Anti-upheaval dynamic loading analysis method and system for underground structure

Abstract

The invention relates to the technical field of load analysis, and discloses an anti-upheaval dynamic loading analysis method and system for an underground structure, which are used for improving the accuracy and efficiency of a load analysis method for a metro structure expanded on two sides of a metro. The method comprises the following steps: performing fractal interpolation and chaotic dynamics analysis on a spatio-temporal data stream to obtain a high-dimensional phase space trajectory; performing topological feature extraction and nonlinear dimension reduction on the high-dimensional phase space trajectory to obtain a main mode and key features of load distribution; probability density estimation is carried out on the main modes and the key features of the load distribution to obtain parameter estimation data of load probability distribution; performing time sequence analysis on the parameter estimation data to obtain a dynamic evolution rule of the load characteristics; and carrying out multi-scale decomposition and reconstruction on the basis of the dynamic evolution law of the load characteristics to obtain layered load value distribution data of the subway structure in the shield interval, and carrying out multi-objective optimization analysis on the layered load value distribution data to obtain a construction suggestion strategy data set.

Description

Technical Field

[0001] The invention relates to the technical field of load analysis, and in particular to an anti-uplift dynamic loading analysis method and system for an underground structure. Background Art

[0002] In recent years, with the acceleration of urbanization, the construction scale of underground projects such as subways has continued to expand. When expanding and constructing 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 stratum stress method and support structure method. Although these methods can predict load distribution to a certain extent, they often ignore the complexity of geological conditions and the dynamic changes of 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 attracted attention. These methods arrange various sensors around shield machines and tunnels to collect various parameters in real time during the construction process, and then use data processing technology to perform load analysis.

[0003] However, the existing load analysis methods based on monitoring data still have some shortcomings. First, faced with massive, multi-source, and heterogeneous monitoring data, traditional data processing methods are difficult to effectively extract and integrate key information. Secondly, the load distribution during the construction process around the shield section is highly nonlinear and non-stationary, and conventional statistical analysis methods are difficult to accurately capture its complex dynamic characteristics. Thirdly, the existing methods focus more on the static distribution of loads and lack in-depth analysis of the temporal and spatial evolution 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, an embodiment of the present invention provides an anti-uplift dynamic loading analysis method and system for underground structures, which are used to improve the accuracy and efficiency of the subway structure load analysis method for subway double-sided extension.

[0005] The present invention provides an anti-uplift dynamic loading analysis method for underground structures, comprising: S1, adaptively fusion-encode the original data collected by subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; S2, performing fractal interpolation and chaotic dynamics analysis on the spatiotemporal data stream to obtain a reconstructed high-dimensional phase space trajectory; S3, performing topological feature extraction and nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main modes and key features of the load distribution; S4. Performing probability density estimation on the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; S5. Performing 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, multi-scale decomposition and reconstruction are performed to obtain the layered load numerical distribution data of the subway structure in the shield section, and multi-objective optimization analysis is performed on the layered load numerical distribution data to obtain a construction recommendation strategy data set.

[0006] The present invention also provides an anti-uplift dynamic loading analysis system for underground structures, comprising: The encoding module is used to adaptively fuse and encode the original data collected through subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; An interpolation module, used for performing fractal interpolation and chaotic dynamics analysis on the spatiotemporal data stream to obtain a reconstructed high-dimensional phase space trajectory; A dimensionality reduction module is used to perform topological feature extraction and nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main mode and key features of the load distribution; An estimation module, used to perform probability density estimation on the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; An analysis module, used for performing time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics; The optimization module is used to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics, obtain the layered load numerical distribution data of the subway structure in the shield section, and perform multi-objective optimization analysis on the layered load numerical distribution data to obtain a construction recommendation strategy data set.

[0007] In the technical solution provided by the present invention, by adaptively fusion encoding the raw data collected by multi-source sensors, efficient data compression and information extraction are achieved, which significantly reduces the 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, the fractal interpolation and chaotic dynamics analysis methods are used to deeply explore the inherent complexity and dynamic characteristics of the load data, laying the foundation for accurately grasping the load change law during the shield construction process. Through topological feature extraction and nonlinear dimensionality reduction technology, the main patterns and key features of the load distribution are successfully captured, greatly improving the understanding and description capabilities of complex load states. The introduction of probability density estimation and parametric modeling enables the uncertainty of load distribution to be quantitatively expressed, 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 technology realizes the accurate description of the layered load in the shield interval, providing the necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction recommendation strategies were obtained, which directly guided construction practice and improved construction efficiency and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0009] Figure 1 A flowchart of a method for dynamic loading analysis of anti-uplift of an underground structure in an embodiment of the present invention; Figure 2 Schematic diagram of an anti-uplift dynamic loading analysis system for underground structures in an embodiment of the present invention. DETAILED DESCRIPTION

[0010] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0011] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are 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 limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0012] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0013] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 , Figure 1 FIG. 1 is a flow chart of a method for dynamic loading analysis of an underground structure against uplift according to an embodiment of the present invention. Figure 1 As shown, the following steps are included: S1, adaptively fusion-encode the original data collected by subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; S2, fractal interpolation and chaotic dynamics analysis are performed on the spatiotemporal data stream to obtain the reconstructed high-dimensional phase space trajectory; S3, extracting topological features and performing nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main modes and key features of the load distribution; S4. Estimating the probability density of the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; S5. Perform time series analysis on parameter estimation data to obtain the dynamic evolution law of load characteristics; S6. Based on the dynamic evolution law of load characteristics, multi-scale decomposition and reconstruction are performed to obtain the layered load numerical distribution data of the subway structure in the shield section, and multi-objective optimization analysis is performed on the layered load numerical distribution data to obtain the construction recommendation strategy data set.

[0014] It should be noted that multi-source sensors, including stress sensors, displacement sensors, pressure sensors, etc., are pre-arranged on the subway structure within the shield section to collect raw data. These raw data are processed by adaptive fusion coding to obtain a spatiotemporal data stream. Technologies such as stress-strain separation, elastic-plastic decoupling, and time-frequency joint analysis are used to effectively extract load response data and modal parameters. For example, for a certain shield section, 10 different types of sensor data may be collected at the same time, generating 1,000 data points per second. Through adaptive fusion coding, these heterogeneous data are uniformly processed to obtain a compressed fusion spatiotemporal data stream of 100 data points per second, which greatly reduces the amount of data while retaining key information.

[0015] Fractal interpolation and chaotic dynamics analysis are performed on the spatiotemporal data stream to obtain the reconstructed high-dimensional phase space trajectory. The inherent complexity of the load data is deeply explored by using fractal theory and chaotic dynamics methods. The data is classified and reconstructed by calculating indicators such as fractal dimension and Lyapunov index. For example, the compressed fusion data stream of a certain shield section may show a fractal dimension of 2.3, indicating that it has a high complexity. After fractal interpolation, the data resolution is improved by 5 times, which better reflects the details of the load change. Topological feature extraction and nonlinear 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 continuous homology analysis and isometric mapping are used to extract the most representative features from high-dimensional data. For example, continuous homology analysis may find that there are three main topological features of the load distribution, corresponding to the influence of different geological conditions. After nonlinear dimensionality reduction, the original 100-dimensional data may be reduced to 10 dimensions, which is easier for subsequent analysis.

[0016] The probability density of the main modes and key features of the load distribution is estimated to obtain the parameter estimation data of the load probability distribution. The probability model of the load distribution is constructed using methods such as kernel density estimation and maximum likelihood estimation. For example, the load distribution at a key point may be estimated as a normal distribution with a mean of 500kN and a standard deviation of 50kN, which provides an important basis for subsequent risk assessment. The time series analysis of the parameter estimation data is performed to obtain the dynamic evolution law of the load characteristics. The time-frequency analysis methods such as Fourier transform and wavelet decomposition are used to reveal the law of load change over time. For example, through analysis, it may be found that the load in a certain section of the shield section shows a 12-hour periodic change law, and the peak value usually occurs around 10 am every day.

[0017] The last step is to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of load characteristics, obtain the layered load numerical distribution data of the subway structure in the shield section, and perform multi-objective optimization analysis on these data to obtain the construction recommendation strategy data set. Combining all the previous analysis results, through empirical mode decomposition, multi-objective optimization and other methods, a specific construction guide was finally formed.

[0018] By executing the above steps, the raw data collected by multi-source sensors are adaptively fused and encoded, achieving efficient data compression and information extraction, 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, the fractal interpolation and chaotic dynamics analysis methods are used to deeply explore the inherent complexity and dynamic characteristics of load data, laying the foundation for accurately grasping the load change law during shield construction. Through topological feature extraction and nonlinear dimensionality reduction technology, the main modes and key features of load distribution are successfully captured, greatly improving the understanding and description of complex load states. The introduction of probability density estimation and parametric modeling enables the uncertainty of load distribution to be quantitatively expressed, 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 technology realizes the accurate description of the layered load in the shield interval, providing necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction recommendation strategies were obtained, which directly guided construction practice and improved construction efficiency and safety.

[0019] In a specific embodiment, the process of executing step S1 may specifically include the following steps: (1) Perform stress-strain separation processing on the raw 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 elastic deformation components and plastic deformation components; (2) Calculate the load-deformation curve based on the elastic deformation component and the plastic deformation component and extract the response data to obtain the load response data; (3) Perform a time-frequency joint analysis on the load response data to obtain the load spectrum diagram, and extract the main frequency characteristics and energy distribution based on the load spectrum diagram to obtain the load modal parameters; (4) Extract nonlinear features of load modal parameters to obtain load nonlinear index, and perform mutual information analysis on load nonlinear index and original data to obtain key sensor weights; (5) Adaptively fuse multi-source data according to the weights of key sensors to obtain fused load data; (6) Perform complexity analysis on the fused load data to obtain the data complexity index, and design an adaptive quantization strategy based on the data complexity index to obtain a quantization coding scheme; (7) The fused payload data is compressed and encoded through a quantization coding scheme to obtain a spatiotemporal data stream.

[0020] Specifically, in the shield section load analysis, the original data is separated into stress data and strain data through stress-strain separation processing. Hooke's law is used. For materials within the linear elastic range, stress σ and strain The relationship between can be expressed as: ; in is Young's modulus. The stress and strain in the original data can be separated.

[0021] The separated stress data and strain data are subjected to elastic-plastic decoupling analysis to obtain elastic deformation components and plastic deformation components. The Ramberg-Osgood model is used, which describes the stress-strain relationship of the material in the elastic-plastic stage: ; in is the material constant, is the strength coefficient, is the strain hardening exponent. The total strain can be decomposed into two parts: elastic strain and plastic strain. According to the elastic deformation component and plastic deformation component obtained, the load-deformation curve is calculated and the response data is extracted to obtain the load response data. Through interpolation and fitting methods, a complete load-deformation relationship curve is constructed.

[0022] Subsequently, the load response data is subjected to a time-frequency joint analysis to obtain the load spectrum diagram. The short-time Fourier transform (STFT) method is used here, and the mathematical expression of STFT is: ; in For signal, is the window function, is the time offset parameter, indicating the center position of the window function; is the angular frequency, is the time variable, is an imaginary unit, ; It is a complex exponential function 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. The main frequency characteristics and energy distribution are extracted according to the load spectrum diagram to obtain the load modal parameters. The main frequency components of the load and the corresponding energy distribution are identified through peak detection and energy integration methods.

[0023] The nonlinear characteristics of the load modal parameters are extracted to obtain the load nonlinear index. The bispectral analysis method is used here, which can detect the second-order nonlinear correlation in the signal. Subsequently, the mutual information analysis of the load nonlinear index and the original data is performed to obtain the key sensor weights. The calculation formula is: ; in for and The joint probability distribution of and They are the first edge probability distribution and the second edge probability distribution respectively; according to the obtained key sensor weights, the multi-source data are adaptively fused to obtain the fused load data. The weighted average method is used to fuse the data according to the weight of each sensor.

[0024] The complexity of the fused load data is analyzed to obtain the data complexity index. The sample entropy method is used here, and the sample entropy reflects the complexity and irregularity of the time series. According to the data complexity index, an adaptive quantization strategy is designed to obtain a quantization coding scheme. Finally, the fused load data is compressed and encoded through the quantization coding scheme to obtain a spatiotemporal data stream. The adaptive arithmetic coding method is used to dynamically adjust the coding strategy according to the statistical characteristics of the data to achieve efficient data compression.

[0025] For example, in a shield tunnel construction, 20 strain sensors and 15 pressure sensors were arranged with a sampling frequency of 100 Hz. After the original data was processed by stress-strain separation, the stress data range was 0-50 MPa and the strain data range was 0-2000. Through the elastic-plastic decoupling analysis, it is found that at the stress level of 30MPa, the elastic strain is about 1000 , the plastic strain is about 200 . Time-frequency joint analysis shows that the main frequency components of the load are concentrated at 2Hz, 5Hz and 8Hz, and their energies account for 40%, 30% and 20% of the total energy respectively. Nonlinear feature extraction and mutual information analysis show 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 encoding, the compression rate of the original data reached 10:1, and a compressed fused spatiotemporal data stream of 350 bytes per second was obtained.

[0026] In a specific embodiment, the process of executing step S2 may specifically include the following steps: (1) Calculate the fractal dimension of the spatiotemporal data stream to obtain the self-similarity index, and perform fractal interpolation on the spatiotemporal data stream based on the self-similarity index to obtain a high-resolution interpolation data set; (2) Reconstruct the phase space of the interpolated data set to obtain a high-dimensional phase space trajectory, and calculate the Lyapunov index of the high-dimensional phase space trajectory to obtain the chaotic characteristic index; (3) According to the chaotic characteristic index, the high-dimensional phase space trajectory is segmented to obtain N sub-trajectories with different dynamic characteristics, where N is an integer between 2 and 5. The N sub-trajectories are recursively quantitatively analyzed to obtain N sets of dynamic characteristic index sets, each of which contains four parameters: periodicity, determinism, laminarity, and complexity. (4) Cluster analysis is performed on the N groups of dynamic characteristic index sets to obtain K stability levels, where K is an integer between 2 and 4, and the spatiotemporal data streams are classified according to the K stability levels to obtain K stability level data subsets; (5) A cross-correlation analysis is performed on the data subsets of K stability levels to obtain a K×K dimensional variable coupling relationship matrix. A multidimensional phase change diagram is constructed based on the coupling relationship matrix to obtain a reconstructed high-dimensional phase space trajectory.

[0027] Specifically, the fractal dimension of the data stream is calculated to obtain the self-similarity index. Here, the box counting method is used to calculate the fractal dimension D, and its formula is: ;

[0028] in To cover the dataset required The number of boxes of different sizes. According to the calculated self-similarity index, fractal interpolation is performed on the spatiotemporal data stream to obtain a high-resolution interpolation data set. Fractal interpolation uses 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, the interpolation data set is reconstructed in phase space to obtain a high-dimensional phase space trajectory. Phase space reconstruction is based on Takens embedding theorem, and the appropriate embedding dimension is selected. and time offset parameters , the one-dimensional time series Map to Dimensional phase space: ; Compute Lyapunov exponents for reconstructed high-dimensional phase space trajectories , and obtain the chaotic characteristic index. The Lyapunov index characterizes the separation rate of adjacent orbits in the phase space, and its calculation formula is: ; in The initial distance is The two tracks in The distance of time.

[0029] According to the obtained chaotic characteristic index, the high-dimensional phase space trajectory is segmented 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 chaotic characteristic index and is segmented at the point where the index value changes significantly. The N sub-trajectories are subjected to recursive quantitative analysis (RQA) 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 recursive graph and calculating various statistics. Subsequently, the N sets of dynamic characteristic index sets are clustered and the K-means algorithm is used to obtain K stability levels, where K is an integer between 2 and 4. The K-means algorithm assigns data points to the nearest cluster center through iterative optimization and updates the cluster center until convergence. According to the obtained K stability levels, the spatiotemporal data stream is classified to obtain K stability level data subsets. Finally, the K stability level data subsets are cross-correlation analyzed 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. Based on this coupling relationship matrix, a multidimensional phase transition diagram is constructed to obtain a reconstructed high-dimensional phase space trajectory.

[0030] For example, in the construction of the subway foundation pit, the compressed fusion spatiotemporal data stream collected was analyzed. First, the fractal dimension was calculated, and D = 1.76 was obtained, indicating that the data has strong self-similarity. Based on this self-similarity index, the original data was fractal interpolated, and the number of data points was increased from 100 to 500 per second. Then the phase space was reconstructed, and the embedding dimension m = 5 was selected, and the time delay , and obtain the 5-dimensional phase space trajectory. Calculate the Lyapunov index , indicating that the system has weak chaotic characteristics. The trajectory is divided into three sub-trajectories according to the change of the value. The three sub-trajectories are subjected to RQA analysis to obtain three 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 three 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. The matrix element values ​​range from -1 to 1, reflecting the degree of correlation between data of different stability levels.

[0031] In a specific embodiment, the process of executing step S3 may specifically include the following steps: (1) Perform persistence homology analysis on the reconstructed high-dimensional phase space trajectory to obtain a topological feature sequence, and calculate the persistence graph of the topological feature sequence to obtain a multi-scale topological structure representation; (2) Extract the Betti number sequence based on 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 eigenvector; (3) Perform isometric mapping on the topological eigenvectors and high-dimensional phase space trajectories 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 the data points; (4) Construct a 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; (5) Calculate the statistical moment for each category in the main pattern classification to obtain the category feature descriptor, and perform principal component analysis on the category feature descriptor to obtain the key feature set after dimensionality reduction; (6) Based on the key feature set and main mode classification, the characteristic representation of the load distribution is constructed to obtain the main modes and key features of the load distribution.

[0032] Specifically, we perform continuous homology analysis on high-dimensional phase space trajectories, which is a computational topology method used to capture the topological characteristics of data sets at different scales. The core of continuous homology analysis is to construct a sequence of simplicial complexes and calculate their homology groups. Define the Vietoris-Rips complex ,in is the distance threshold. With the increase of , we get a series of nested complexes, forming a filter flow:

[0033] in is the distance threshold, satisfying By calculating the homology group of this filter flow, we can obtain the topological characteristic sequence.

[0034] Next, we calculate a persistence graph for the topological feature sequence. A persistence graph is a visualization tool used to represent the “birth” and “death” of topological features. Indicates that a topological feature is within the distance threshold Appears at By analyzing the life cycle length of the features in the persistence graph By analyzing the topological structure characteristics of the dataset at different scales and their distribution, we can construct a multi-scale topological structure representation. This representation method can reveal stable topological features in the data, as well as transient features that appear and disappear quickly with scale changes.

[0035] According to the multi-scale topological structure representation, the Betti number sequence is extracted. The Betti number is an important invariant in the topological space. The kth 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., rings). The Betti number sequence constitutes a set of topological invariants. Statistical analysis of this set, including calculation of mean, variance, skewness, and kurtosis, is performed to obtain the topological eigenvector. Then, isometric mapping is performed on the topological eigenvector and the high-dimensional phase space trajectory to obtain a low-dimensional embedding space. Isometric mapping is a nonlinear dimensionality reduction technique whose goal is to maintain the geodesic distance between high-dimensional data points in a low-dimensional space. The objective function of isometric mapping can be expressed as: ; in is the midpoint of the high-dimensional space and The geodesic distance between and is the corresponding low-dimensional representation. In the obtained low-dimensional embedding space, the geodesic distance matrix is ​​calculated to reflect the intrinsic geometric relationship between the data points. According to the intrinsic geometric relationship, a neighbor graph is constructed to obtain the local structure of the data manifold. The neighbor graph is usually constructed using k-nearest neighbor or Nearest neighbor method. Spectral clustering is performed on this local structure to obtain the main pattern classification. The core of spectral clustering is to calculate the eigenvector of the graph Laplacian matrix L, which is defined as: ; in is the adjacency matrix, is the degree matrix.

[0036] Statistical moments, including mean, variance, skewness and kurtosis, are calculated for each category in the main mode classification to obtain the category feature descriptors. Principal component analysis (PCA) is performed on these feature descriptors to obtain the key feature set after dimensionality reduction. PCA finds the main direction of change of the data by calculating the eigenvectors of the covariance matrix. Finally, based on the key feature set and the main mode classification, the feature representation of the load distribution is constructed to obtain the main mode and key features of the load distribution.

[0037] For example, in the construction of the subway foundation pit, the reconstructed 10-dimensional phase space trajectory is analyzed. First, the topological feature sequence is obtained through the persistence homology analysis, which contains the information of the 0-dimensional, 1-dimensional and 2-dimensional homology groups. After calculating the persistence graph, it is found that the average duration of the 0-dimensional feature is 0.5, the 1-dimensional feature is 0.3, and the 2-dimensional feature is 0.1. The Betti number sequence is extracted and obtained (indicates that the data set is connected), (indicating the existence of three one-dimensional rings), (Indicates the existence of 1 2D void). Statistical analysis of the Betti number sequence was performed to obtain a 4D topological feature vector. The 10-dimensional data was reduced to 3D by isometric mapping, and the geodesic distance matrix was calculated in 3D space. A k-nearest neighbor graph (k=5) was constructed, and then spectral clustering was performed to obtain 4 main mode categories. Statistical moments were calculated for each category to obtain a 16-dimensional (4 categories × 4 statistics) category feature descriptor. PCA was performed on these 16-dimensional descriptors, retaining the principal components required to explain 95% of the variance, and finally a 6-dimensional key feature set was obtained. These analysis results provide deep insights into the load distribution in the shield section. For example, the three 1D rings may correspond to the stress distribution pattern around the tunnel, while the 2D voids may reflect the discontinuity of the geological structure. The four main mode categories may represent different geological conditions or construction stages.

[0038] In a specific embodiment, the process of executing step S4 may specifically include the following steps: (1) Perform kernel density estimation on the main modes and key features of the load distribution to obtain a non-parametric probability density function, and numerically integrate the non-parametric probability density function to obtain a cumulative distribution function; (2) Calculate the quantile based on the cumulative distribution function to obtain the characteristic statistics of the probability distribution, and perform moment estimation on the characteristic statistics to obtain the initial estimate of the distribution parameters; (3) Perform maximum likelihood estimation on the initial estimate to obtain the optimized distribution parameter set, and construct a parameterized probability density function based on the distribution parameter set to obtain the parameter probability distribution model of the load; (4) Perform Monte Carlo sampling on the optimal probability distribution function to obtain a load sample set, and calculate the statistical moment of the load sample set to obtain the statistical characteristic parameters of the load; (5) 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 parameter estimation data of the load probability distribution.

[0039] Specifically, in the process of shield section load analysis, it is a crucial step to estimate the probability density of the main modes and key characteristics of load distribution. First, the kernel density estimation method is used to perform non-parametric probability density estimation on the data. The formula of kernel density estimation is as follows:

[0040] in, is the estimated probability density function, is the sample size, is the bandwidth parameter, is the kernel function, is the sample point. Common kernel functions include Gaussian kernel, Epanechnikov kernel, etc. Selecting a suitable bandwidth parameter h is crucial to the accuracy of the estimation result. After obtaining the non-parametric probability density function, the cumulative distribution function (CDF) is calculated by numerical integration. Numerical integration can use methods such as trapezoidal rule or Simpson's rule. The calculation formula of the cumulative distribution function is:

[0041] 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 estimates of the distribution parameters. The moment estimation method is based on the relationship between the sample moment and the population moment. For example, for the normal distribution, the sample mean and sample variance are unbiased estimates of the population mean and population variance, respectively. Next, the maximum likelihood estimation (MLE) method is used to optimize the initial estimates to obtain the optimized distribution parameter set. The goal of maximum likelihood estimation is to find the parameter value that maximizes the probability of the observed data. For a given probability density function ,in is the parameter to be estimated, and the likelihood function is defined as:

[0042] Maximum likelihood estimation is to find The largest The estimated value is usually obtained by solving the derivative of the log-likelihood function to zero.

[0043] According to the optimized distribution parameter set, a parameterized probability density function is constructed to obtain the parameter probability distribution model of the load. In order to verify the fitting effect of the model, the Kolmogorov-Smirnov (KS) test is performed on the parameter probability distribution model. The KS test evaluates the goodness of fit by comparing the maximum difference between the theoretical distribution and the empirical distribution. The KS statistic is defined as:

[0044] in for Statistics, is the empirical distribution function, is the theoretical distribution function, i.e., the cumulative distribution function. According to the results of the KS test, the best fitting distribution type is selected to obtain the optimal probability distribution function of the load. In order 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 a complex system by generating a large number of random samples. The statistical moments of the obtained load sample set, including mean, variance, skewness, and kurtosis, are calculated to obtain the statistical characteristic parameters of the load.

[0045] Finally, according to the statistical characteristic parameters and the optimal probability distribution function, the parameterized representation of the load probability distribution is constructed, and the parameter estimation data of the load probability distribution is obtained.

[0046] For example, in the construction of the subway foundation pit, the load data of a 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 by cross-validation. The obtained non-parametric probability density function shows that the load distribution presents a bimodal feature. The cumulative distribution function is calculated by numerical integration, and the 25%, 50% and 75% quantiles are calculated to be 450kN, 500kN and 560kN respectively. Based on these statistics, it is preliminarily estimated that the data may conform to the mixed Gaussian distribution. The parameters of the mixed Gaussian distribution are optimized using the maximum likelihood estimation method. The results show that the load distribution can be described by a mixture of two Gaussian distributions, where the first distribution has a mean of 480kN, a standard deviation of 30kN, and a weight of 0.6; the second distribution has a mean of 540kN, a standard deviation of 25kN, and a weight of 0.4. The KS test is performed, and the p value obtained is 0.08, which is greater than the significance level of 0.05, indicating that the mixed Gaussian distribution can fit the actual data well. Monte Carlo sampling is performed on this mixed Gaussian distribution to generate 10,000 sample points. The statistical characteristics of these samples are calculated, and the overall mean is 504kN, the standard deviation is 42kN, the skewness is 0.3, and the kurtosis is 2.8.

[0047] In a specific embodiment, the process of executing step S5 may specifically include the following steps: (1) The parameter estimation data is segmented into time windows to obtain a set of time series segments, and the time series segments are Fourier transformed to obtain a frequency domain feature sequence; (2) Calculate the power spectrum density based on the frequency domain characteristic sequence to obtain the frequency distribution of the load characteristics, and perform peak detection on the frequency distribution to obtain the main frequency components; (3) Perform autocorrelation analysis on the main frequency components to obtain the time delay parameters, and construct the phase space based on the time delay parameters to obtain the dynamic trajectory of the load characteristics; (4) Calculate the Lyapunov index for the dynamic trajectory to obtain the chaos degree index of the system, and judge the long-term behavior characteristics of the system based on the chaos degree index to obtain the stability evaluation data of the load evolution; (5) Perform wavelet decomposition on the time series fragments 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; (6) Based on the main change modes and stability assessment data, the trend change of load characteristics is analyzed to obtain the dynamic evolution law of load characteristics.

[0048] Specifically, the parameter estimation data is segmented into time windows, and the continuous data stream is segmented into several overlapping or non-overlapping time segments. The choice of time windows directly affects the results of subsequent analysis, and the window size is usually determined based on the characteristics of the data and the purpose of the analysis. For example, for load data collected once an hour, 24 hours can be selected as a time window to capture daily variations. 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, discrete Fourier transform (DFT) or fast Fourier transform (FFT) algorithms are usually used. The frequency domain feature sequence obtained after the transformation contains the amplitude and phase information of each frequency component.

[0049] 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 in frequency and helps to identify the dominant frequency components. Common 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 the local maximum. 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 the time series with itself at different time delays, which helps to discover the periodicity and dependence structure in the sequence. The time delay parameter usually selects the delay time when the autocorrelation function first reaches the local minimum. Based on this time delay parameter, the delayed coordinate method is used to construct the phase space to obtain the dynamic trajectory of the load characteristics. The Lyapunov exponent is calculated for the constructed dynamic trajectory to obtain the chaos degree index of the system. The Lyapunov exponent measures the separation rate of adjacent orbits in the phase space. The positive maximum Lyapunov exponent indicates that the system has chaotic characteristics. According to the calculated chaos degree index, the long-term behavior characteristics of the system are judged, thereby obtaining the stability evaluation data of the load evolution.

[0050] At the same time, the time series fragments are subjected to wavelet decomposition to obtain multi-scale time-frequency features. Wavelet decomposition can provide information in both time and frequency domains, and is particularly suitable for analyzing non-stationary signals. Commonly used wavelet functions include Haar wavelets, Daubechies wavelets, 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, cycles, and noise by performing singular value decomposition on the trajectory matrix. Finally, based on the identified main change patterns and the previously obtained stability assessment data, a trend change analysis of the load characteristics is performed to obtain the dynamic evolution law of the load characteristics. This step combines all the previous analysis results and reveals the change trend of the load over time, periodic characteristics, and potential instability.

[0051] For example, in the construction of the subway foundation pit, the load data of a key point is analyzed. First, the load data of 30 consecutive days is divided into 24-hour time windows to obtain 30 time series segments. FFT is performed on each segment to obtain 30 sets of frequency domain feature sequences. After calculating the power spectrum density, it is found that the main frequency components are concentrated near 0.04Hz (corresponding to a 25-hour period) and 0.00231Hz (corresponding to a 6-day period). Autocorrelation analysis determines that the optimal time delay is 6 hours, and the phase space is constructed based on this to obtain the dynamic trajectory of the load characteristics. The Lyapunov index is calculated to be 0.02, indicating that the system has weak chaotic characteristics. The wavelet decomposition uses Db4 wavelet with a decomposition layer of 5 to obtain 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 presents complex dynamic characteristics, including obvious daily cycle fluctuations and a long-term trend of slow rise.

[0052] In a specific embodiment, the process of executing step S6 may specifically include the following steps: (1) Perform empirical mode decomposition on the dynamic evolution law of load characteristics to obtain multiple eigenmodes, and perform Hilbert transform on the eigenmodes to obtain instantaneous frequency and instantaneous amplitude; (2) A time-frequency energy distribution diagram is constructed based on the instantaneous frequency and instantaneous amplitude to obtain a multi-scale representation of the load characteristics. The multi-scale representation is then threshold segmented to obtain load components of different scales. (3) Reconstruct and superimpose load components of different scales to obtain the layered load numerical distribution data of the subway structure in the shield section, and perform spatial interpolation on the layered load numerical distribution data to obtain a continuous load distribution field; (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; (5) Perform multi-objective optimization on the interval stability score and load distribution field to obtain a candidate construction parameter scheme group, and perform sensitivity analysis on the candidate construction parameter scheme group to obtain key control parameters; (6) Based on the key control parameters and candidate construction parameter scheme groups, a construction strategy data set is generated to obtain the optimal control scheme for shield construction.

[0053] It should be noted that the dynamic evolution law of load characteristics is subjected to empirical mode decomposition (EMD), which 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 obtain a series of IMFs with frequencies from high to low by repeatedly extracting the local extreme envelope of the signal. , the EMD process can be expressed as: ; in For the i The intrinsic mode functions, is the residual item.

[0054] Perform Hilbert transform on each IMF obtained to obtain the instantaneous frequency and instantaneous amplitude. The formula of Hilbert transform is:

[0055] Through Hilbert transform, the analytical signal of the signal can be obtained, and then the instantaneous frequency and instantaneous amplitude can be calculated. yes The Hilbert transform of is the input signal, is the time variable, is the integration variable, represents the Cauchy principal value integral.

[0056] According to the calculated instantaneous frequency and instantaneous amplitude, a time-frequency energy distribution diagram is constructed, which provides a multi-scale representation for the load characteristics. The time-frequency energy distribution diagram intuitively 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 of 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 of one scale. The load components of different scales are reconstructed and superimposed to obtain the layered load numerical distribution data of the subway structure in the shield section. The reconstruction process is to weight the load components of each scale according to their contribution in the original signal. The layered load numerical distribution data is spatially interpolated to obtain a continuous load distribution field. Spatial interpolation methods include Kriging interpolation, inverse distance weighted method, etc. Selecting a suitable 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 index 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. A 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 uncertainty of multiple evaluation factors, and obtains the final evaluation result by establishing a fuzzy relationship matrix and a weight vector. Multi-objective optimization is performed on the interval stability score and the load distribution field to obtain a candidate construction parameter scheme group. Multi-objective optimization takes into account multiple objectives such as safety and economy, and uses algorithms such as NSGA-II to find the Pareto optimal solution set. A sensitivity analysis is performed on the candidate construction parameter scheme group 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.

[0057] Finally, according to the key control parameters and candidate construction parameter scheme groups, a construction recommendation strategy data set is generated to obtain the optimal control scheme for shield construction. The previous analysis results are converted into specific construction guidance to provide direct support for engineering practice.

[0058] For example, in the construction of the subway foundation pit, the load data of 30 consecutive days were analyzed. First, 5 IMFs and 1 residual term were obtained through EMD. The first IMF was Hilbert transformed, and the instantaneous frequency fluctuated between 0.8-1.2Hz, and the instantaneous amplitude varied between 0.5-2kN. After constructing the time-frequency energy distribution diagram, the energy threshold was set to 5% of the total energy, and 3 main load components were obtained, corresponding to high frequency (1-2Hz), medium frequency (0.1-0.5Hz) and low frequency (<0.05Hz) components. These 3 load components were reconstructed and Kriging interpolation was performed on 100 discrete measuring points to obtain a continuous load distribution field. The maximum stress gradient was calculated to be 0.5MPa / m, and the maximum deformation rate was 0.1%. Through fuzzy comprehensive evaluation, the interval stability score was 0.75 (full score 1). Multi-objective optimization considered the two goals of safety and construction efficiency, and obtained 10 sets of candidate construction parameter schemes. Sensitivity analysis shows that the advancement speed and grouting pressure are the most critical control parameters. The final construction suggestions include: in high stress gradient areas (>0.4MPa / m), the advancement speed is controlled at 20-25mm / min, and the grouting pressure is maintained at 0.3-0.35MPa; in low stress gradient areas (<0.2MPa / m), the advancement speed can be appropriately increased to 30-35mm / min, while the grouting pressure can be reduced to 0.25-0.3MPa. These suggestions provide data support for the refined control of shield construction, which helps to improve construction efficiency and safety.

[0059] The embodiment of the present invention also provides an anti-uplift dynamic loading analysis system for underground structures, such as Figure 2 As shown, the anti-uplift dynamic loading analysis system for underground structures specifically includes: The encoding module 201 is used to perform adaptive fusion encoding on the original data collected by subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; An interpolation module 202 is used to perform fractal interpolation and chaotic dynamics analysis on the spatiotemporal data stream to obtain a reconstructed high-dimensional phase space trajectory; A dimensionality reduction module 203 is used to perform topological feature extraction and nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main mode and key features of the load distribution; An estimation module 204 is used to perform probability density estimation on the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; An analysis module 205 is used to perform time series analysis on the parameter estimation data to obtain a dynamic evolution law of load characteristics; The optimization module 206 is used to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics, obtain the layered load numerical distribution data of the subway structure in the shield section, and perform multi-objective optimization analysis on the layered load numerical distribution data to obtain a construction recommendation strategy data set.

[0060] Through the collaborative work of the above modules, the adaptive fusion encoding of the raw data collected by multi-source sensors is carried out to achieve efficient data compression and information extraction, significantly reduce the data transmission and storage requirements, and retain key load information. This method not only improves the data processing efficiency, but also provides high-quality input for subsequent analysis. Secondly, the fractal interpolation and chaotic dynamics analysis methods are used to deeply explore the inherent complexity and dynamic characteristics of the load data, laying the foundation for accurately grasping the load change law during shield construction. Through topological feature extraction and nonlinear dimensionality reduction technology, the main modes and key features of the load distribution are successfully captured, greatly improving the understanding and description of complex load states. The introduction of probability density estimation and parametric modeling enables the uncertainty of load distribution to be quantitatively expressed, 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 technology realizes the accurate description of the layered load in the shield interval, providing necessary data support for refined construction control. In addition, through multi-objective optimization and sensitivity analysis, practical construction recommendation strategies were obtained, which directly guided construction practice and improved construction efficiency and safety.

[0061] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for dynamic loading analysis of anti-uplift of underground structures, characterized in that: include: S1, adaptively fusion-encode the original data collected by subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; S2, performing fractal interpolation and chaotic dynamics analysis on the spatiotemporal data stream to obtain a reconstructed high-dimensional phase space trajectory; S3, performing topological feature extraction and nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main modes and key features of the load distribution; S4. Performing probability density estimation on the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; S5. Performing 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, multi-scale decomposition and reconstruction are performed to obtain the layered load numerical distribution data of the subway structure in the shield section, and multi-objective optimization analysis is performed on the layered load numerical distribution data to obtain a construction recommendation strategy data set.

2. The method for dynamic loading analysis of underground structure against uplift according to claim 1, characterized in that: Step S1 includes: Performing stress-strain separation processing on the original data collected by the multi-source sensors to obtain separated stress data and strain data, and performing elastic-plastic decoupling analysis on the stress data and strain data to obtain elastic deformation components and plastic deformation components; Calculating a load-deformation curve according to the elastic deformation component and the plastic deformation component and extracting response data to obtain load response data; Performing a time-frequency joint analysis on the load response data to obtain a load spectrum diagram, and extracting the main frequency characteristics and energy distribution according to the load spectrum diagram to obtain load modal parameters; Performing nonlinear feature extraction on the load modal parameters to obtain a load nonlinear index, and performing mutual information analysis on the load nonlinear index and the original data to obtain a key sensor weight; Adaptively fusing multi-source data according to the key sensor weights to obtain fused load data; Performing complexity analysis on the fused load data to obtain a data complexity index, and designing an adaptive quantization strategy according to the data complexity index to obtain a quantization coding scheme; The fused payload data is compressed and encoded by the quantization encoding scheme to obtain a spatiotemporal data stream.

3. The anti-uplift dynamic loading analysis method for underground structures according to claim 1, characterized in that: Step S2 includes: Performing fractal dimension calculation on the spatiotemporal data stream to obtain a self-similarity index, and performing fractal interpolation on the spatiotemporal data stream according to the self-similarity index to obtain a high-resolution interpolation data set; Reconstructing the interpolation data set in phase space to obtain a high-dimensional phase space trajectory, and calculating the Lyapunov exponent of the high-dimensional phase space trajectory to obtain a chaos characteristic index; The high-dimensional phase space trajectory is segmented according to the chaotic characteristic index to obtain N sub-trajectories with different dynamic characteristics, where N is an integer between 2 and 5, and the N sub-trajectories are respectively recursively quantitatively analyzed to obtain N sets of dynamic characteristic indicator sets, each set of indicators including four parameters: periodicity, determinism, laminarity and complexity; Performing cluster analysis on the N groups of dynamic characteristic indicator sets to obtain K stability levels, where K is an integer between 2 and 4, and classifying the spatiotemporal data streams according to the K stability levels to obtain data subsets of K stability levels; A cross-correlation analysis is performed on the data subsets of the K stability levels to obtain a K×K dimensional variable coupling relationship matrix, and a multidimensional phase change diagram is constructed according to the coupling relationship matrix to obtain a reconstructed high-dimensional phase space trajectory.

4. The method for dynamic loading analysis of underground structure against uplift according to claim 1, characterized in that: The S3 step includes: Performing a persistence homology analysis on the reconstructed high-dimensional phase space trajectory to obtain a topological feature sequence, and calculating a persistence graph for the topological feature sequence to obtain a multi-scale topological structure representation; Extracting a Betti number sequence according to the multi-scale topological structure representation to obtain a topological invariant set, and performing statistical analysis on the topological invariant set to obtain a topological feature vector; Performing isometric mapping on the topological eigenvector and the high-dimensional phase space trajectory to obtain a low-dimensional embedding space, and calculating a geodesic distance matrix in the low-dimensional embedding space to obtain an intrinsic geometric relationship between data points; Constructing a neighbor graph according to the intrinsic geometric relationship to obtain a local structure of the data manifold, and performing spectral clustering on the local structure to obtain a main pattern classification; Calculating statistical moments for each category in the main pattern classification to obtain category feature descriptors, and performing principal component analysis on the category feature descriptors to obtain a key feature set after dimensionality reduction; According to the key feature set and main mode classification, a characteristic representation of the load distribution is constructed, and the main modes and key features of the load distribution are obtained.

5. The method for dynamic loading analysis of underground structure against uplift according to claim 1, characterized in that: Step S4 includes: Performing kernel density estimation on the main modes and key features of the load distribution to obtain a non-parametric probability density function, and numerically integrating 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 initial estimated values ​​of distribution parameters; Performing maximum likelihood estimation on the initial estimated value to obtain an optimized distribution parameter set, and constructing a parameterized probability density function based on the distribution parameter set to obtain a parameter probability distribution model of the load; Performing a Kolmogorov-Smirnov test on the parameter 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 on the load sample set to obtain statistical characteristic parameters of the load; According to the statistical characteristic parameters and the optimal probability distribution function, a parameterized representation of the load probability distribution is constructed to obtain parameter estimation data of the load probability distribution.

6. The method for dynamic loading analysis of underground structure against uplift according to claim 1, characterized in that: Step S5 includes: Performing time window segmentation on the parameter estimation data to obtain a time series segment set, and performing Fourier transform on the time series segment set to obtain a frequency domain feature sequence; Calculating the power spectrum 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 time delay parameters, and constructing a phase space according to the time delay parameters to obtain a dynamic trajectory of the load characteristics; Calculating the Lyapunov index for the dynamic trajectory to obtain a chaos degree index of the system, and judging the long-term behavior characteristics of the system based on the chaos degree index to obtain stability evaluation data of load evolution; Performing wavelet decomposition on the time series fragments to obtain multi-scale time-frequency characteristics, and performing singular spectrum analysis on the multi-scale time-frequency characteristics to obtain the main variation mode of the load characteristics; The trend change analysis of the load characteristics is performed based on the main change modes and stability assessment data to obtain the dynamic evolution law of the load characteristics.

7. The method for dynamic loading analysis of anti-uplift of underground structures according to claim 6, characterized in that: Step S6 includes: Performing empirical mode decomposition on the dynamic evolution law of the load characteristics to obtain multiple eigenmodes, and performing Hilbert transform on the eigenmodes to obtain instantaneous frequency and instantaneous amplitude; A time-frequency energy distribution diagram is constructed according to the instantaneous frequency and the instantaneous amplitude to obtain a multi-scale representation of the load characteristics, and threshold segmentation is performed on the multi-scale representation to obtain load components of different scales; Reconstructing and superimposing the load components of different scales to obtain layered load numerical distribution data of the subway structure in the shield section, and performing spatial interpolation on the layered load numerical distribution data to obtain a continuous load distribution field; Calculating the stress gradient and deformation rate according to the continuous load distribution field to obtain the stress state index of the shield section, and performing fuzzy comprehensive evaluation on the stress state index to obtain the section stability score; Perform multi-objective optimization on the interval stability score and the load distribution field to obtain a candidate construction parameter scheme group, and perform sensitivity analysis on the candidate construction parameter scheme group to obtain key control parameters; According to the key control parameters and the candidate construction parameter scheme group, a construction suggestion strategy data set is generated to obtain an optimized control scheme for shield construction.

8. An anti-uplift dynamic loading analysis system for underground structures, used to execute the anti-uplift dynamic loading analysis method for underground structures according to any one of claims 1 to 7, characterized in that: include: The encoding module is used to adaptively fuse and encode the original data collected through subway structure mapping in the shield tunnel section to obtain a spatiotemporal data stream; An interpolation module, used for performing fractal interpolation and chaotic dynamics analysis on the spatiotemporal data stream to obtain a reconstructed high-dimensional phase space trajectory; A dimensionality reduction module is used to perform topological feature extraction and nonlinear dimensionality reduction on the reconstructed high-dimensional phase space trajectory to obtain the main mode and key features of the load distribution; An estimation module, used to perform probability density estimation on the main modes and key features of the load distribution to obtain parameter estimation data of the load probability distribution; An analysis module, used for performing time series analysis on the parameter estimation data to obtain the dynamic evolution law of the load characteristics; The optimization module is used to perform multi-scale decomposition and reconstruction based on the dynamic evolution law of the load characteristics, obtain the layered load numerical distribution data of the subway structure in the shield section, and perform multi-objective optimization analysis on the layered load numerical distribution data to obtain a construction recommendation strategy data set.

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