A dynamic loading analysis method and system for anti-heave of underground structures

Abstract

The present invention relates to the technical field of load analysis, and discloses an anti-heave dynamic loading analysis method and system for underground structures, which are used to improve the accuracy and efficiency of the load analysis method for subway structures during bilateral expansion of subways. The method includes: performing fractal interpolation and chaotic dynamics analysis on spatio-temporal data streams to obtain high-dimensional phase space trajectories; extracting topological features and performing non-linear dimensionality reduction on the high-dimensional phase space trajectories to obtain the main patterns and key features of load distributions; performing probability density estimation on the main patterns and key features of load distributions to obtain parameter estimation data of load probability distributions; performing time series analysis on the parameter estimation data to obtain the dynamic evolution law of load characteristics; based on the dynamic evolution law of load characteristics, performing multi-scale decomposition and reconstruction to obtain the hierarchical load numerical distribution data of the subway structure within the shield section, and performing multi-objective optimization analysis on the hierarchical load numerical distribution data to obtain a construction suggestion strategy dataset.

Description

Technical Field

[0001] The present invention relates to the technical field of load analysis, and particularly to a method and system for anti - heave dynamic loading analysis of underground structures. Background Art

[0002] In recent years, with the acceleration of the urbanization process, the construction scale of underground projects such as subways has been continuously expanding. When carrying out expansion construction around operating subways, the load analysis of subway structures, especially shield sections, has always been an important challenge faced by the engineering community. Traditional load analysis methods mainly rely on empirical formulas and simplified models, such as the stratum stress method, the support structure method, etc. Although these methods can predict the load distribution to a certain extent, they often ignore the complexity of geological conditions and the dynamic changes during the construction process. In recent years, with the development of sensing technology and data analysis methods, load analysis methods based on monitoring data have gradually received attention. These methods collect various parameters during the construction process in real - time by arranging various sensors around the shield machine and the tunnel, and then use data - processing technology for load analysis.

[0003] However, the existing load analysis methods based on monitoring data still have some deficiencies. First, in the face of massive, multi - source, and heterogeneous monitoring data, traditional data - processing methods are difficult to effectively extract and fuse key information. Second, the load distribution during the construction process around the shield section has highly non - linear and non - stationary characteristics, and conventional statistical analysis methods are difficult to accurately capture its complex dynamic characteristics. Third, existing methods mostly focus on the static distribution of loads and lack in - depth analysis of the spatio - temporal evolution law of loads. Finally, the connection between the load analysis results and the optimization of construction parameters is not close enough, making it difficult to provide direct guidance for engineering practice. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide a method and system for anti - heave dynamic loading analysis of underground structures, which are used to improve the accuracy and efficiency of the load analysis method for subway structures during double - side expansion of subways.

[0005] The present invention provides a method for anti - heave dynamic loading analysis of underground structures, including:

[0006] S1. Perform adaptive fusion coding on the original data collected by surveying and mapping the subway structure in the shield section to obtain a spatio - temporal data stream;

[0007] S2. Perform fractal interpolation and chaotic dynamics analysis on the spatio - temporal data stream to obtain a reconstructed high - dimensional phase - space trajectory;

[0008] S3. Extract topological features and perform non - linear dimensionality reduction on the reconstructed high - dimensional phase - space trajectory to obtain the main patterns and key features of the load distribution;

[0009] S4. Perform probability density estimation on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution;

[0010] S5. Conduct time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics;

[0011] S6. Based on the dynamic evolution law of the load characteristics, perform multi-scale decomposition and reconstruction to obtain the hierarchical load numerical distribution data of the subway structure within the shield section, and conduct multi-objective optimization analysis on the hierarchical load numerical distribution data to obtain a construction suggestion strategy dataset.

[0012] The present invention also provides an anti-heave dynamic loading analysis system for an underground structure, including:

[0013] An encoding module, configured to perform adaptive fusion encoding on the original data collected by surveying and mapping the subway structure within the shield section to obtain a spatio-temporal data stream;

[0014] An interpolation module, configured to perform fractal interpolation and chaotic dynamics analysis on the spatio-temporal data stream to obtain a reconstructed high-dimensional phase space trajectory;

[0015] A dimension reduction module, configured to extract topological features and perform non-linear dimension reduction on the reconstructed high-dimensional phase space trajectory to obtain the main patterns and key features of the load distribution;

[0016] An estimation module, configured to perform probability density estimation on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution;

[0017] An analysis module, configured to conduct time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics;

[0018] An optimization module, configured to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics to obtain the hierarchical load numerical distribution data of the subway structure within the shield section, and conduct multi-objective optimization analysis on the hierarchical load numerical distribution data to obtain a construction suggestion strategy dataset.

[0019] In the technical solution provided by the present invention, through adaptive fusion coding of the original data collected by multi-source sensors, efficient data compression and information extraction are achieved, significantly reducing data transmission and storage requirements while retaining key load information. This method not only improves data processing efficiency but also provides high-quality input for subsequent analysis. Secondly, by using fractal interpolation and chaotic dynamics analysis methods, the inherent complexity and dynamic characteristics of load data are deeply explored, laying a foundation for accurately grasping the load change law during shield tunneling construction. Through topological feature extraction and nonlinear dimensionality reduction techniques, the main patterns and key features of load distribution are successfully captured, greatly improving the ability to understand and describe complex load states. The introduction of probability density estimation and parametric modeling enables the quantitative expression of the uncertainty of load distribution, providing a reliable basis for risk assessment and decision-making. The application of time series analysis methods reveals the dynamic evolution law of load characteristics, making it possible to predict the load change trend. The use of multi-scale decomposition and reconstruction techniques realizes the accurate description of the layered load in the shield section, providing the necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction suggestion strategies are obtained, directly guiding construction practice and improving construction efficiency and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] Figure 1 It is a flowchart of a method for dynamic loading analysis of anti-heave of an underground structure in an embodiment of the present invention;

[0022] Figure 2 It is a schematic diagram of a system for dynamic loading analysis of anti-heave of an underground structure in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] The technical solutions of the present invention will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0024] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0025] In addition, the technical features involved in different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0026] For ease of understanding, the specific process of the embodiment of the present invention is described below. Please refer to Figure 1 , Figure 1 which is a flowchart of a method for analyzing the anti - uplift dynamic loading of an underground structure in an embodiment of the present invention. As Figure 1 shown, it includes the following steps:

[0027] S1. Perform adaptive fusion coding on the original data collected by surveying and mapping the subway structure in the shield tunnel section to obtain a spatio - temporal data stream;

[0028] S2. Perform fractal interpolation and chaotic dynamics analysis on the spatio - temporal data stream to obtain a reconstructed high - dimensional phase - space trajectory;

[0029] S3. Extract topological features and perform non - linear dimensionality reduction on the reconstructed high - dimensional phase - space trajectory to obtain the main patterns and key features of the load distribution;

[0030] S4. Perform probability density estimation on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution;

[0031] S5. Perform time - series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics;

[0032] S6. Based on the dynamic evolution law of the load characteristics, perform multi - scale decomposition and reconstruction to obtain the numerical distribution data of the layered load of the subway structure in the shield tunnel section, and perform multi - objective optimization analysis on the numerical distribution data of the layered load to obtain a construction suggestion strategy dataset.

[0033] It should be noted that multi-source sensors, including stress sensors, displacement sensors, pressure sensors, etc., are pre-arranged on the subway structure in the shield section to collect raw data. These raw data are processed through adaptive fusion coding to obtain spatio-temporal data streams. Technologies such as stress-strain separation, elastic-plastic decoupling, and time-frequency joint analysis are adopted to effectively extract load response data and modal parameters. For example, for a certain shield section, data from 10 different types of sensors may be collected simultaneously, generating 1000 data points per second. Through adaptive fusion coding, these heterogeneous data are uniformly processed to obtain a compressed and fused spatio-temporal data stream of 100 data points per second, greatly reducing the data volume while retaining key information.

[0034] Fractal interpolation and chaotic dynamics analysis are performed on the spatio-temporal data stream to obtain the reconstructed high-dimensional phase space trajectory. Using fractal theory and chaotic dynamics methods, the inherent complexity of the load data is deeply explored. By calculating indicators such as fractal dimension and Lyapunov exponent, the data is classified and reconstructed. For example, the compressed and fused data stream of a certain shield section may exhibit a fractal dimension of 2.3, indicating its high complexity. After fractal interpolation, the data resolution is increased by 5 times, better reflecting the details of load changes. Topological feature extraction and non-linear dimensionality reduction are performed on the reconstructed high-dimensional phase space trajectory to obtain the main patterns and key features of the load distribution. Advanced mathematical tools such as persistent homology analysis and isometric mapping are used to extract the most representative features from the high-dimensional data. For example, through persistent homology analysis, it may be found that there are 3 main topological features in the load distribution, corresponding to the influence of different geological conditions. After non-linear dimensionality reduction, the originally 100-dimensional data may be reduced to 10 dimensions, making it easier for subsequent analysis.

[0035] Probability density estimation is performed on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution. Methods such as kernel density estimation and maximum likelihood estimation are used to construct a probability model of the load distribution. For example, the load distribution at a certain key point may be estimated as a normal distribution with a mean of 500 kN and a standard deviation of 50 kN, which provides an important basis for subsequent risk assessment. Then, time series analysis is performed on the parameter estimation data to obtain the dynamic evolution law of the load characteristics. Time-frequency analysis methods such as Fourier transform and wavelet decomposition are used to reveal the law of load variation over time. For example, through analysis, it may be found that the load in a certain shield section shows a variation law with a period of 12 hours, and the peak usually appears around 10 am every day.

[0036] The last step is to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of load characteristics, obtain the numerical distribution data of the hierarchical loads of the subway structure within the shield section, and conduct multi-objective optimization analysis on these data to obtain a dataset of construction advice strategies. Integrating all the previous analysis results, through methods such as empirical mode decomposition and multi-objective optimization, specific construction guidance is finally formed.

[0037] By implementing the above steps, through adaptive fusion coding of the raw data collected by multi-source sensors, efficient data compression and information extraction are achieved, significantly reducing data transmission and storage requirements while retaining key load information. This method not only improves the data processing efficiency but also provides high-quality input for subsequent analysis. Secondly, by using fractal interpolation and chaotic dynamics analysis methods, the inherent complexity and dynamic characteristics of the load data are deeply explored, laying a foundation for accurately grasping the load change law during the shield construction process. Through topological feature extraction and nonlinear dimensionality reduction techniques, the main patterns and key features of the load distribution are successfully captured, greatly improving the ability to understand and describe complex load states. The introduction of probability density estimation and parametric modeling enables the quantification of the uncertainty of the load distribution, providing a reliable basis for risk assessment and decision-making. The application of time series analysis methods reveals the dynamic evolution law of load characteristics, making it possible to predict the load change trend. The use of multi-scale decomposition and reconstruction techniques realizes the accurate description of the hierarchical loads in the shield section, providing the necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction advice strategies are obtained, directly guiding construction practice and improving construction efficiency and safety.

[0038] In a specific embodiment, the process of executing step S1 may specifically include the following steps:

[0039] (1) Perform stress-strain separation processing on the raw data collected by multi-source sensors to obtain the separated stress data and strain data, and conduct elastoplastic decoupling analysis on the stress data and strain data to obtain elastic deformation components and plastic deformation components;

[0040] (2) Calculate the load-deformation curve and extract response data based on the elastic deformation components and plastic deformation components to obtain load response data;

[0041] (3) Conduct time-frequency joint analysis on the load response data to obtain a load frequency spectrum diagram, and extract the main frequency characteristics and energy distribution based on the load frequency spectrum diagram to obtain load modal parameters;

[0042] (4) Extract non-linear characteristics of the load modal parameters to obtain load non-linear indicators, and conduct mutual information analysis on the load non-linear indicators and the raw data to obtain the weights of key sensors;

[0043] (5) Adaptive fusion of multi-source data is performed according to the key sensor weights to obtain fused load data;

[0044] (6) Complexity analysis is carried out on the fused load data to obtain a data complexity index, and an adaptive quantization strategy is designed according to the data complexity index to obtain a quantization coding scheme;

[0045] (7) Compression coding of the fused load data is performed through the quantization coding scheme to obtain a spatio-temporal data stream.

[0046] Specifically, in the shield tunnel section load analysis, the original data is separated into stress data and strain data through stress-strain separation processing. Hooke's law is utilized. For materials within the linear elastic range, the stress σ and strain relationship can be expressed as:

[0047] ;

[0048] where is Young's modulus. The stress and strain in the original data can be separated.

[0049] Elastoplastic decoupling analysis is carried out on the separated stress data and strain data to obtain elastic deformation components and plastic deformation components. The Ramberg-Osgood model is used, and this model describes the stress-strain relationship of materials in the elastoplastic stage:

[0050] ;

[0051] where is a material constant, is the strength coefficient, is the strain hardening index. The total strain can be decomposed into elastic strain and plastic strain. According to the obtained elastic deformation components and plastic deformation components, the load-deformation curve is calculated and response data is extracted to obtain load response data. Through interpolation and fitting methods, a complete load-deformation relationship curve is constructed.

[0052] Subsequently, time-frequency joint analysis is carried out on the load response data to obtain a load spectrogram. Here, the short-time Fourier transform (STFT) method is adopted, and the mathematical expression of STFT is:

[0053] ;

[0054] where is the signal, is the window function, is the time offset parameter, representing the center position of the window function; is the angular frequency, is a time variable, is the imaginary unit, ; is the complex exponential function, which is used to transform the signal into the frequency domain; through STFT, the energy distribution of the signal at different times and frequencies can be obtained. According to the load frequency spectrum diagram, the main frequency characteristics and energy distribution are extracted to obtain the load modal parameters. Through peak detection and energy integration methods, the main frequency components of the load and the corresponding energy distribution are identified.

[0055] Nonlinear feature extraction is performed on the load modal parameters to obtain the load nonlinear index. Here, the bispectrum analysis method is used, and the bispectrum can detect the second-order nonlinear correlation in the signal. Subsequently, mutual information analysis is performed on the load nonlinear index and the original data to obtain the key sensor weights. Mutual information The calculation formula is:

[0056] ;

[0057] where is and 's joint probability distribution, and are the first marginal probability distribution and the second marginal probability distribution respectively; according to the obtained key sensor weights, the multi-source data is adaptively fused to obtain the fused load data. The weighted average method is used to fuse the data according to the weights of each sensor.

[0058] Complexity analysis is performed on the fused load data to obtain the data complexity index. Here, the Sample Entropy method is used, and the sample entropy reflects the complexity and irregularity of the time series. An adaptive quantization strategy is designed according to the data complexity index to obtain the quantization coding scheme. Finally, the fused load data is compressed and encoded through the quantization coding scheme to obtain the spatio-temporal data stream. The adaptive arithmetic coding method is adopted, and the coding strategy is dynamically adjusted according to the statistical characteristics of the data to achieve efficient data compression.

[0059] For example, during the construction of a certain shield tunnel section, 20 strain sensors and 15 pressure sensors are arranged, and the sampling frequency is 100Hz. After the original data is processed by stress-strain separation, the stress data range is 0 - 50MPa, and the strain data range is 0 - 2000 . Through elastoplastic decoupling analysis, it is found that at a stress level of 30MPa, the elastic strain is about 1000 , and the plastic strain is about 200 Time-frequency joint analysis shows that the main frequency components of the load are concentrated at 2 Hz, 5 Hz, and 8 Hz, and the energies account for 40%, 30%, and 20% of the total energy respectively. Nonlinear feature extraction and mutual information analysis indicate that 5 strain sensors and 3 pressure sensors contribute the most to the load characteristics, and the sum of their weights accounts for 75% of the total weight. Finally, through adaptive quantization and coding, the compression ratio of the original data reaches 10:1, and a compressed fusion spatio-temporal data stream of 350 bytes per second is obtained.

[0060] In a specific embodiment, the process of performing step S2 may specifically include the following steps:

[0061] (1) Calculate the fractal dimension of the spatio-temporal data stream to obtain a self-similarity index, and perform fractal interpolation on the spatio-temporal data stream according to the self-similarity index to obtain a high-resolution interpolation data set;

[0062] (2) Reconstruct the phase space of the interpolation data set to obtain a high-dimensional phase space trajectory, and calculate the Lyapunov exponent for the high-dimensional phase space trajectory to obtain a chaos characteristic index;

[0063] (3) Segment the high-dimensional phase space trajectory according to the chaos characteristic index to obtain N sub-trajectories with different dynamic characteristics, where N is an integer between 2 and 5, and perform recursive quantitative analysis on the N sub-trajectories respectively to obtain N sets of dynamic characteristic index sets, and each set of index sets includes four parameters: periodicity, determinacy, laminarity, and complexity;

[0064] (4) Perform clustering analysis on the N sets of dynamic characteristic index sets to obtain K stability levels, where K is an integer between 2 and 4, and classify the spatio-temporal data stream according to the K stability levels to obtain K data subsets with stability levels;

[0065] (5) Perform cross-correlation analysis on the K data subsets with stability levels to obtain a K×K-dimensional variable coupling relationship matrix, and construct a multi-dimensional phase transition diagram according to the coupling relationship matrix to obtain a reconstructed high-dimensional phase space trajectory.

[0066] Specifically, calculate the fractal dimension of the data stream to obtain a self-similarity index. Here, the box-counting method is used to calculate the fractal dimension D, and its formula is:

[0067] ;

[0068] where is the number of The number of boxes of a certain size. Based on the calculated self-similarity index, fractal interpolation is performed on the spatio-temporal data stream to obtain a high-resolution interpolated data set. Fractal interpolation utilizes the self-similarity characteristics of the data to insert new data points between the original data points, thereby improving the resolution of the data. Next, phase space reconstruction is carried out on the interpolated data set to obtain high-dimensional phase space trajectories. Phase space reconstruction is based on the Takens embedding theorem, and appropriate embedding dimensions and time offset parameters are selected to map the one-dimensional time series onto dimensional phase space:

[0069] ;

[0070] Calculate the Lyapunov exponent for the reconstructed high-dimensional phase space trajectories to obtain the chaos characteristic index. The Lyapunov exponent characterizes the separation rate of neighboring orbits in the phase space, and its calculation formula is:

[0071] ;

[0072] where is the distance between two orbits with an initial distance of at time .

[0073] Based on the obtained chaos characteristic index, segment the high-dimensional phase space trajectories to obtain N sub-trajectories with different dynamic characteristics, where N is an integer between 2 and 5. The segmentation method is based on the changing trend of the chaos characteristic index, and cuts are made at the points where the index value changes significantly. Perform recurrence quantification analysis (RQA) on these N sub-trajectories respectively to obtain N sets of dynamic characteristic index sets. Each set of index sets contains four parameters: periodicity, determinism, laminarity, and complexity. The RQA method quantifies the dynamic characteristics of the system by constructing a recurrence plot and calculating various statistics. Subsequently, perform clustering analysis on the N sets of dynamic characteristic index sets using the K-means algorithm to obtain K stability levels, where K is an integer between 2 and 4. The K-means algorithm iteratively optimizes, assigns data points to the nearest cluster center, and updates the cluster center until convergence. Classify the spatio-temporal data stream according to the obtained K stability levels to obtain K subsets of data with different stability levels. Finally, perform cross-correlation analysis on the K subsets of data with different stability levels to obtain a K×K dimensional variable coupling relationship matrix. Cross-correlation analysis calculates the correlation coefficients between different data subsets, reflecting the coupling strength between them. Construct a multi-dimensional phase transition diagram based on this coupling relationship matrix to obtain the reconstructed high-dimensional phase space trajectories.

[0074] For example, in the construction of a subway expansion foundation pit, the collected compressed and fused spatio-temporal data stream is analyzed. First, the fractal dimension is calculated, and D = 1.76 is obtained, indicating that the data has strong self-similarity. Based on this self-similarity index, fractal interpolation is performed on the original data, increasing the number of data points from 100 per second to 500. Then, phase space reconstruction is carried out, and the embedding dimension m = 5 and time delay are selected to obtain a 5-dimensional phase space trajectory. The Lyapunov exponent is calculated , indicating that the system has weak chaotic characteristics. According to the change of the value, the trajectory is divided into 3 sub-trajectories. RQA analysis is performed on these 3 sub-trajectories to obtain 3 sets of dynamic characteristic index sets. For example, the periodicity of the first set of index sets is 0.8, the determinism is 0.7, the laminarity is 0.6, and the complexity is 0.5. K-means clustering (K = 3) is performed on these 3 sets of index sets to obtain three stability levels: high, medium, and low. Finally, a 3×3 coupling relationship matrix is obtained through cross-correlation analysis, and the matrix element values range from -1 to 1, reflecting the correlation degree between data of different stability levels.

[0075] In a specific embodiment, the process of executing step S3 may specifically include the following steps:

[0076] (1) Perform persistent homology analysis on the reconstructed high-dimensional phase space trajectory to obtain a topological feature sequence, and calculate a persistence diagram for the topological feature sequence to obtain a multi-scale topological structure representation;

[0077] (2) Extract the Betti number sequence according to the multi-scale topological structure representation to obtain a set of topological invariants, and perform statistical analysis on the set of topological invariants to obtain a topological feature vector;

[0078] (3) Perform isometric mapping on the topological feature vector and the high-dimensional phase space trajectory to obtain a low-dimensional embedding space, and calculate the geodesic distance matrix in the low-dimensional embedding space to obtain the intrinsic geometric relationship between data points;

[0079] (4) Construct a nearest neighbor graph according to the intrinsic geometric relationship to obtain the local structure of the data manifold, and perform spectral clustering on the local structure to obtain the main mode classification;

[0080] (5) Calculate the statistical moment for each category in the main mode classification to obtain a category feature descriptor, and perform principal component analysis on the category feature descriptor to obtain a key feature set after dimensionality reduction;

[0081] (6) Construct a feature representation of the load distribution according to the key feature set and the main mode classification to obtain the main mode and key features of the load distribution.

[0082] Specifically, persistent homology analysis is performed on the high-dimensional phase space trajectory. This is a computational topology method used to capture the topological features of a dataset at different scales. The core of persistent homology analysis is to construct a sequence of simplicial complexes and calculate their homology groups. Define the Vietoris-Rips complex , where is the distance threshold. As increases, a series of nested complexes are obtained, forming a filtration:

[0083]

[0084] where is the distance threshold, satisfying . By calculating the homology groups of this filtration, a sequence of topological features is obtained.

[0085] Next, calculate the persistence diagram for the sequence of topological features. The persistence diagram is a visualization tool used to represent the "birth" and "death" of topological features. Each point in the persistence diagram represents a topological feature that appears at distance threshold and disappears at . By analyzing the lifetime lengths and distributions of the features in the persistence diagram, the topological structure features of the dataset at different scales can be obtained, thus constructing a multi-scale topological structure representation. This representation method can reveal the topological features that stably exist in the data, as well as the transient features that quickly appear and disappear with scale changes.

[0086] According to the multi-scale topological structure representation, extract the sequence of Betti numbers. The Betti number is an important invariant of a topological space. The k-th Betti number represents the number of k-dimensional holes. For example, represents the number of connected components, represents the number of one-dimensional holes (i.e., loops). The sequence of Betti numbers constitutes a set of topological invariants. Perform statistical analysis on this set, including calculating the mean, variance, skewness, and kurtosis, etc., to obtain the topological feature vector. Then, perform isometric mapping on the topological feature vector and the high-dimensional phase space trajectory to obtain a low-dimensional embedding space. Isometric mapping is a non-linear dimensionality reduction technique, and its goal is to preserve the geodesic distance between high-dimensional data points in the low-dimensional space. The objective function of isometric mapping can be expressed as:

[0087] ;

[0088] where is the geodesic distance between points and in the high-dimensional space, and is the corresponding low-dimensional representation. In the obtained low-dimensional embedding space, calculate the geodesic distance matrix to reflect the intrinsic geometric relationship between data points. Construct a nearest neighbor graph based on the intrinsic geometric relationship to obtain the local structure of the data manifold. The construction of the nearest neighbor graph usually adopts the k-nearest neighbor or nearest neighbor method. Perform spectral clustering on this local structure to obtain the main mode classification. The core of spectral clustering is to calculate the eigenvectors of the graph Laplacian matrix L, which is defined as:

[0089] ;

[0090] where is the adjacency matrix, is the degree matrix.

[0091] Calculate the statistical moments for each category in the main mode classification, including mean, variance, skewness, and kurtosis, to obtain the category feature descriptors. Perform principal component analysis (PCA) on these feature descriptors to obtain the key feature set after dimensionality reduction. PCA finds the main directions of data variation by calculating the eigenvectors of the covariance matrix. Finally, based on the key feature set and the main mode classification, construct the feature representation of the load distribution to obtain the main mode and key features of the load distribution.

[0092] For example, in the construction of a subway expansion foundation pit, analyze the reconstructed 10-dimensional phase space trajectory. First, obtain the topological feature sequence through persistent homology analysis, including information on 0-dimensional, 1-dimensional, and 2-dimensional homology groups. After calculating the persistence diagram, it is found that the average persistence time of 0-dimensional features is 0.5, 1-dimensional features is 0.3, and 2-dimensional features is 0.1. Extract the Betti number sequence to obtain (indicating that the data set is connected), (indicating the existence of 3 one-dimensional loops), (indicating the existence of 1 two-dimensional hole). Perform statistical analysis on the Betti number sequence to obtain a 4-dimensional topological feature vector. Reduce the 10-dimensional data to 3 dimensions through isometric mapping, and calculate the geodesic distance matrix in the 3-dimensional space. Construct a k-nearest neighbor graph (k = 5), and then perform spectral clustering to obtain 4 main mode categories. Calculate the statistical moments for each category to obtain 16-dimensional (4 categories × 4 statistics) category feature descriptors. Perform PCA on these 16-dimensional descriptors, retaining the principal components required to explain 95% of the variance, and finally obtain a 6-dimensional key feature set. These analysis results provide in-depth insights into understanding the load distribution of the shield tunnel section. For example, the 3 one-dimensional loops may correspond to the stress distribution pattern around the tunnel, while the 2-dimensional hole may reflect the discontinuity of the geological structure. The 4 main mode categories may represent different geological conditions or construction stages.

[0093] In a specific embodiment, the process of executing step S4 may specifically include the following steps:

[0094] (1) Perform kernel density estimation on the main patterns and key features of the load distribution to obtain a non-parametric probability density function, and perform numerical integration on the non-parametric probability density function to obtain a cumulative distribution function;

[0095] (2) Calculate quantiles based on the cumulative distribution function to obtain characteristic statistics of the probability distribution, and perform moment estimation on the characteristic statistics to obtain initial estimated values of the distribution parameters;

[0096] (3) Perform maximum likelihood estimation on the initial estimated values to obtain an optimized set of distribution parameters, and construct a parametric probability density function based on the set of distribution parameters to obtain a parametric probability distribution model of the load;

[0097] (4) Perform Monte Carlo sampling on the optimal probability distribution function to obtain a load sample set, and calculate statistical moments for the load sample set to obtain statistical characteristic parameters of the load;

[0098] (5) Based on the statistical characteristic parameters and the optimal probability distribution function, construct a parametric representation of the load probability distribution to obtain parametric estimation data of the load probability distribution.

[0099] Specifically, in the process of shield tunnel section load analysis, performing probability density estimation on the main patterns and key features of the load distribution is a crucial step. First, use the kernel density estimation method to perform non-parametric probability density estimation on the data. The formula for kernel density estimation is as follows:

[0100]

[0101] Where, is the estimated probability density function, is the number of samples, is the bandwidth parameter, is the kernel function, is the sample point. Commonly used kernel functions include Gaussian kernel, Epanechnikov kernel, etc. Selecting an appropriate bandwidth parameter h is crucial for the accuracy of the estimation results. After obtaining the non-parametric probability density function, calculate the cumulative distribution function (CDF) through numerical integration methods. Numerical integration can use methods such as the trapezoidal rule or Simpson's rule. The calculation formula for the cumulative distribution function is:

[0102]

[0103] According to the cumulative distribution function, different quantiles are calculated to obtain the characteristic statistics of the probability distribution. Commonly used quantiles include the median (50% quantile), quartiles (25% and 75% quantiles), etc. Moment estimation is performed on these characteristic statistics to obtain the initial estimated values of the distribution parameters. The method of moment estimation is based on the relationship between sample moments and population moments. For example, for a normal distribution, the sample mean and sample variance are unbiased estimators of the population mean and population variance respectively. Next, the maximum likelihood estimation (MLE) method is used to optimize the initial estimated values to obtain the optimized set of distribution parameters. The goal of maximum likelihood estimation is to find the parameter values that maximize the probability of the observed data. For a given probability density function , where are the parameters to be estimated, the likelihood function is defined as:

[0104]

[0105] Maximum likelihood estimation is to find the that maximizes value. Usually, the estimated value is obtained by solving the derivative of the log-likelihood function equal to zero.

[0106] According to the optimized set of distribution parameters, a parametric probability density function is constructed to obtain the parametric probability distribution model of the load. To verify the fitting effect of the model, the Kolmogorov-Smirnov (K-S) test is performed on the parametric probability distribution model. The K-S test evaluates the goodness of fit by comparing the maximum difference between the theoretical distribution and the empirical distribution. The K-S statistic is defined as:

[0107]

[0108] where is the statistic, is the empirical distribution function, is the theoretical distribution function, that is, the cumulative distribution function. According to the results of the K-S test, the best-fitting distribution type is selected to obtain the optimal probability distribution function of the load. To further analyze the load characteristics, Monte Carlo sampling is performed on the optimal probability distribution function to obtain a load sample set. Monte Carlo sampling simulates the behavior of complex systems by generating a large number of random samples. Statistical moments, including the mean, variance, skewness, and kurtosis, are calculated for the obtained load sample set to obtain the statistical characteristic parameters of the load.

[0109] Finally, based on the statistical characteristic parameters and the optimal probability distribution function, a parametric representation of the load probability distribution is constructed to obtain the parametric estimation data of the load probability distribution.

[0110] For example, in the construction of a subway expansion foundation pit, the load data of a certain key point is analyzed. First, the Gaussian kernel function is used for kernel density estimation, and the bandwidth parameter h is determined to be 0.5 through cross-validation. The resulting non-parametric probability density function shows that the load distribution presents a bimodal characteristic. The cumulative distribution function is calculated through numerical integration, and the 25%, 50%, and 75% quantiles are calculated to be 450 kN, 500 kN, and 560 kN respectively. Based on these statistics, it is initially estimated that the data may conform to a mixture Gaussian distribution. The maximum likelihood estimation method is used to optimize the parameters of the mixture Gaussian distribution. The results obtained show that the load distribution can be described by the mixture of two Gaussian distributions, where the mean of the first distribution is 480 kN, the standard deviation is 30 kN, and the weight is 0.6; the mean of the second distribution is 540 kN, the standard deviation is 25 kN, and the weight is 0.4. The K-S test is performed, and the resulting p-value is 0.08, which is greater than the significance level of 0.05, indicating that the mixture Gaussian distribution can well fit the actual data. Monte Carlo sampling is performed on this mixture Gaussian distribution to generate 10,000 sample points. The statistical characteristics of these samples are calculated, and the overall mean is 504 kN, the standard deviation is 42 kN, the skewness is 0.3, and the kurtosis is 2.8.

[0111] In a specific embodiment, the process of executing step S5 may specifically include the following steps:

[0112] (1) Perform time window segmentation on the parameter estimation data to obtain a set of time series segments, and perform Fourier transform on the set of time series segments to obtain a frequency domain feature sequence;

[0113] (2) Calculate the power spectral density according to the frequency domain feature sequence to obtain the frequency distribution of the load characteristics, and perform peak detection on the frequency distribution to obtain the main frequency components;

[0114] (3) Perform autocorrelation analysis on the main frequency components to obtain the time delay parameter, and construct a phase space according to the time delay parameter to obtain the dynamic trajectory of the load characteristics;

[0115] (4) Calculate the Lyapunov exponent for the dynamic trajectory to obtain the chaos degree index of the system, and judge the long-term behavior characteristics of the system according to the chaos degree index to obtain the stability evaluation data of the load evolution;

[0116] (5) Perform wavelet decomposition on the time series segments to obtain multi-scale time-frequency characteristics, and perform singular spectrum analysis on the multi-scale time-frequency characteristics to obtain the main change patterns of the load characteristics;

[0117] (6) Perform trend change analysis on the load characteristics according to the main change patterns and stability evaluation data to obtain the dynamic evolution law of the load characteristics.

[0118] Specifically, the parameter estimation data is segmented by time windows, and the continuous data stream is segmented into several overlapping or non - overlapping time segments. The selection of the time window directly affects the results of subsequent analysis, and the window size is usually determined according to the characteristics of the data and the purpose of analysis. For example, for load data collected hourly, 24 hours can be selected as a time window to capture the daily variation pattern. Fourier transform is performed on each time - series segment to convert the time - domain signal into a frequency - domain representation. Fourier transform can reveal the different frequency components contained in the signal, which helps to identify periodic patterns and hidden frequency features. For discrete time series, the discrete Fourier transform (DFT) or fast Fourier transform (FFT) algorithms are usually used. The resulting frequency - domain feature sequence contains the amplitude and phase information of each frequency component.

[0119] The power spectral density (PSD) is calculated based on the frequency - domain feature sequence to obtain the frequency distribution of the load characteristics. The power spectral density reflects the distribution of signal power over frequency, which helps to identify the dominant frequency components. Commonly used PSD estimation methods include the periodogram method and the Welch method. Peak detection is performed on the obtained frequency distribution to identify the main frequency components. Peak detection is usually achieved by setting a threshold or finding local maxima. Autocorrelation analysis is performed on the identified main frequency components to obtain the time - delay parameter. Autocorrelation analysis is used to evaluate the correlation of a time series with itself at different time delays, which helps to discover the periodicity and dependence structure in the series. The time - delay parameter is usually selected as the delay time when the autocorrelation function first reaches a local minimum. Based on this time - delay parameter, the phase space is constructed using the delay - coordinate method to obtain the dynamic trajectory of the load characteristics. The Lyapunov exponent is calculated for the constructed dynamic trajectory to obtain an index of the chaos degree of the system. The Lyapunov exponent measures the separation rate of neighboring orbits in the phase space, and a positive maximum Lyapunov exponent indicates that the system has chaotic characteristics. Based on the calculated chaos - degree index, the long - term behavior characteristics of the system are judged, and thus the stability evaluation data of the load evolution is obtained.

[0120] Meanwhile, wavelet decomposition is performed on the time - series segments to obtain multi - scale time - frequency features. Wavelet decomposition can provide information in both the time and frequency domains simultaneously, and is particularly suitable for analyzing non - stationary signals. Commonly used wavelet functions include the Haar wavelet, Daubechies wavelet, etc. Singular spectrum analysis is performed on the obtained multi - scale time - frequency features to identify the main change patterns of the load characteristics. Singular spectrum analysis decomposes the original signal into components such as trends, periods, and noise by performing singular - value decomposition on the trajectory matrix. Finally, based on the identified main change patterns and the previously obtained stability evaluation data, trend - change analysis of the load characteristics is performed to obtain the dynamic evolution law of the load characteristics. This step synthesizes all the previous analysis results and reveals the change trend, periodic characteristics, and potential instability of the load over time.

[0121] For example, in the construction of a foundation pit for subway expansion, the load data of a certain key point is analyzed. First, the load data for 30 consecutive days is segmented with a 24-hour time window, resulting in 30 time series segments. Perform FFT on each segment to obtain 30 groups of frequency domain feature sequences. After calculating the power spectral density, it is found that the main frequency components are concentrated around 0.04 Hz (corresponding to a 25-hour period) and 0.00231 Hz (corresponding to a 6-day period). Autocorrelation analysis determines the optimal time delay to be 6 hours, based on which the phase space is constructed to obtain the dynamic trajectory of the load characteristics. Calculating the Lyapunov exponent gives 0.02, indicating that the system has weak chaotic characteristics. Wavelet decomposition uses the Db4 wavelet with 5 decomposition levels to obtain the time-frequency characteristics at different scales. Singular spectrum analysis identifies two main change patterns: one shows an obvious daily change pattern, and the other reflects the trend change on a longer time scale. Comprehensive analysis shows that the load at this point exhibits complex dynamic characteristics, including obvious daily periodic fluctuations and a slowly rising long-term trend.

[0122] In a specific embodiment, the process of executing step S6 may specifically include the following steps:

[0123] (1) Perform empirical mode decomposition on the dynamic evolution law of the load characteristics to obtain multiple intrinsic modes, and perform Hilbert transform on the intrinsic modes to obtain the instantaneous frequency and instantaneous amplitude;

[0124] (2) Construct a time-frequency energy distribution diagram based on the instantaneous frequency and instantaneous amplitude to obtain a multi-scale representation of the load characteristics, and perform threshold segmentation on the multi-scale representation to obtain load components at different scales;

[0125] (3) Reconstruct and superimpose the load components at different scales to obtain the hierarchical load numerical distribution data of the subway structure within the shield section, and perform spatial interpolation on the hierarchical load numerical distribution data to obtain a continuous load distribution field;

[0126] (4) Calculate the stress gradient and deformation rate based on the continuous load distribution field to obtain the stress state index of the shield section, and perform fuzzy comprehensive evaluation on the stress state index to obtain the section stability score;

[0127] (5) Perform multi-objective optimization on the section stability score and the load distribution field to obtain a group of candidate construction parameter schemes, and perform sensitivity analysis on the group of candidate construction parameter schemes to obtain the key control parameters;

[0128] (6) Generate a construction suggestion strategy dataset based on the key control parameters and the group of candidate construction parameter schemes to obtain an optimized control scheme for shield construction.

[0129] It should be noted that empirical mode decomposition (EMD) is used for the dynamic evolution law of load characteristics. This is an adaptive signal processing method that can decompose complex signals into a finite number of intrinsic mode functions (IMFs). The core idea of EMD is to repeatedly extract the local extreme envelopes of the signal to obtain a series of IMFs with frequencies decreasing from high to low. For a time series , the process of EMD can be expressed as:

[0130] ;

[0131] where is the i th intrinsic mode function, and is the residual term.

[0132] Perform Hilbert transform on each obtained IMF to obtain the instantaneous frequency and instantaneous amplitude. The formula for Hilbert transform is:

[0133]

[0134] Through Hilbert transform, the analytic signal of the signal can be obtained, and then the instantaneous frequency and instantaneous amplitude can be calculated. is the Hilbert transform of is the input signal, is the time variable, is the integration variable, and represents the Cauchy principal value integral.

[0135] Based on the calculated instantaneous frequency and instantaneous amplitude, a time-frequency energy distribution diagram is constructed, which provides a multi-scale representation of the load characteristics. The time-frequency energy distribution diagram visually shows the energy distribution of the signal at different times and frequencies. Threshold segmentation is performed on the multi-scale representation to obtain load components at different scales. Threshold segmentation divides the time-frequency plane into different regions by setting an energy threshold, and each region corresponds to a load component at a certain scale. The load components at different scales are reconstructed and superimposed to obtain the numerical distribution data of the layered load of the subway structure in the shield section. The reconstruction process is to weighted sum the load components at each scale according to their contributions in the original signal. Spatial interpolation is performed on the numerical distribution data of the layered load to obtain a continuous load distribution field. Spatial interpolation methods include Kriging interpolation, inverse distance weighted method, etc. Selecting an appropriate interpolation method can obtain a smooth and continuous distribution field between discrete measurement points. According to the continuous load distribution field, the stress gradient and deformation rate are calculated to obtain the stress state indicators of the shield section. The stress gradient reflects the rate of change of stress in space, while the deformation rate describes the degree of deformation of the material. These indicators comprehensively reflect the stress condition of the shield section. Fuzzy comprehensive evaluation is performed on the stress state indicators to obtain the interval stability score. The fuzzy comprehensive evaluation method takes into account the uncertainties of multiple evaluation factors and obtains the final evaluation result by establishing a fuzzy relation matrix and a weight vector. Multi-objective optimization is performed on the interval stability score and the load distribution field to obtain a set of candidate construction parameter solutions. Multi-objective optimization considers multiple objectives such as safety and economy and uses algorithms such as NSGA-II to find the Pareto optimal solution set. Sensitivity analysis is performed on the set of candidate construction parameter solutions to obtain the key control parameters. Sensitivity analysis determines which parameters have the greatest impact on the results by changing the input parameters and observing the output changes.

[0136] Finally, based on the key control parameters and the set of candidate construction parameter solutions, a construction suggestion strategy dataset is generated to obtain an optimized control scheme for shield construction. The previous analysis results are transformed into specific construction guidance to provide direct support for engineering practice.

[0137] For example, in the construction of a subway expansion foundation pit, the load data for 30 consecutive days are analyzed. First, 5 IMFs and 1 residual term are obtained through EMD. The Hilbert transform is performed on the first IMF, and the instantaneous frequency is found to fluctuate between 0.8 - 1.2 Hz, while the instantaneous amplitude varies between 0.5 - 2 kN. After constructing the time-frequency energy distribution map, an energy threshold of 5% of the total energy is set, and 3 main load components are obtained, corresponding to high-frequency (1 - 2 Hz), medium-frequency (0.1 - 0.5 Hz), and low-frequency (<0.05 Hz) components respectively. These 3 load components are reconstructed, and Kriging interpolation is performed at 100 discrete measurement points to obtain a continuous load distribution field. The calculated maximum stress gradient is 0.5 MPa / m, and the maximum deformation rate is 0.1%. Through fuzzy comprehensive evaluation, the interval stability score is obtained as 0.75 (full score 1). Multi-objective optimization considers two objectives, safety and construction efficiency, and 10 sets of candidate construction parameter schemes are obtained. Sensitivity analysis shows that the propulsion speed and grouting pressure are the most critical control parameters. The final generated construction suggestions include: controlling the propulsion speed at 20 - 25 mm / min and maintaining the grouting pressure at 0.3 - 0.35 MPa in high stress gradient areas (>0.4 MPa / m); appropriately increasing the propulsion speed to 30 - 35 mm / min and reducing the grouting pressure to 0.25 - 0.3 MPa in low stress gradient areas (<0.2 MPa / m). These suggestions provide data support for the refined control of shield construction and help improve construction efficiency and safety.

[0138] An embodiment of the present invention also provides a dynamic loading analysis system for anti-heave of underground structures, as Figure 2 shown. This dynamic loading analysis system for anti-heave of underground structures specifically includes:

[0139] An encoding module 201, configured to perform adaptive fusion encoding on the original data collected by surveying and mapping the subway structure in the shield section to obtain a spatio-temporal data stream;

[0140] An interpolation module 202, configured to perform fractal interpolation and chaotic dynamics analysis on the spatio-temporal data stream to obtain a reconstructed high-dimensional phase space trajectory;

[0141] A dimension reduction module 203, configured to extract topological features and perform non-linear dimension reduction on the reconstructed high-dimensional phase space trajectory to obtain the main patterns and key features of the load distribution;

[0142] An estimation module 204, configured to perform probability density estimation on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution;

[0143] An analysis module 205, configured to perform time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics;

[0144] An optimization module 206, configured to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics, obtain the numerical distribution data of the hierarchical loads of the subway structure within the shield section, and perform multi-objective optimization analysis on the numerical distribution data of the hierarchical loads to obtain a dataset of construction suggestion strategies.

[0145] Through the collaborative work of the above-mentioned various modules, by adaptively fusing and encoding the raw data collected by multi-source sensors, efficient data compression and information extraction are achieved, significantly reducing the data transmission and storage requirements while retaining the key load information. This method not only improves the data processing efficiency but also provides high-quality input for subsequent analysis. Secondly, by using the fractal interpolation and chaotic dynamics analysis methods, the inherent complexity and dynamic characteristics of the load data are deeply explored, laying a foundation for accurately grasping the load change law during the shield construction process. Through the topological feature extraction and nonlinear dimensionality reduction techniques, the main patterns and key features of the load distribution are successfully captured, greatly improving the ability to understand and describe complex load states. The introduction of probability density estimation and parametric modeling enables the quantification of the uncertainty of the load distribution, providing a reliable basis for risk assessment and decision-making. The application of the time series analysis method reveals the dynamic evolution law of the load characteristics, making it possible to predict the load change trend. The use of multi-scale decomposition and reconstruction techniques realizes the accurate description of the hierarchical loads in the shield section, providing the necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction suggestion strategies are obtained, directly guiding construction practice and improving construction efficiency and safety.

[0146] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic loading analysis method for anti - heave of underground structures, characterized in that, Including: S1. Perform adaptive fusion coding on the original data collected by subway structure surveying and mapping in the shield tunnel section to obtain a spatio-temporal data stream; S2. Perform fractal interpolation and chaotic dynamics analysis on the spatio-temporal data stream to obtain a reconstructed high-dimensional phase space trajectory; S3. Extract topological features and perform non-linear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main patterns and key features of the load distribution; Among them, step S3 includes: Perform persistent homology analysis on the reconstructed high-dimensional phase space trajectory to obtain a topological feature sequence, calculate a persistence diagram for the topological feature sequence to obtain a multi-scale topological structure representation; extract a Betti number sequence from the multi-scale topological structure representation to obtain a set of topological invariants, and perform statistical analysis on the set of topological invariants to obtain a topological feature vector; perform isometric mapping on the topological feature vector and the high-dimensional phase space trajectory to obtain a low-dimensional embedded space, and calculate a geodesic distance matrix in the low-dimensional embedded space to obtain the intrinsic geometric relationship between data points; construct a nearest neighbor graph based on the intrinsic geometric relationship to obtain the local structure of the data manifold, and perform spectral clustering on the local structure to obtain the main pattern classification; calculate statistical moments for each category in the main pattern classification to obtain a category feature descriptor, and perform principal component analysis on the category feature descriptor to obtain a key feature set after dimensionality reduction; construct a feature representation of the load distribution based on the key feature set and the main pattern classification to obtain the main patterns and key features of the load distribution; S4. Perform probability density estimation on the main patterns and key features of the load distribution to obtain parameter estimation data of the load probability distribution; S5. Perform time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics; S6. Based on the dynamic evolution law of the load characteristics, perform multi-scale decomposition and reconstruction to obtain the hierarchical load numerical distribution data of the subway structure in the shield tunnel section, and perform multi-objective optimization analysis on the hierarchical load numerical distribution data to obtain a construction suggestion strategy dataset.

2. The anti - heave dynamic loading analysis method for an underground structure according to claim 1, characterized in that, Step S1 includes: Perform stress-strain separation processing on the original data collected by multi-source sensors to obtain separated stress data and strain data, and perform elastic-plastic decoupling analysis on the stress data and strain data to obtain an elastic deformation component and a plastic deformation component; Calculate a load-deformation curve based on the elastic deformation component and the plastic deformation component and extract response data to obtain load response data; Perform time-frequency joint analysis on the load response data to obtain a load frequency spectrum diagram, and extract the main frequency feature and energy distribution from the load frequency spectrum diagram to obtain load modal parameters; Extract non-linear features from the load modal parameters to obtain a load non-linearity index, and perform mutual information analysis on the load non-linearity index and the original data to obtain the key sensor weights; Perform adaptive fusion on the multi-source data according to the key sensor weights to obtain fused load data; Perform complexity analysis on the fused load data to obtain a data complexity index, and design an adaptive quantization strategy according to the data complexity index to obtain a quantization coding scheme; The fused load data is compressed and encoded through the quantization coding scheme to obtain a spatio-temporal data stream.

3. A dynamic loading analysis method for anti - heave of an underground structure according to claim 1, characterized in that, Step S2 includes: Calculating the fractal dimension of the spatio-temporal data stream to obtain a self-similarity index, and performing fractal interpolation on the spatio-temporal data stream according to the self-similarity index to obtain a high-resolution interpolation data set; Performing phase space reconstruction on the interpolation data set to obtain a high-dimensional phase space trajectory, and calculating the Lyapunov exponent for the high-dimensional phase space trajectory to obtain a chaos characteristic index; Segmenting the high-dimensional phase space trajectory according to the chaos characteristic index to obtain N sub-trajectories with different dynamic characteristics, where N is an integer between 2 and 5, and performing recursive quantitative analysis on the N sub-trajectories respectively to obtain N sets of dynamic characteristic index sets, and each set of index sets includes four parameters: periodicity, determinacy, laminarity, and complexity; Performing cluster analysis on the N sets of dynamic characteristic index sets to obtain K stability levels, where K is an integer between 2 and  4, and classifying the spatio-temporal data stream according to the K stability levels to obtain data subsets with K stability levels; Performing cross-correlation analysis on the data subsets with K stability levels to obtain a K×K-dimensional variable coupling relationship matrix, and constructing a multi-dimensional phase transition diagram according to the coupling relationship matrix to obtain a reconstructed high-dimensional phase space trajectory.

4. The anti - heave dynamic loading analysis method for an underground structure according to claim 1, wherein, Step S4 includes: Performing kernel density estimation on the main patterns and key features of the load distribution to obtain a non-parametric probability density function, and performing numerical integration on the non-parametric probability density function to obtain a cumulative distribution function; Calculating quantiles according to the cumulative distribution function to obtain characteristic statistics of the probability distribution, and performing moment estimation on the characteristic statistics to obtain an initial estimated value of the distribution parameter; Performing maximum likelihood estimation on the initial estimated value to obtain an optimized set of distribution parameters, and constructing a parametric probability density function according to the set of distribution parameters to obtain a parametric probability distribution model of the load; Performing a Kolmogorov-Smirnov test on the parametric probability distribution model to obtain a goodness-of-fit index, and selecting the best-fitting distribution type according to the goodness-of-fit index to obtain an optimal probability distribution function of the load; Performing Monte Carlo sampling on the optimal probability distribution function to obtain a load sample set, and calculating statistical moments for the load sample set to obtain statistical characteristic parameters of the load; Constructing a parametric representation of the load probability distribution according to the statistical characteristic parameters and the optimal probability distribution function to obtain parametric estimation data of the load probability distribution.

5. A method for analyzing the anti - heave dynamic loading of an underground structure according to claim 1, characterized in that, Step S5 includes: Dividing the parametric estimation data into time window segments to obtain a set of time series segments, and performing Fourier transform on the set of time series segments to obtain a frequency domain characteristic sequence; Calculating the power spectral density according to the frequency domain characteristic sequence to obtain the frequency distribution of the load characteristics, and performing peak detection on the frequency distribution to obtain the main frequency components; Performing autocorrelation analysis on the main frequency components to obtain a time delay parameter, and constructing a phase space according to the time delay parameter to obtain a dynamic trajectory of the load characteristics; Calculate the Lyapunov exponent for the dynamic trajectory to obtain the chaos degree index of the system, and judge the long-term behavior characteristics of the system according to the chaos degree index to obtain the stability evaluation data of the load evolution; Perform wavelet decomposition on the time series segment to obtain multi-scale time-frequency features, and perform singular spectrum analysis on the multi-scale time-frequency features to obtain the main change patterns of the load features; Conduct trend change analysis of the load features based on the main change patterns and stability evaluation data to obtain the dynamic evolution law of the load features.

6. The anti-heave dynamic loading analysis method for an underground structure according to claim 5, characterized in that Step S6 includes: Perform empirical mode decomposition on the dynamic evolution law of the load features to obtain multiple intrinsic modes, and perform Hilbert transform on the intrinsic modes to obtain the instantaneous frequency and instantaneous amplitude; Construct a time-frequency energy distribution map based on the instantaneous frequency and instantaneous amplitude to obtain a multi-scale representation of the load features, and perform threshold segmentation on the multi-scale representation to obtain load components at different scales; Reconstruct and superimpose the load components at different scales to obtain the hierarchical load numerical distribution data of the subway structure in the shield tunnel section, and perform spatial interpolation on the hierarchical load numerical distribution data to obtain a continuous load distribution field; Calculate the stress gradient and deformation rate based on the continuous load distribution field to obtain the stress state index of the shield tunnel section, and perform fuzzy comprehensive evaluation on the stress state index to obtain the section stability score; Perform multi-objective optimization on the section stability score and the load distribution field to obtain a group of candidate construction parameter schemes, and perform sensitivity analysis on the group of candidate construction parameter schemes to obtain the key control parameters; Generate a construction suggestion strategy data set based on the key control parameters and the group of candidate construction parameter schemes to obtain the optimized control scheme for shield tunneling construction.

7. An anti-heave dynamic loading analysis system for an underground structure, which is used to execute the anti-heave dynamic loading analysis method of the underground structure according to any one of claims 1 to 6, characterized in that, It includes: An encoding module for adaptively fusing and encoding the original data collected by surveying and mapping the subway structure in the shield tunnel section to obtain a spatio-temporal data stream; An interpolation module for performing fractal interpolation and chaotic dynamics analysis on the spatio-temporal data stream to obtain a reconstructed high-dimensional phase space trajectory; A dimensionality reduction module for extracting topological features and performing non-linear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main patterns and key features of the load distribution; The dimensionality reduction module is further configured to: perform persistent homology analysis on the reconstructed high-dimensional phase space trajectory to obtain a topological feature sequence, calculate a persistence diagram for the topological feature sequence to obtain a multi-scale topological structure representation; extract a Betti number sequence from the multi-scale topological structure representation to obtain a set of topological invariants, and perform statistical analysis on the set of topological invariants to obtain a topological feature vector; perform isometric mapping on the topological feature vector and the high-dimensional phase space trajectory to obtain a low-dimensional embedding space, and calculate a geodesic distance matrix in the low-dimensional embedding space to obtain the intrinsic geometric relationship between data points; construct a nearest neighbor graph based on the intrinsic geometric relationship to obtain the local structure of the data manifold, and perform spectral clustering on the local structure to obtain the main mode classification; calculate the statistical moments for each category in the main mode classification to obtain a category feature descriptor, and perform principal component analysis on the category feature descriptor to obtain a key feature set after dimensionality reduction; construct a feature representation of the load distribution based on the key feature set and the main mode classification to obtain the main mode and key features of the load distribution; An estimation module, configured to perform probability density estimation on the main mode and key features of the load distribution to obtain parameter estimation data of the load probability distribution; An analysis module, configured to perform time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics; An optimization module, configured to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics to obtain the hierarchical load numerical distribution data of the subway structure in the shield section, and perform multi-objective optimization analysis on the hierarchical load numerical distribution data to obtain a construction suggestion strategy data set.

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