A foundation pit deformation prediction method and system based on time series analysis

Abstract

The present application relates to the technical field of foundation pit deformation monitoring and prediction, in particular to a foundation pit deformation prediction method and system based on time series analysis. The method comprises the following steps: extracting hour-level propagation characteristics and propagation rate attenuation index by establishing an instability case library, identifying instability source candidate areas using non-local gradient, determining propagation acceleration factors according to the comparison between time variation rate and propagation rate attenuation index, calculating wave superposition coefficients and performing under-consolidation correction to obtain expansion velocity when there are multiple instability sources, calculating the remaining time window according to the expansion velocity and propagation path, and obtaining the final prediction result by dynamically matching historical statistical rules with the current actual working conditions through time axis compression technology when the remaining time window is less than the warning threshold. The present application constructs a two-dimensional attenuation model of instability wave space and time, combines soil mechanics mechanism with wave propagation theory, and significantly improves the timeliness and accuracy of short and urgent engineering foundation pit deformation prediction.

Description

Technical Field

[0001] This invention relates to the field of foundation pit deformation monitoring and prediction technology, specifically to a foundation pit deformation prediction method and system based on time series analysis. Background Technology

[0002] Foundation pit engineering is a crucial component of urban underground space development, and its deformation monitoring and prediction are essential for ensuring construction safety. Especially in tight, short-term projects, rapid excavation can lead to insufficient soil consolidation time, easily causing rapid instability within hours, thus placing higher demands on the timeliness of prediction methods.

[0003] Existing methods for predicting foundation pit deformation are mainly based on time-series analysis, such as ARIMA models and LSTM neural networks. While these methods can predict deformation trends, they have the following drawbacks: First, the early warning timeliness is poor, with prediction cycles typically on the order of days, while the instability evolution cycle of short-term and urgent projects is only a few hours, resulting in excessively long warning times that render them meaningless. Second, they lack modeling of instability propagation mechanisms, making it impossible to identify the location of instability sources, propagation paths, and expansion speeds, thus hindering the provision of spatial information support for emergency decision-making. Third, they neglect the underconsolidation effect under rapid excavation conditions, leading to inaccurate predictions of the accelerated instability process in short-term and urgent projects in soft soil strata. Summary of the Invention

[0004] This invention provides a method and system for predicting foundation pit deformation based on time series analysis, aiming to solve the problem of insufficient timeliness in early warning of foundation pit instability in short-term and urgent engineering projects.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention provides a method for predicting foundation pit deformation based on time-series analysis, comprising:

[0007] S100: Collect historical foundation pit monitoring time series data, extract feature vectors after normalization and cluster them to form multiple deformation pattern families; establish an instability case library, collect short and urgent engineering cases with excavation rates greater than the rate threshold, and extract the propagation time, propagation path and propagation rate attenuation index of instability from the source point to the boundary measuring point.

[0008] S200: Based on the engineering parameters of the foundation pit to be predicted, retrieve similar deformation pattern families, extract feature vectors, and reconstruct the initial prediction curve;

[0009] S300: Obtain the measured displacement data of the foundation pit to be predicted, establish a multi-point displacement difference field, calculate the nonlocal gradient and identify candidate regions of instability source;

[0010] S400: When the nonlocal gradient of the candidate region of the instability source exceeds the gradient threshold, the propagation acceleration factor is determined by comparing with the historical parameters of the instability case library based on the nonlocal gradient time series, and the expansion speed is obtained based on the propagation acceleration factor.

[0011] S500: Calculate the remaining time window based on the expansion speed, spatial distribution of measurement points, and propagation path. When the remaining time window is less than the warning threshold, compress the initial prediction curve according to the time difference to obtain the final prediction result.

[0012] As a preferred embodiment of the present invention, the step of extracting the propagation rate attenuation index includes:

[0013] Extract the propagation time of instability from the source point to measurement points at different distances from the instability case, and calculate the propagation rate at the measurement points at different distances;

[0014] Establish the relationship between propagation rate and distance from the source point, and extract the spatial decay exponent by fitting a power function.

[0015] The relationship between propagation rate and propagation time of unstable wave was established, and the time decay exponent was extracted by fitting an exponential function.

[0016] A two-dimensional decay model is constructed by combining the spatial decay index and the temporal decay index, and the characteristic parameters of the two-dimensional model are used as the propagation rate decay index.

[0017] As a preferred embodiment of the present invention, the step of calculating the nonlocal gradient includes:

[0018] A preset radius is set for each measuring point, and the preset radius is determined based on the stiffness of the support structure and the size of the excavation zone;

[0019] Calculate the ratio of the displacement difference to the distance between the measured point and all measured points within the preset radius, and use the Gaussian kernel function as the weight to perform a weighted summation to obtain the nonlocal gradient;

[0020] The standard deviation of the Gaussian kernel function is determined based on the excavation partition feature size and support stiffness.

[0021] As a preferred embodiment of the present invention, the step of identifying candidate regions of instability sources includes:

[0022] Establish the nonlocal gradient spatial distribution of all measurement points, and identify the local maxima regions of the nonlocal gradient as initial candidate regions;

[0023] Calculate the autocorrelation coefficient of the nonlocal gradient time series of the initial candidate region. If the autocorrelation coefficient is less than the correlation threshold, it is determined to be a construction disturbance and is excluded.

[0024] Calculate the displacement phase difference between the measuring point in the initial candidate region and the neighboring measuring points. The neighboring measuring points refer to the several measuring points that are spatially closest to the measuring points in the initial candidate region. When the phase difference is greater than the phase threshold, it is determined to be a measuring point fault and eliminated.

[0025] The reserved region is designated as the candidate region for the instability source.

[0026] As a preferred embodiment of the present invention, when there are multiple candidate regions for instability sources and the distance between the regions is less than the critical distance, the propagation acceleration factor is corrected by instability wave superposition:

[0027] The amplitude and initial phase of the dominant frequency component are extracted by performing a Fourier transform on the nonlocal gradient time series of the candidate region of the instability source.

[0028] Calculate the midpoint position of the line connecting the candidate regions of the unstable source, and determine the superposition type based on the phase difference of the main frequency component of the unstable source at the midpoint position;

[0029] When the phase difference is less than a quarter of a period, it is superimposed in the same direction. A superposition amplification factor greater than 1 is calculated based on the amplitude of the instability source and the distance between regions.

[0030] When the phase difference is greater than a quarter of a period, it is considered anisotropic superposition, and a superposition suppression coefficient less than 1 is calculated based on the phase difference.

[0031] The propagation acceleration factor is corrected by using the superposition coefficient of unstable waves.

[0032] As a preferred embodiment of the present invention, when the excavation rate is greater than the rate threshold and the soil compression modulus is less than the compression modulus threshold, the propagation acceleration factor is underconsolidated:

[0033] Calculate the excess pore water pressure dissipation based on the excavation rate and soil consolidation coefficient;

[0034] When the dissipation is less than the dissipation threshold, the propagation acceleration factor is multiplied by the underconsolidation amplification factor.

[0035] The underconsolidation amplification factor is positively correlated with the amplitude of excess pore water pressure.

[0036] As a preferred embodiment of the present invention, the step of determining the propagation acceleration factor includes:

[0037] The nonlocal gradient time series of the candidate region of the instability source is subjected to exponential fitting to extract the time evolution index of the current case;

[0038] Extract evolution rate parameters from the instability case library for historical cases with the same soil type as the current soil layer;

[0039] The propagation acceleration factor is obtained by calculating the ratio of the current case evolution rate parameter to the historical case evolution rate parameter.

[0040] As a preferred embodiment of the present invention, the calculation steps of the remaining time window include:

[0041] Extract the propagation paths of historical cases similar to the current candidate instability source area from the instability case database, and map the historical propagation paths to the current project based on the current spatial distribution of the measurement points;

[0042] Calculate the propagation distance from the candidate region of the instability source to the boundary measurement point along the propagation path;

[0043] Divide the propagation distance by the propagation speed to obtain the instability arrival time of the boundary measurement point;

[0044] The shortest instability arrival time is selected as the remaining time window.

[0045] As a preferred embodiment of the present invention, the time axis compression step includes:

[0046] Calculate the displacement value corresponding to the warning trigger time based on the warning threshold and the expansion speed;

[0047] Extract the predicted time for the initial prediction curve to reach the displacement value;

[0048] Calculate the time difference between the remaining time window and the predicted time;

[0049] The time axis of the initial prediction curve is compressed based on the time difference;

[0050] Calculate the deformation rate of the predicted curve after compression, and calculate the theoretical maximum deformation rate based on the soil compression modulus and excavation depth.

[0051] When the deformation rate after compression exceeds the theoretical maximum deformation rate, the compression coefficient is adjusted so that the deformation rate does not exceed the theoretical maximum value.

[0052] This invention also proposes a foundation pit deformation prediction system based on time-series analysis, comprising:

[0053] The case library module is used to collect historical foundation pit monitoring time series data, extract feature vectors after normalization, and cluster them to form multiple deformation pattern families; and to establish an instability case library, collect short and urgent engineering cases with excavation rates greater than the rate threshold, and extract the propagation time, propagation path, and propagation rate attenuation index of instability from the source point to the boundary measuring point.

[0054] The initial curve reconstruction module is used to retrieve similar deformation mode families based on the engineering parameters of the foundation pit to be predicted, extract feature vectors, and reconstruct the initial prediction curve.

[0055] The instability source identification module is used to acquire the measured displacement data of the foundation pit to be predicted, establish a multi-measurement point displacement difference field, calculate the nonlocal gradient, and identify candidate regions of instability sources.

[0056] The acceleration factor calculation module is used to determine the propagation acceleration factor based on the nonlocal gradient time series by comparing it with historical parameters in the instability case library when the nonlocal gradient of the candidate region of the instability source exceeds the gradient threshold, and to obtain the expansion speed based on the propagation acceleration factor.

[0057] The time window prediction module is used to calculate the remaining time window based on the expansion speed, spatial distribution of measurement points, and propagation path. When the remaining time window is less than the warning threshold, the initial prediction curve is compressed along the time axis according to the time difference to obtain the final prediction result.

[0058] The beneficial effects of this invention are:

[0059] 1. This invention constructs a two-dimensional spatial-temporal decay model of instability effects, realizing instability source identification, propagation path prediction, and remaining time window calculation. It solves the shortcomings of traditional time series methods that can only predict single-point displacement and cannot provide spatial information, and significantly improves the timeliness of early warning for short-term and urgent projects.

[0060] 2. This invention combines soil mechanics mechanisms with instability propagation laws by dynamically correcting the propagation acceleration factor, correcting the underconsolidation effect, and correcting the wave superposition, accurately capturing the instability acceleration process of short-term engineering projects in soft soil strata, and effectively reducing the underreporting rate.

[0061] 3. This invention achieves dynamic matching between historical patterns and current operating conditions through time axis compression technology, and introduces physical constraints to avoid prediction exceeding limits. It integrates data-driven and physical mechanisms to improve the accuracy and rationality of prediction. Attached Figure Description

[0062] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0063] Figure 1 This is a flowchart illustrating a method for predicting foundation pit deformation based on time-series analysis according to the present invention.

[0064] Figure 2 This is a schematic diagram of the structure of a foundation pit deformation prediction system based on time-series analysis according to the present invention. Detailed Implementation

[0065] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0066] Example 1: As Figure 1 As shown, the present invention provides a method for predicting foundation pit deformation based on time-series analysis, comprising:

[0067] S100: Collect historical foundation pit monitoring time series data, extract feature vectors after normalization and cluster them to form multiple deformation pattern families; establish an instability case library, collect short and urgent engineering cases with excavation rates greater than the rate threshold, and extract the propagation time, propagation path and propagation rate attenuation index of instability from the source point to the boundary measuring point.

[0068] Furthermore, the step of extracting the propagation rate attenuation index includes:

[0069] Extract the propagation time of instability from the source point to measurement points at different distances from the instability case, and calculate the propagation rate at the measurement points at different distances;

[0070] Establish the relationship between propagation rate and distance from the source point, and extract the spatial decay exponent by fitting a power function.

[0071] The relationship between propagation rate and propagation time of unstable wave was established, and the time decay exponent was extracted by fitting an exponential function.

[0072] A two-dimensional decay model is constructed by combining the spatial decay index and the temporal decay index, and the characteristic parameters of the two-dimensional model are used as the propagation rate decay index.

[0073] Specifically, monitoring time-series data from historical foundation pit projects are collected, including the coordinates of measuring points, time-series displacement values, excavation progress information, and soil parameters. To eliminate dimensional differences between different projects, the displacement time-series data is normalized.

[0074] ;

[0075] in, This is the original displacement value. These are the normalized displacement values. and These are the minimum and maximum values ​​of the time series data at that measurement point, respectively.

[0076] Feature vectors are extracted from the normalized time-series curves. These feature vectors include the maximum deformation rate, peak deformation acceleration, curve concavity / convexity parameters, duration of the stable phase, and number of abrupt change points. Clustering algorithms are used to perform cluster analysis on the feature vectors, forming multiple deformation pattern families, each representing a typical deformation development pattern. In one embodiment, the K-means clustering algorithm is used, and the number of clusters is determined according to the elbow rule. The resulting deformation pattern families include slow-stable, linear-growing, logarithmic-growing, exponential-growing, bimodal, step-change, and oscillating-instability patterns.

[0077] An instability case database was established by selecting instability cases from historical engineering data that meet the characteristics of short-term, rapid excavation projects. The rate threshold was determined based on soil consolidation theory: when the excavation rate is too fast, the excess pore water pressure in the soil cannot dissipate in time, easily leading to rapid instability. It should be noted that the rate threshold is set at 0.5 m / day, a value determined based on the matching relationship between soil consolidation time and the excavation cycle. Selected instability cases must meet the following conditions: the excavation rate is greater than the rate threshold, there is a clear instability trigger moment, and the time for instability to propagate from the source point to the boundary measuring point is within the hour range.

[0078] For each instability case, the location of the instability source, propagation path, propagation time, and propagation rate attenuation index are extracted. The abrupt change moments of the displacement time-series curves at multiple measurement points are analyzed to identify the measurement point where the earliest abnormal deformation occurs as the instability source. The spatial propagation trajectory of the instability signal is traced, and the sequence of measurement points affected sequentially from the source is recorded, forming a propagation path node chain. The time difference between the arrival of the instability signal from the source point to each measurement point is recorded. ,in Indicates the first There are 10 measurement points.

[0079] The propagation rate decay exponent is used to quantify the spatial and temporal diffusion and decay of unstable waves. It extracts the propagation time of the unstable wave from the source point to measurement points at different distances from unstable case studies. and the corresponding distance Calculate the propagation rate at each measuring point:

[0080] ;

[0081] in, For the first The propagation rate at each measuring point The distance from the measuring point to the source point. This represents the time it takes for instability to occur.

[0082] The relationship between propagation speed and distance from the source point is established using a power function model for fitting:

[0083] ;

[0084] in, Distance from source point The propagation rate at that location, The initial velocity of the source point, This represents the spatial decay exponent. The data is linearized by taking the logarithm:

[0085] ;

[0086] The spatial decay index was obtained by least squares fitting. The physical meaning of this index is the degree to which the propagation speed decreases with increasing distance; the larger the index, the faster the attenuation.

[0087] The relationship between propagation rate and unstable wave propagation time was established using an exponential function model for fitting:

[0088] ;

[0089] in, Propagation time of unstable wave The corresponding propagation rate, The initial propagation speed of the source point. The time decay exponent, This is the time it takes for an unstable wave to propagate from its source.

[0090] Logarithmic linearization of historical case data:

[0091] ;

[0092] The time decay exponent was extracted by fitting using the least squares method. . The larger the value, the faster the propagation rate decays and the shorter the time scale of the instability effect.

[0093] Comprehensive spatial decay index and time decay index Construct a two-dimensional decay model:

[0094] ;

[0095] in, The spatial distance from the source point. The time taken for the unstable wave to propagate is denoted as . This model describes the propagation rate of the unstable wave as being simultaneously constrained by both spatial distance and propagation time. The characteristic parameters are then compared... It is stored as a propagation rate decay index in the instability case library.

[0096] It should be noted that the attenuation index varies among different soil types: soft soil layers, due to their greater damping, typically have a higher attenuation index than hard soil layers; the spatial attenuation index of cohesive soils... The typical range is 0.3~0.6, the time decay index. The typical range is 0.1 to 0.4. The case library records the soil layer parameters corresponding to each case, facilitating the subsequent retrieval of similar working conditions.

[0097] The instability case library stores the following fields for each case in a structured format: project type, excavation depth, soil parameters (including compression modulus, shear wave velocity, and consolidation coefficient), excavation rate, coordinates of the instability source point, propagation path node sequence, and spatial decay index. Time decay index The propagation time of instability from the source point to the boundary measurement point. This case database provides a data foundation for subsequent similar case retrieval and determination of propagation acceleration factors.

[0098] S200: Based on the engineering parameters of the foundation pit to be predicted, retrieve similar deformation pattern families, extract feature vectors, and reconstruct the initial prediction curve;

[0099] Specifically, the engineering parameters of the foundation pit to be predicted are obtained, including excavation depth, support type, soil layer distribution, excavation rate, and foundation pit plan dimensions. The engineering parameters of the foundation pit to be predicted are then matched with the deformation pattern family established in S100 to retrieve the most similar deformation pattern family.

[0100] Similarity is calculated using weighted Euclidean distance. Let the engineering parameter vector of the foundation pit to be predicted be... , Variation mode family Typical engineering parameter vectors are Then the similarity distance is:

[0101] ;

[0102] in, For the first The weighting coefficients for each parameter are determined based on their influence on the deformation mode. It should be noted that the weighting coefficients for excavation depth and soil compression modulus are usually larger because these two parameters have the most significant impact on the deformation mode. (Selecting distance...) The smallest family of deformable patterns is considered as a family of similar deformable patterns.

[0103] Feature vectors are extracted from all historical cases within the similar deformation pattern family. These feature vectors are defined consistent with those in S100 and include maximum deformation rate, peak deformation acceleration, curve concavity / convexity parameters, duration of the stable phase, and number of abrupt change points. Statistical analysis is performed on the extracted feature vectors, calculating the mean and standard deviation of each feature to form the typical feature vectors for this pattern family. .

[0104] The initial prediction curve is reconstructed based on typical eigenvectors. The reconstruction process employs a basis function superposition method, representing the deformed curve as a linear combination of multiple basis functions:

[0105] ;

[0106] in, To predict displacement, For time, For the first basis functions For the corresponding coefficients, The number of basis functions is denoted by . The selection of basis functions is determined based on the characteristics of the deformable mode family. Commonly used basis functions include polynomial functions, logarithmic functions, and exponential functions. In one embodiment, for an exponentially growing deformable mode family, a combination of exponential and logarithmic functions is used as the basis functions; for a bimodal oscillating deformable mode family, a superposition of Gaussian functions is used as the basis functions.

[0107] coefficient It is obtained through typical eigenvector inversion. Specifically, the slope characteristic of the curve is determined based on the maximum deformation rate in the eigenvectors, the curvature characteristic is determined based on the peak deformation acceleration, the overall shape of the curve is determined based on the curve's concavity / convexity parameters, and the time scale of the curve is determined based on the duration of the stable phase. The coefficients are solved using constrained optimization methods. This makes the eigenvectors of the reconstructed curves similar to the typical eigenvectors. The error is minimized:

[0108] ;

[0109] in, The eigenvectors are calculated to reconstruct the curve.

[0110] Solving for the coefficients Then, according to the formula An initial prediction curve is generated. This curve reflects the typical pattern of deformation development under similar engineering conditions and serves as the basis for subsequent adjustments based on measured data. It should be noted that the initial prediction curve is based only on historical statistical patterns and does not yet consider real-time monitoring data of the foundation pit to be predicted. Therefore, it needs to be dynamically adjusted in subsequent steps using measured displacement data.

[0111] S300: Obtain the measured displacement data of the foundation pit to be predicted, establish a multi-point displacement difference field, calculate the nonlocal gradient and identify candidate regions of instability source;

[0112] Furthermore, the step of calculating the nonlocal gradient includes:

[0113] A preset radius is set for each measuring point, and the preset radius is determined based on the stiffness of the support structure and the size of the excavation zone;

[0114] Calculate the ratio of the displacement difference to the distance between the measured point and all measured points within the preset radius, and use the Gaussian kernel function as the weight to perform a weighted summation to obtain the nonlocal gradient;

[0115] The standard deviation of the Gaussian kernel function is determined based on the excavation partition feature size and support stiffness.

[0116] Furthermore, the step of identifying candidate regions for instability sources includes:

[0117] Establish the nonlocal gradient spatial distribution of all measurement points, and identify the local maxima regions of the nonlocal gradient as initial candidate regions;

[0118] Calculate the autocorrelation coefficient of the nonlocal gradient time series of the initial candidate region. If the autocorrelation coefficient is less than the correlation threshold, it is determined to be a construction disturbance and is excluded.

[0119] Calculate the displacement phase difference between the measuring point in the initial candidate region and the neighboring measuring points. The neighboring measuring points refer to the several measuring points that are spatially closest to the measuring points in the initial candidate region. When the phase difference is greater than the phase threshold, it is determined to be a measuring point fault and eliminated.

[0120] The reserved region is designated as the candidate region for the instability source.

[0121] Specifically, the measured displacement data of the foundation pit to be predicted is obtained. The measured displacement data comes from multiple monitoring points deployed around the foundation pit, and the spatial coordinates of each monitoring point are recorded. and the displacement value at the corresponding time .

[0122] A multi-point displacement difference field is established to characterize the spatial distribution of foundation pit deformation. The displacement difference field is defined as the displacement difference between adjacent measuring points, and the calculation formula is as follows:

[0123] ;

[0124] in, For measuring points With measuring points The displacement difference between them and The two measuring points are at time [time]. The displacement values ​​are calculated. By calculating the displacement difference between all pairs of measuring points, a differential field covering the entire monitoring area is formed.

[0125] Calculate the nonlocal gradient for each measuring point. The nonlocal gradient is used to quantify the degree of deformation non-uniformity in the area surrounding the measuring point, and can capture long-range deformation correlations that traditional local gradients cannot identify. A preset radius is set for each measuring point. The preset radius is determined based on the stiffness of the support structure and the size of the excavation zone. The greater the stiffness of the support structure, the wider the deformation influence range, and the larger the preset radius; the larger the size of the excavation zone, the longer the deformation transmission distance, and the larger the preset radius. In one embodiment, the preset radius... The value is taken as 1.5 to 2 times the feature size of the excavation zone.

[0126] Calculate measuring points With preset radius All measuring points The ratio of displacement difference to distance:

[0127] ;

[0128] in, For measuring point pair gradient contribution, Let be the distance between the two measurement points. A weighted summation is performed using a Gaussian kernel function as the weights to obtain the distance between the measurement points. Nonlocal gradient:

[0129] ;

[0130] in, For measuring points nonlocal gradient, Indicates the measuring point preset radius The set of all measuring points within the range, Weights for the Gaussian kernel function:

[0131] ;

[0132] in, For measuring points With measuring points The distance between them is the standard deviation of the Gaussian kernel function.

[0133] Standard deviation The dimensions of the excavation zones are determined based on their characteristic dimensions and the support stiffness. The characteristic dimensions of the excavation zones are taken as the geometric mean of the longer and shorter sides. ,in and These are the long and short side dimensions of the excavation section, respectively. Standard deviation. With the excavation zone feature size Proportional:

[0134] ;

[0135] in, This is a coefficient related to the support stiffness. The greater the support stiffness, the wider the range of deformation influence. The larger the value, the smaller the support stiffness, and the smaller the range of deformation influence. The smaller the value, the better. For diaphragm walls or bored pile support, The value ranges from 0.3 to 0.5; for steel-cement-soil mixing pile support, The value ranges from 0.2 to 0.3; for sheet pile support, The value ranges from 0.15 to 0.25.

[0136] Taking a typical working condition as an example: the long side of the excavation zone m, shorter side m, feature size m, using diaphragm wall support ,but m.

[0137] Establish the nonlocal gradient spatial distribution of all measurement points, and identify local maxima regions of the nonlocal gradient as initial candidate regions. A local maximum region refers to a measurement point that satisfies the following condition: the nonlocal gradient of that measurement point... The nonlocal gradient is greater than that of all its neighboring measurement points. All local maxima are identified using a spatial scanning algorithm, and spatially adjacent maxima are merged into an initial candidate region.

[0138] The initial candidate regions are screened to exclude gradient anomalies caused by non-instability factors. The nonlocal gradient time series of the initial candidate regions are then calculated. Autocorrelation coefficient:

[0139] ;

[0140] in, Lag time The autocorrelation coefficient, This is the time mean of the nonlocal gradient. When the autocorrelation coefficient... When the correlation coefficient is less than the correlation threshold, it indicates that the time series of the nonlocal gradient exhibits random fluctuation characteristics, and is therefore identified as a short-term anomaly caused by construction disturbance and excluded. It should be noted that the correlation threshold is usually set between 0.3 and 0.5. This threshold is determined based on the autocorrelation characteristics of the instability process. The instability evolution is persistent, and its autocorrelation coefficient is significantly higher than that of random disturbances.

[0141] Calculate the measurement points within the initial candidate region The displacement phase difference with neighboring measurement points q is used to identify measurement point faults. The instantaneous phase is extracted by performing a Hilbert transform on the displacement time series. Calculate the phase difference:

[0142] ;

[0143] When phase difference When the value exceeds the phase threshold, it indicates that the deformation response of the measuring point is inconsistent with that of the surrounding measuring points, and the point is identified as faulty and eliminated. The neighboring measuring points refer to the several measuring points spatially closest to the measuring points within the initial candidate region. The number is determined based on the measuring point density and is used to determine whether the deformation response of the measuring point is consistent with that of the surrounding measuring points. In one embodiment, when the measuring points are arranged in a regular grid, the neighboring measuring points are the measuring points directly adjacent to that measuring point, and are selected as 4 (in the four directions of up, down, left, and right) or 8 (including the diagonal direction); when the measuring points are arranged irregularly, the neighboring measuring points are the 4 to 8 measuring points closest to that measuring point. It should be noted that the phase threshold is typically set to a value... That is, 90 degrees, because the phase difference between adjacent measuring points during normal deformation propagation generally does not exceed this value.

[0144] The retained regions are designated as candidate instability sources. These candidate regions exhibit the following characteristics: nonlocal gradients are local maxima, the time series shows significant autocorrelation, and the measurement points within the region have consistent phases. These candidate regions may develop into instability sources and require further monitoring and analysis in subsequent steps.

[0145] S400: When the nonlocal gradient of the candidate region of the instability source exceeds the gradient threshold, the propagation acceleration factor is determined by comparing with the historical parameters of the instability case library based on the nonlocal gradient time series, and the expansion speed is obtained based on the propagation acceleration factor.

[0146] Specifically, the nonlocal gradient changes in the candidate region of the instability source are monitored, and when the nonlocal gradient... Exceeding the gradient threshold At this time, an instability warning mechanism is triggered. It should be noted that the gradient threshold... The gradient threshold for soft soil layers is determined based on soil type and support stiffness; it is typically lower than that for hard soil layers, ranging from 0.002 to 0.008. .

[0147] Calculate the time rate of change of the nonlocal gradient in the candidate region of the instability source:

[0148] ;

[0149] in, For the rate of change over time, The monitoring time interval. The rate of change over time reflects the acceleration of instability evolution; the larger the rate of change, the faster the instability develops.

[0150] Cases with propagation times on the order of hours were retrieved from the instability case database. Search criteria included: propagation time between 0.5 and 8 hours, soil type matching the current project, and similar excavation depth. The propagation rate decay index was extracted from the retrieved cases. ,in The spatial decay index for historical cases. This is the time decay index for historical cases.

[0151] Nonlocal gradient time series of candidate regions of instability sources Perform exponential fitting:

[0152] ;

[0153] in, The initial nonlocal gradient at the moment of instability triggering. This is the exponent of the time evolution of the current case. Through logarithmic linearization:

[0154] ;

[0155] The least squares method is used for fitting to extract the time evolution index of the current case. .

[0156] Extract historical cases with the same soil type as the current instability case library and obtain their time decay index. It should be noted that the time decay index of historical cases... Propagation rate attenuation model established from S100 This index reflects the decay characteristics of propagation rate over time in historical instability cases. The time evolution index of the current case... This reflects the growth rate of the nonlocal gradient in the instability source region over time. Although the two have different physical meanings, they both reflect the time-scale characteristics of the instability process and are numerically comparable.

[0157] The propagation acceleration factor is obtained by calculating the ratio of the current case's time evolution index to the historical case's time decay index.

[0158] ;

[0159] This indicates that the current rate of instability evolution is faster than in typical historical cases, and the spread of instability is accelerating; This indicates that the instability evolution is relatively slow.

[0160] Determine if multiple candidate regions for instability sources exist. Calculate the spatial distance between each candidate region for instability sources. ,in and Number the different candidate regions. When the distance between regions... Less than the critical distance In this case, it is assumed that multiple instability sources may interact, requiring the calculation of the instability wave superposition coefficient for correction. It should be noted that the critical distance... The value is determined based on the excavation dimensions and support stiffness of the foundation pit, and is usually taken as 0.3 to 0.5 times the characteristic dimensions of the foundation pit.

[0161] Calculate the nonlocal gradient time series of candidate regions for instability sources, and perform a Fourier transform on the time series:

[0162] ;

[0163] in, For frequency domain representation, This refers to the angular frequency. The amplitude of the dominant frequency component is extracted from the frequency spectrum. and initial phase The dominant frequency component is the frequency component with the largest amplitude.

[0164] Calculate candidate regions for instability sources and Midpoint of the line connecting them :

[0165] ;

[0166] The superposition type is determined by the phase difference between the dominant frequency components of the two unstable sources at the midpoint. The phases of the two unstable sources at the midpoint are:

[0167] ;

[0168] in, and Let be the propagation speeds of the two unstable sources. Calculate the phase difference at the midpoint:

[0169] ;

[0170] When phase difference Less than a quarter of a cycle, that is When this occurs, it is determined to be a case of co-current superposition. In the case of co-current superposition, the two unstable waves are close in phase at their midpoints, and their peaks reinforce each other. The superposition amplification factor is calculated as follows:

[0171] ;

[0172] in, To add the magnification factor, The superposition amplification factor is positively correlated with the product of the amplitudes of the two instability sources and negatively correlated with the distance between regions.

[0173] When phase difference More than a quarter of a cycle, that is When this occurs, it is determined to be anisotropic superposition. In the case of anisotropic superposition, the two unstable waves are out of phase at the midpoint, and their peaks and troughs cancel each other out. The superposition suppression coefficient is calculated as follows:

[0174] ;

[0175] in, To superimpose the suppression coefficient, .

[0176] The propagation acceleration factor is obtained by correcting the superposition coefficient of the unstable wave. :

[0177] ;

[0178] Determine if underconsolidation correction is needed. (Based on excavation rate) The rate is greater than the threshold of 0.5 m / day and the soil compression modulus When the compressibility modulus is less than the threshold value, an underconsolidation correction is applied to the propagation acceleration factor. It should be noted that the compressibility modulus threshold is 5 MPa, a value determined based on the consolidation characteristics of saturated soft soil. Soil layers with a compressibility modulus less than this value are difficult to fully consolidate under rapid excavation conditions.

[0179] Based on excavation rate and soil consolidation coefficient Calculate the excess pore water pressure dissipation:

[0180] ;

[0181] in, For dissipation, This refers to the time elapsed since the excavation began. This represents the soil layer thickness. The smaller the dissipation rate, the lower the degree of dissipation of excess pore water pressure, indicating that the soil is in an underconsolidated state.

[0182] When dissipation When the value is less than the dissipation threshold, multiply the propagation acceleration factor by the underconsolidation amplification factor:

[0183] ;

[0184] in, As the final propagation accelerator, This is the underconsolidation amplification factor. It should be noted that the dissipation threshold is usually taken as 0.5 to 0.7, indicating that underconsolidation correction is required when the excess pore water pressure dissipates less than 50% to 70%.

[0185] underconsolidation amplification factor It is positively correlated with the amplitude of excess pore water pressure, and the calculation formula is:

[0186] ;

[0187] in, This is the proportionality coefficient. This represents the excess pore water pressure amplitude. The excess pore water pressure amplitude is obtained through calculations based on soil mechanics theory or through field measurements using pore pressure gauges, and the unit is kPa. (Proportionality coefficient) Units are In one embodiment, the value is between 0.05 and 0.15. It should be noted that the amplitude of excess pore water pressure... It can be estimated using empirical formulas:

[0188] ;

[0189] in, The pore pressure coefficient is taken as 0.3 to 0.5 for normally consolidated soft soil and 0.5 to 0.8 for underconsolidated soft soil. The unit is the weight of the soil. ; The depth is measured in meters (m).

[0190] Calculate expansion speed The expansion velocity is the propagation speed of the unstable wave in space:

[0191] ;

[0192] in, The initial propagation rate is retrieved from the instability case database, representing the historical cases. The spread velocity reflects the actual propagation speed of the unstable wave under the current operating conditions, taking into account the acceleration factor, wave superposition effect, and underconsolidation effect.

[0193] S500: Calculate the remaining time window based on the expansion speed, spatial distribution of measurement points, and propagation path. When the remaining time window is less than the warning threshold, compress the initial prediction curve according to the time difference to obtain the final prediction result.

[0194] Furthermore, the calculation steps for the remaining time window include:

[0195] Extract the propagation paths of historical cases similar to the current candidate instability source area from the instability case database, and map the historical propagation paths to the current project based on the current spatial distribution of the measurement points;

[0196] Calculate the propagation distance from the candidate region of the instability source to the boundary measurement point along the propagation path;

[0197] Divide the propagation distance by the propagation speed to obtain the instability arrival time of the boundary measurement point;

[0198] The shortest instability arrival time is selected as the remaining time window.

[0199] Specifically, propagation paths of historical cases with similar locations to the current candidate instability source are extracted from the instability case database. Location similarity is determined by comparing the relative positions of the instability sources within the foundation pit. The relative positions are represented using normalized coordinates, i.e., the coordinates of the instability source divided by the characteristic dimensions of the foundation pit. Historical cases with a relative position deviation of less than 0.2 are selected as reference cases.

[0200] Based on the current spatial distribution of measurement points, historical propagation paths are mapped to the current project. The mapping process employs coordinate transformation, scaling and rotating the coordinates of measurement points from historical cases to align them with the current project's measurement point layout. Specifically, a coordinate system for historical cases is established. To the current engineering coordinate system Transformation relationship:

[0201] ;

[0202] in, This is the scaling factor. Let be a rotation matrix. For rotation angle, This is the translation vector. The transformation parameters are determined by minimizing the positional error between historical case measurement points and current engineering measurement points.

[0203] Calculate the propagation distance from the candidate instability source region to the boundary monitoring point along the mapped propagation path. The boundary monitoring point refers to the monitoring point located near the boundary of the foundation pit support, typically the monitoring point closest to the edge of the foundation pit. The propagation path is the shortest path from the instability source to the boundary monitoring point or the propagation path along the support structure. Propagation distance Calculated by accumulating the distances between adjacent nodes on the path:

[0204] ;

[0205] in, The number of nodes along the propagation path. For the first The coordinates of each node.

[0206] Divide the propagation distance by the expansion speed The instability arrival time of the boundary measurement points is obtained:

[0207] ;

[0208] in, This is the estimated time for the unstable wave to propagate from the current candidate unstable source region to the boundary measurement point.

[0209] When multiple boundary measurement points exist, calculate the instability arrival time for each boundary measurement point separately. Select the shortest instability arrival time as the remaining time window.

[0210] ;

[0211] in, For the remaining time window, Number the boundary measurement points. The remaining time window represents the shortest time from the current moment to the arrival of the instability wave at the foundation pit boundary, and is a key time parameter for early warning decision-making.

[0212] Determine the remaining time window Is it less than the warning threshold? It should be noted that the warning threshold is determined based on the project's emergency response capabilities, including personnel evacuation time and the implementation time of reinforcement measures. The warning threshold is typically set between 2 and 4 hours. When an emergency warning is triggered, the time axis of the initial prediction curve needs to be compressed.

[0213] Furthermore, the timeline compression step includes:

[0214] Calculate the displacement value corresponding to the warning trigger time based on the warning threshold and the expansion speed;

[0215] Extract the predicted time for the initial prediction curve to reach the displacement value;

[0216] Calculate the time difference between the remaining time window and the predicted time;

[0217] The time axis of the initial prediction curve is compressed based on the time difference;

[0218] Calculate the deformation rate of the predicted curve after compression, and calculate the theoretical maximum deformation rate based on the soil compression modulus and excavation depth.

[0219] When the deformation rate after compression exceeds the theoretical maximum deformation rate, the compression coefficient is adjusted so that the deformation rate does not exceed the theoretical maximum value.

[0220] Specifically, the displacement value corresponding to the warning trigger time is calculated based on the warning threshold and the expansion rate. The warning trigger time is the current time plus the remaining time window, i.e. Based on the expansion velocity and deformation mechanism calculated by S400, the displacement value at the time of warning triggering is estimated:

[0221] ;

[0222] in, The displacement value at the time the warning is triggered. This is the current measured displacement value. This represents the deformation rate. The deformation rate is calculated based on the relationship between the expansion rate and the soil deformation modulus.

[0223] Extract the initial predicted curve to reach the displacement value The prediction time. The initial prediction curve is the prediction curve reconstructed from historical similar cases in S200. By solving the equation Get the predicted time .

[0224] Calculate the time difference between the remaining time window and the predicted time:

[0225] ;

[0226] Time difference This reflects the time scale deviation between the actual instability evolution rate and the initial prediction curve. A positive time difference indicates that the actual instability rate is faster than predicted, requiring time axis compression of the prediction curve; a negative time difference indicates that the actual instability rate is slower than predicted.

[0227] The time axis of the initial prediction curve is compressed based on the time difference. The time axis compression uses a compression factor. accomplish:

[0228] ;

[0229] in, The compressed prediction curve has a compression coefficient. for:

[0230] ;

[0231] A compression factor greater than 1 indicates that the time axis is compressed, and the predicted curve reaches the same displacement value in a shorter time.

[0232] Calculate the deformation rate of the predicted curve after compression:

[0233] ;

[0234] Based on soil compression modulus and excavation depth Calculate the theoretical maximum deformation rate. The theoretical maximum deformation rate is determined based on the ultimate strain rate of the soil. The maximum strain of the soil under excavation and unloading conditions is:

[0235] ;

[0236] in, The maximum stress release caused by excavation can be approximated by the effective vertical stress before excavation. , The effective unit weight of soil is given in units of 1000 kJ / m³. ; This is the compressive modulus, expressed in kPa. The maximum deformation is... .

[0237] The theoretical maximum deformation rate is the maximum deformation amount divided by the minimum response time:

[0238] ;

[0239] In one embodiment, the minimum response time is taken as the time required for the soil shear wave to propagate through the excavation depth, i.e. ,in Let be the shear wave velocity, in m / s. Substituting this into the above equation, we get:

[0240] ;

[0241] For soft soil layers, effective density Take 8 to 10 Excavation depth Take 10 to 20 m, compression modulus Take 3 to 5 MPa, shear wave velocity Using a range of 100 to 150 m / s, the theoretical maximum deformation rate was calculated. It is approximately 0.2 to 0.5 m / h.

[0242] When the deformation rate after compression Exceeding the theoretical maximum deformation rate At this time, the compression coefficient is adjusted so that the deformation rate does not exceed the theoretical maximum value. The adjusted compression coefficient... satisfy:

[0243] ;

[0244] Recalculate the compressed prediction curve based on the adjusted compression factor:

[0245] ;

[0246] This is the final prediction result. The final prediction result comprehensively considers the deformation patterns of similar historical cases, the evolution rate of the current instability source, the propagation characteristics of the instability wave, and the physical constraints of soil deformation. It can accurately predict the rapid development trend of foundation pit deformation in short-term and urgent projects, and provide a reliable basis for emergency decision-making in engineering.

[0247] Through the five steps S100 to S500 described above, a complete method for predicting foundation pit deformation based on time-series analysis has been implemented. This method dynamically matches historical statistical patterns with current actual working conditions by establishing an instability case library, identifying instability sources, quantifying propagation acceleration, and calculating the remaining time window. This method is particularly suitable for short-term, urgent projects with high excavation rates and instability propagation times on the order of hours. It can accurately predict the remaining time window in the early stages of instability evolution, providing technical support for emergency decision-making.

[0248] Example 2:

[0249] The foundation pit for a subway station has an excavation depth of 18.5m and employs a support system consisting of a diaphragm wall and three layers of concrete supports. Due to the tight schedule, the construction unit adopted a phased rapid excavation scheme, achieving an average excavation rate of 0.65m / day, typical of a short-term, urgent project. The site contains an approximately 8m thick layer of silty clay with a compression modulus of only 3.2MPa. The rapid excavation resulted in excess pore water pressure that could not dissipate in time, posing a risk of instability. Therefore, the following measures were taken... Figure 2 The system shown is a foundation pit deformation prediction system based on time series analysis for dynamic monitoring and early warning.

[0250] The system's case library module pre-collected monitoring data from 328 historical foundation pit projects, formed 7 deformation pattern families through normalization and feature extraction, and selected 62 short-term and rapid project instability cases to establish an instability case library, extracting the propagation rate attenuation index of each case.

[0251] Thirty-two horizontal displacement monitoring points were set up around the foundation pit, with a monitoring frequency of once every four hours. The system's initial curve reconstruction module retrieved similar exponentially growing deformation patterns from the deformation pattern family based on engineering parameters such as the excavation depth and soil parameters, and reconstructed the initial prediction curve.

[0252] On the 12th day of excavation, the system's instability source identification module acquired real-time monitoring data, established a multi-point displacement difference field, and calculated the nonlocal gradient at each point. The nonlocal gradient at the southeast corner measuring point reached 0.0067. It exceeds the gradient threshold of 0.005. After screening by autocorrelation coefficient and phase difference, the region was identified as a candidate region for instability source.

[0253] The system's acceleration factor calculation module then started, calculating the time change rate of the nonlocal gradient in the candidate region of the instability source to be 0.0018. Five similar soft soil cases with propagation times in the hourly range were retrieved from the instability case database. By comparing the time decay index of the current case with that of historical cases, the propagation acceleration factor was determined to be 1.81. The module further determined that the excavation rate of 0.65 m / day exceeded the rate threshold and the soil compression modulus of 3.2 MPa was less than the compression modulus threshold. It automatically performed underconsolidation correction, calculated the dissipation degree of excess pore water pressure, and corrected the propagation acceleration factor from 1.81 to 2.15, resulting in an expansion rate of 12.5 m / h.

[0254] The system's time window prediction module, based on the propagation velocity and spatial distribution of measuring points, calculated the propagation distance of the unstable wave to the measuring point on the northern boundary as 52m, resulting in a remaining time window of 4.2 hours. Since the remaining time window is close to the warning threshold of 4 hours, the module compresses the time axis of the initial prediction curve to generate the final prediction result, predicting that the displacement in this area will reach the critical value within 4 to 5 hours. The system immediately triggers an emergency warning, pushing the warning information to the construction management platform.

[0255] Upon receiving the early warning, the construction team immediately implemented emergency measures, including reducing the excavation rate and adding temporary supports. Actual monitoring showed that the area reached the critical deformation value approximately four hours after the warning, which highly matched the system's prediction.

[0256] To verify the prediction performance of the system of the present invention, the system was compared with traditional time series prediction methods under the same monitoring data. The results are shown in Table 1 below:

[0257] Table 1 Prediction Comparison Table

[0258]

[0259] The comparison results show that traditional ARIMA and LSTM models require a long training period with historical data, with prediction cycles of 16.5 hours and 11.2 hours respectively. However, the instability evolution cycle of short-term, urgent projects is only a few hours, leading to prediction lag and an inability to capture rapid instability characteristics in a timely manner, rendering early warnings meaningless. The displacement prediction errors of traditional methods reach 22.3% and 15.7% respectively, with false negative rates as high as 35% and 28%, failing to meet the real-time early warning requirements of short-term, urgent projects.

[0260] The system of this invention constructs a case library of short-term and rapid engineering instability cases through a case library building module, introduces nonlocal gradient calculation to capture spatial deformation non-uniformity through an instability source identification module, combines propagation rate attenuation index and underconsolidation correction to quantify the instability evolution speed through an acceleration factor calculation module, and dynamically matches historical statistical patterns with current actual working conditions through time axis compression through a time window prediction module, thus forming a complete technical system for predicting short-term and rapid engineering deformation.

[0261] The system reduces the early warning time to 4.1 hours, a time window that matches the instability evolution cycle of urgent projects, providing a reasonable response time for emergency decision-making. Displacement prediction error is reduced to 6.8%, and the false alarm rate is reduced to 5.0%, significantly improving the accuracy and reliability of foundation pit deformation prediction for urgent projects. Although the false alarm rate of this invention's system is 12.0%, slightly higher than the ARIMA model, considering that the consequences of false alarms are far more severe than false alarms in urgent projects, the false alarm rate of this invention remains within an acceptable range while maintaining a low false alarm rate.

[0262] The successful early warning of this project verifies the practical value of the system of this invention in the case of rapid excavation in soft soil strata. In particular, for the hourly instability propagation process that is difficult to deal with by traditional methods, this system can accurately capture the instability evolution characteristics and provide timely early warning through the collaborative work of multiple modules, providing an effective technical means for risk management of similar short and urgent projects.

[0263] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting foundation pit deformation based on time-series analysis, characterized in that, include: S100: Collect historical foundation pit monitoring time series data, normalize it, extract feature vectors, and cluster them to form multiple deformation pattern families; Establish an instability case library, collect short-term and urgent engineering cases where the excavation rate exceeds the rate threshold, and extract the propagation time, propagation path, and propagation rate attenuation index of instability from the source point to the boundary measuring point; S200: Based on the engineering parameters of the foundation pit to be predicted, retrieve similar deformation pattern families, extract feature vectors, and reconstruct the initial prediction curve; S300: Obtain the measured displacement data of the foundation pit to be predicted, establish a multi-point displacement difference field, calculate the nonlocal gradient and identify candidate regions of instability source; The steps for calculating the nonlocal gradient include: A preset radius is set for each measuring point, and the preset radius is determined based on the stiffness of the support structure and the size of the excavation zone; Calculate the ratio of the displacement difference to the distance between the measured point and all measured points within the preset radius, and use the Gaussian kernel function as the weight to perform a weighted summation to obtain the nonlocal gradient; The standard deviation of the Gaussian kernel function is determined based on the excavation partition characteristic dimensions and support stiffness; The step of identifying candidate regions for instability sources includes: Establish the nonlocal gradient spatial distribution of all measurement points, and identify the local maxima regions of the nonlocal gradient as initial candidate regions; Calculate the autocorrelation coefficient of the nonlocal gradient time series of the initial candidate region. If the autocorrelation coefficient is less than the correlation threshold, it is determined to be a construction disturbance and is excluded. Calculate the displacement phase difference between the measuring point in the initial candidate region and the neighboring measuring points. The neighboring measuring points refer to the several measuring points that are spatially closest to the measuring points in the initial candidate region. When the phase difference is greater than the phase threshold, it is determined to be a measuring point fault and eliminated. The reserved region is designated as the candidate region for the instability source. S400: When the nonlocal gradient of the candidate region of the instability source exceeds the gradient threshold, the propagation acceleration factor is determined by comparing with the historical parameters of the instability case library based on the nonlocal gradient time series, and the expansion speed is obtained based on the propagation acceleration factor. S500: Calculate the remaining time window based on the expansion speed, spatial distribution of measurement points, and propagation path. When the remaining time window is less than the warning threshold, compress the initial prediction curve according to the time difference to obtain the final prediction result.

2. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, The steps for extracting the propagation rate attenuation index include: Extract the propagation time of instability from the source point to measurement points at different distances from the instability case, and calculate the propagation rate at the measurement points at different distances; Establish the relationship between propagation rate and distance from the source point, and extract the spatial decay exponent by fitting a power function. The relationship between propagation rate and propagation time of unstable wave was established, and the time decay exponent was extracted by fitting an exponential function. A two-dimensional decay model is constructed by combining the spatial decay index and the temporal decay index, and the characteristic parameters of the two-dimensional model are used as the propagation rate decay index.

3. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, When multiple candidate regions for instability sources exist and the distance between regions is less than the critical distance, the propagation acceleration factor is corrected by instability wave superposition: The amplitude and initial phase of the dominant frequency component are extracted by performing a Fourier transform on the nonlocal gradient time series of the candidate region of the instability source. Calculate the midpoint position of the line connecting the candidate regions of the unstable source, and determine the superposition type based on the phase difference of the main frequency component of the unstable source at the midpoint position; When the phase difference is less than a quarter of a period, it is superimposed in the same direction. A superposition amplification factor greater than 1 is calculated based on the amplitude of the instability source and the distance between regions. When the phase difference is greater than a quarter of a period, it is considered anisotropic superposition, and a superposition suppression coefficient less than 1 is calculated based on the phase difference. The propagation acceleration factor is corrected by using the superposition coefficient of unstable waves.

4. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, When the excavation rate is greater than the rate threshold and the soil compression modulus is less than the compression modulus threshold, the propagation acceleration factor is underconsolidated: Calculate the excess pore water pressure dissipation based on the excavation rate and soil consolidation coefficient; When the dissipation is less than the dissipation threshold, the propagation acceleration factor is multiplied by the underconsolidation amplification factor. The underconsolidation amplification factor is positively correlated with the amplitude of excess pore water pressure.

5. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, The steps for determining the propagation acceleration factor include: The nonlocal gradient time series of the candidate region of the instability source is subjected to exponential fitting to extract the time evolution index of the current case; Extract evolution rate parameters from the instability case library for historical cases with the same soil type as the current soil layer; The propagation acceleration factor is obtained by calculating the ratio of the current case evolution rate parameter to the historical case evolution rate parameter.

6. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, The calculation steps for the remaining time window include: Extract the propagation paths of historical cases similar to the current candidate instability source area from the instability case database, and map the historical propagation paths to the current project based on the current spatial distribution of the measurement points; Calculate the propagation distance from the candidate region of the instability source to the boundary measurement point along the propagation path; Divide the propagation distance by the propagation speed to obtain the instability arrival time of the boundary measurement point; The shortest instability arrival time is selected as the remaining time window.

7. The method for predicting foundation pit deformation based on time-series analysis according to claim 1, characterized in that, The time axis compression steps include: Calculate the displacement value corresponding to the warning trigger time based on the warning threshold and the expansion speed; Extract the predicted time for the initial prediction curve to reach the displacement value; Calculate the time difference between the remaining time window and the predicted time; The time axis of the initial prediction curve is compressed based on the time difference; Calculate the deformation rate of the predicted curve after compression, and calculate the theoretical maximum deformation rate based on the soil compression modulus and excavation depth. When the deformation rate after compression exceeds the theoretical maximum deformation rate, the compression coefficient is adjusted so that the deformation rate does not exceed the theoretical maximum value.

8. A foundation pit deformation prediction system based on time-series analysis, characterized in that, The system is used to execute the foundation pit deformation prediction method based on time-series analysis as described in any one of claims 1-7, wherein the method includes: The case library module is used to collect historical foundation pit monitoring time series data, extract feature vectors after normalization, and cluster them to form multiple deformation pattern families; and to establish an instability case library, collect short and urgent engineering cases with excavation rates greater than the rate threshold, and extract the propagation time, propagation path, and propagation rate attenuation index of instability from the source point to the boundary measuring point. The initial curve reconstruction module is used to retrieve similar deformation mode families based on the engineering parameters of the foundation pit to be predicted, extract feature vectors, and reconstruct the initial prediction curve. The instability source identification module is used to acquire the measured displacement data of the foundation pit to be predicted, establish a multi-measurement point displacement difference field, calculate the nonlocal gradient, and identify candidate regions of instability sources. The acceleration factor calculation module is used to determine the propagation acceleration factor based on the nonlocal gradient time series by comparing it with historical parameters in the instability case library when the nonlocal gradient of the candidate region of the instability source exceeds the gradient threshold, and to obtain the expansion speed based on the propagation acceleration factor. The time window prediction module is used to calculate the remaining time window based on the expansion speed, spatial distribution of measurement points, and propagation path. When the remaining time window is less than the warning threshold, the initial prediction curve is compressed along the time axis according to the time difference to obtain the final prediction result.

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