In the second MSA, the opposite of the first MSA, the router uses environment variable vectors as queries, aggregating messages as keys and values, and transmitting received messages between vectors. This establishes... Full pairwise full connections between environmental variables enable the extraction of spatial features among environmental variables; A scale fusion mechanism is introduced into the hierarchical encoder-decoder architecture. In the encoder, except for the first layer, each layer merges two adjacent vectors to obtain vectors with a larger time scale; using... The layer decoder performs predictions by linearly projecting the output of each layer to obtain the prediction result for that layer. The prediction results for each layer are summed to obtain the final prediction result. .

5. The method for predicting the crack opening of a concrete dam according to claim 4, characterized in that, In step S5, the hyperparameters of each Crossformer model are optimized using the Snow Ablation Optimization Algorithm (SAO).

6. The method for predicting the crack opening of a concrete dam according to claim 5, characterized in that, The hyperparameters include time periods. Number of routers , number of attention Number of encoder and decoder layers Training rounds and hidden layer dimension In the initial stage of SAO, the randomly generated hyperparameter set samples are modeled as a... The matrix, Indicates the size of the group. The dimension of the solution space is represented; the root mean square error is used as the fitness function; in the exploration phase of SAO, Brownian motion is used to simulate the random motion of water vapor in the parameter space; in the development phase of SAO, the degree-day method is used to simulate the snow melting process; a dual-population mechanism is used to achieve a balance between exploration and development.

7. A system for predicting the crack opening of a concrete dam, characterized in that, include: The data acquisition module is used to collect crack aperture and environmental variables that affect its changes, and to obtain the time series of crack aperture and the time series of each environmental variable. A primary decomposition module is used to decompose the crack aperture time series into several intrinsic mode functions using the improved empirical mode decomposition algorithm (IEMD). The reconstruction module calculates the multi-scale entropy feature vectors of each intrinsic mode function (EMF) using the Spatial Post-Multi-Scale Fusion Entropy (SPMFE) algorithm. It then reduces the dimensionality of these feature vectors using the t-distributed random neighborhood embedding (t-SNE) algorithm and reconstructs EMFs with similar entropy features by superimposing them into trend components, periodic components, and random components. Each EMF is then divided into equal parts. Each segment is calculated using the Spatial Post-Multi-Scale Fusion Entropy (SPMFE) algorithm. Entropy values ​​at different scales form The entropy-valued eigenvector is calculated using the following formula: in, For intrinsic mode functions, , This represents the number of sampling points; grayscale matrix various gray levels The probability of; The t-distributed random neighborhood embedding algorithm t-SNE is used to... The entropy value eigenvector is projected into a two-dimensional eigenvector, and the intrinsic mode functions with similar two-dimensional features are superimposed and reconstructed into trend components, periodic components and random components; The secondary decomposition module is used to perform secondary decomposition on the random components using the Continuous Variational Mode Decomposition (SVMD) algorithm to obtain several random component subsequences. The prediction module uses monitoring data of various environmental variables as input factors and constructs multiple Crossformer models to perform component-level predictions, using trend components, periodic components, and random component subsequences as prediction targets. The prediction results of all components are superimposed to obtain the final prediction result of the crack aperture time series.

8. A device for predicting the crack opening of a concrete dam, characterized in that, The device includes a processor and a memory, wherein the memory stores computer instructions, and the processor executes the computer instructions stored in the memory. When the computer instructions are executed by the processor, the concrete dam crack opening prediction device implements the steps of the concrete dam crack opening prediction method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the concrete dam crack opening prediction method as described in any one of claims 1 to 6.

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