Method for detecting leakage of underground continuous wall based on hydraulic chromatography

Abstract

The application discloses a diaphragm wall leakage detection method based on a hydraulic chromatography method, and belongs to the field of geotechnical seepage monitoring and hydraulic inversion; an excitation point and an observation point are arranged on the accessible side of the diaphragm wall, at least two rounds of controlled water injection or water pumping are implemented, and multi-point water head data are synchronously collected. The water head during a non-excitation period is extracted as a background observation sequence, a background water head and an uncertainty thereof are recursively estimated by using an unscented Kalman filter or a particle filter, the original water head is background-subtracted, and an observation error covariance matrix is constructed. A three-dimensional transient seepage forward model is established, low-dimensional parameters of external boundary conditions are parameterized, and joint inversion is performed on equivalent permeation parameters or equivalent source terms of leakage, set Kalman inversion is iteratively updated, covariance localization processing is performed, and three-dimensional distribution and leakage intensity parameters of the leakage channel are output.

Description

Technical Field

[0001] This invention relates to the field of seepage monitoring in geotechnical engineering, and in particular to a method for detecting leakage in diaphragm walls based on hydraulic tomography. Background Technology

[0002] Diaphragm walls, used as retaining and waterproofing structures for deep foundation pits, are widely applied in urban rail transit, underground complexes, and municipal engineering projects. With increasing project scale and sensitivity to surrounding environments, the leakage risks caused by defects in diaphragm walls, such as joints, mud inclusions, and honeycomb-like voids, are receiving growing attention. Existing leakage detection technologies mainly include empirical judgment methods based on on-site inspections and leakage point observations, hydraulic response analysis methods based on pore pressure or water level monitoring, and quantitative assessment methods that obtain water head changes through water injection or pumping tests and combine them with numerical simulations or inversion calculations. In recent years, hydraulic tomography has been introduced into the identification of underground seepage parameters. Through multiple rounds of controlled hydraulic excitation and multi-point response joint inversion, the ability to identify the spatial distribution of seepage parameters has been improved, providing a new technical approach for the location and quantitative characterization of leakage channels.

[0003] However, existing technologies for detecting leakage in diaphragm walls still have the following shortcomings in engineering sites: First, the outer side of the wall is often inaccessible due to roads, buildings, or backfill, resulting in a limited number of excitation and observation points with restricted spatial distribution. Traditional methods struggle to achieve three-dimensional localization of leakage channels under conditions of few measurement points. Second, factors such as pit dewatering and groundwater level fluctuations cause continuous changes in the background hydraulic field, making the test response signal easily submerged or aliased by background disturbances. Existing analysis methods lack effective background correction and uncertainty quantification mechanisms. Third, the retaining system and adjacent structures have significant influences, and the strata are heterogeneous, making it difficult to accurately obtain boundary conditions such as outer boundary head or flux. Conventional inversion methods are prone to misjudgment or quantitative bias under uncertain boundary conditions, making it difficult to reliably assess leakage intensity and equivalent permeability parameters.

[0004] Therefore, there is a need for a method to detect leakage in diaphragm walls that can overcome the shortcomings of the existing technologies. Summary of the Invention

[0005] One objective of this invention is to propose a method for detecting leakage in diaphragm walls based on hydraulic tomography. Addressing the problems in existing technologies, such as the inaccessibility of the outer side of the diaphragm wall leading to limited test point placement, continuous changes in the background hydraulic field caused by foundation pit dewatering and groundwater level fluctuations resulting in susceptibility to interference with the test response, and the difficulty in accurately obtaining external boundary conditions due to the heterogeneity of the retaining system and strata, thus affecting the accuracy of leakage channel location and quantitative assessment, the following technical solution is proposed: At least one hydraulic excitation point and multiple observation points are set up on the accessible side of the diaphragm wall; at least two rounds of controlled water injection or dewatering excitation are implemented, and water head data are collected simultaneously; extracting… A state-space model is established using data from non-excitation periods. The background head and its uncertainty are recursively estimated using an unscented Kalman filter or particle filter algorithm, and background subtraction is performed on the original head data. An observation error covariance matrix is ​​constructed based on the background uncertainty and measurement noise. A three-dimensional transient seepage forward model is established, representing the outer boundary conditions of the detection area in a low-dimensional parameterized form and concatenating them with equivalent seepage parameters or equivalent source term parameters to construct the parameter vector to be inverted. An ensemble Kalman inversion iterative joint update is used, and covariance localization is performed to output the three-dimensional distribution of the seepage channel, the seepage intensity, and the equivalent seepage parameters. Compared to existing technologies, this invention has the technical advantages of suppressing the influence of background disturbances, handling boundary uncertainties, and achieving three-dimensional localization and quantitative characterization of seepage channels under conditions with fewer measurement points.

[0006] This invention provides a method for detecting leakage in diaphragm walls based on hydraulic tomography, comprising:

[0007] S1. Deploy at least one hydraulic excitation point and multiple observation points on the accessible side of the diaphragm wall, implement at least two rounds of controlled hydraulic excitation, record the hydraulic excitation data, and collect raw head observation data to obtain the raw dataset; S2. Extract the raw head observation data during the non-excitation period from the raw dataset as the background observation sequence, and use the hydraulic excitation data as known input to obtain the background head estimation data and its background uncertainty data through recursive estimation; S3. Based on the background head estimation data, perform background subtraction on the raw head observation data to obtain the background-corrected head response data, and then compare the background uncertainty data with the measured head response data. S4. Construct the observation error covariance matrix using noise statistical parameters; S5. Establish a three-dimensional transient seepage forward model of the detection area based on hydraulic excitation data, represent the outer boundary conditions of the detection area as boundary parameter vectors in a low-dimensional parameterized manner, represent the seepage channels as seepage parameter vectors, and concatenate the two to construct the parameter vector to be inverted; S6. Based on the background-corrected head response data, the observation error covariance matrix, and the three-dimensional transient seepage forward model, use iterative inversion based on ensemble statistics to jointly update the parameter vector to be inverted, and obtain the three-dimensional spatial distribution of the seepage channels and the seepage intensity and / or equivalent permeability parameters.

[0008] Optionally, S1 includes:

[0009] The detection area is a three-dimensional area consisting of the underground continuous wall and the strata on both sides of the wall within a preset horizontal influence range and a preset depth range.

[0010] Within the detection area, determine the location of the accessible side of the underground continuous wall, wherein the accessible side is the inside of the foundation pit, or the side that meets the construction conditions for setting up the hydraulic excitation point and the observation point;

[0011] At least one hydraulic excitation point and multiple observation points are set at the location of the observation points, and the multiple observation points are distributed along the depth direction of the underground continuous wall to cover at least two different depth intervals.

[0012] For each round of controlled hydraulic excitation, the excitation control parameters for that round of controlled hydraulic excitation are determined. The excitation control parameters include the excitation method, the excitation duration, and the target flow rate or target pressure.

[0013] Based on the excitation control parameters, water injection or pumping is performed at the hydraulic excitation point to form controlled hydraulic excitation for the vessel, and the actual execution value of the excitation control parameters is recorded during the execution process to obtain hydraulic excitation data;

[0014] While performing the controlled hydraulic excitation, the multiple observation points are simultaneously collected using a unified time reference to obtain raw head observation data;

[0015] The original dataset is obtained by collecting hydraulic excitation data corresponding to at least two rounds of controlled hydraulic excitation and raw head observation data.

[0016] In the at least two rounds of controlled hydraulic excitation, the two adjacent rounds of controlled hydraulic excitation differ in at least one of the following: the location of the hydraulic excitation point, the excitation method, the target flow rate, the target pressure, the excitation duration, and the excitation sequence.

[0017] Furthermore, the process for determining that at least one of the excitation control parameters differs between two adjacent rounds of controlled hydraulic excitation includes adaptive excitation design: after completing the data acquisition for the previous round of controlled hydraulic excitation, the sensitivity index corresponding to the candidate excitation scheme is calculated based on the three-dimensional transient seepage forward model and the current parameter set, and the candidate excitation scheme that makes the sensitivity index satisfy the preset optimal criterion is selected as the excitation control parameter for the next round of controlled hydraulic excitation; the sensitivity index includes at least one of the determinant of the Fisher information matrix, the trace of the Fisher information matrix, or the gradient norm of the observation residual with respect to the leakage parameter vector.

[0018] Optionally, S2 includes:

[0019] The original head observation data and their corresponding sampling time sequences of the multiple observation points are extracted from the original dataset, and the original head observation data of the non-excitation period before and after the start of each round of controlled hydraulic excitation are extracted as background observation sequences.

[0020] A state-space model is established to characterize the changes in the background hydraulic field. The state-space model includes a state equation for describing the evolution of the background hydraulic field over time and an observation equation for mapping the state variables to the background observation sequence. At least one of the state equation and the observation equation contains an input term with the hydraulic excitation data as a known input term, which is used to estimate the background head component that is not affected by the controlled hydraulic excitation.

[0021] The initial state and noise statistics parameters are set for the state-space model;

[0022] The state-space model is recursively estimated using an unscented Kalman filter or a particle filter algorithm according to the sampling time sequence to obtain background head estimation data corresponding to the multiple observation points. The state estimation uncertainty obtained during the recursive estimation process is output as background uncertainty data corresponding to the background head estimation data.

[0023] Optionally, S3 includes:

[0024] Based on the sampling time sequence of the original head observation data, the background head estimation data is time-aligned to obtain the background head estimation value corresponding to each sampling time.

[0025] For each observation point, at each sampling time, the estimated background head value is subtracted from the original head observation data to obtain the background-corrected head response data;

[0026] The background uncertainty variance of each observation point at each sampling time is determined based on the background uncertainty data, and the background uncertainty variance is superimposed with the preset or calibrated sensor measurement noise variance, or weighted superimposed according to the preset weight, to obtain the observation error variance of each observation point at each sampling time.

[0027] An observation error covariance matrix is ​​constructed based on the observation error variance, such that the diagonal elements of the observation error covariance matrix correspond to the observation error variance of each observation point at each sampling time in the background-corrected head response data.

[0028] Optionally, S4 includes:

[0029] The excitation boundary terms of the three-dimensional transient seepage forward model are determined based on hydraulic excitation data;

[0030] In the three-dimensional transient seepage forward model, the outer boundary of the detection area is divided into a preset number of boundary segments, and the boundary conditions of each boundary segment are represented by piecewise constants, piecewise linear representations, or expansions of preset basis functions. The boundary head or boundary flux of each boundary segment is used as the boundary parameters to form a boundary parameter vector.

[0031] The preset basis functions include at least one of Fourier basis functions, polynomial basis functions, spline basis functions, and radial basis functions; in the three-dimensional transient seepage forward model, the seepage channel is represented as an equivalent permeability parameter distribution or an equivalent seepage source term distribution located within the underground continuous wall, and the parameters of the equivalent permeability parameter distribution or the equivalent seepage source term distribution are used as the seepage parameter vector;

[0032] The leakage channel is divided into multiple units according to the diaphragm wall section and depth layer. The leakage parameter vector includes the equivalent permeability parameter or equivalent leakage source term intensity of each unit. The boundary parameter vector and the leakage parameter vector are concatenated to construct the parameter vector to be inverted.

[0033] The detection area is divided into planar partitions based on the diaphragm wall sectional information, and into vertical partitions based on the depth stratification information. The relevant cutoff range between different partitions is determined based on the hydraulic influence radius, thereby generating a localization matrix for set covariance localization.

[0034] The hydraulic influence radius is determined by empirical parameters, or by field tests, or by calculation using the three-dimensional transient seepage forward model combined with formation parameters.

[0035] Furthermore, the boundary parameter vector represented in a low-dimensional parameterized manner satisfies continuity constraints or smoothness constraints. The continuity constraints include the boundary head or boundary flux of adjacent boundary segments being equal at the segment boundaries. The smoothness constraints include the second-order difference of the boundary head or boundary flux of adjacent boundary segments being less than a preset threshold. Moreover, the continuity constraints or smoothness constraints are achieved by introducing virtual observation terms or penalty terms in the ensemble Kalman inversion iterative update.

[0036] Optionally, S5 includes:

[0037] A parameter set is generated based on the parameter vector to be inverted, and each set of parameters in the parameter set is substituted into the three-dimensional transient seepage forward model to obtain the simulated head response corresponding to each set of parameters.

[0038] The observation residuals are constructed using the deviation between the background-corrected head response data and the simulated head response, and the observation error covariance matrix is ​​used to weight the observation residuals.

[0039] The parameter set is iteratively updated by ensemble Kalman inversion based on the observed residuals. In each iteration, the ensemble covariance used for updating is localized using a localization matrix.

[0040] The localization process includes performing Schur element-wise product of the localization matrix and the set covariance; terminating the iterative update when a preset convergence condition is met, the preset convergence condition includes one or a combination of the following: the norm of the observation residual is less than a first threshold, the norm of the change in the parameter vector to be inverted in two adjacent iterations is less than a second threshold, and the number of iterations reaches the upper limit.

[0041] Output the three-dimensional spatial distribution of the leakage channels determined by the parameter set, and at least one of the leakage intensity and equivalent permeability parameters corresponding to the leakage channels;

[0042] Furthermore, after each iteration update, a sparsification projection process is performed on the leakage parameter vector. The sparsification projection process includes at least one of the following: setting the update amount of the equivalent permeation parameter less than the leakage threshold to zero, setting the intensity of the equivalent leakage source term less than the leakage threshold to zero, retaining only a preset number of leakage units as non-zero and setting the remaining leakage units as background values; the leakage threshold is determined by the set variance, set mean, or preset empirical threshold of the parameter set.

[0043] On the other hand, the present invention also provides a system for detecting leakage in underground diaphragm walls based on hydraulic tomography, comprising:

[0044] The data acquisition module is used to set up hydraulic excitation points and observation points, implement at least two rounds of controlled hydraulic excitation and collect head data to obtain the raw dataset.

[0045] The background estimation module is used to extract the background observation sequence and perform recursive estimation to obtain background head estimation data and its background uncertainty data.

[0046] The background correction and error matrix module is used to perform background subtraction and construct the observation error covariance matrix.

[0047] The forward modeling and parameter construction module is used to establish a three-dimensional transient seepage forward model and construct boundary parameter vectors, leakage parameter vectors, and parameter vectors to be inverted.

[0048] The joint inversion module is used to iteratively invert and update the parameter vector to be inverted based on set statistics, and outputs at least one of the three-dimensional distribution of leakage channels, leakage intensity, and equivalent permeability parameters.

[0049] The beneficial effects of this invention are:

[0050] 1. Under engineering conditions where the outside of the wall is inaccessible, the number of sampling points is small, and the spatial distribution is limited, at least two rounds of controlled hydraulic excitation and multi-point synchronous response acquisition are used. Combined with a three-dimensional transient seepage forward model and ensemble Kalman inversion, the three-dimensional positioning of the leakage channel in the plane and depth directions is realized, thereby improving the spatial resolution and positioning reliability of leakage identification.

[0051] 2. By recursively estimating the background observation sequence during non-excitation periods, the background head and its uncertainty are obtained, and the original head data are subjected to background subtraction. At the same time, the observation error covariance matrix is ​​constructed based on the background uncertainty and measurement noise, thereby effectively suppressing background disturbances caused by foundation pit drainage and groundwater level fluctuations, and improving the robustness of excitation response extraction and the noise resistance of the inversion results.

[0052] 3. By parameterizing the boundary conditions outside the detection area in a low dimension and updating them together with the equivalent permeability parameters or equivalent source term parameters during the inversion process, and by reducing the influence of spurious correlations through covariance localization, it is possible to quantitatively characterize the leakage intensity and equivalent permeability parameters even under conditions of uncertain boundary conditions, heterogeneous formations, and significant influence from adjacent structures, thereby reducing misjudgments and quantitative biases caused by boundary errors. Attached Figure Description

[0053] 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:

[0054] Figure 1 This is a flowchart of a method for detecting leakage in diaphragm walls based on hydraulic tomography.

[0055] Figure 2 This is a flowchart of step S4, 3D forward modeling and parameter construction, of the present invention. Detailed Implementation

[0056] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0057] refer to Figures 1-2 A method for detecting leakage in diaphragm walls based on hydraulic chromatography, including:

[0058] S1. Deploy at least one hydraulic excitation point and multiple observation points on the accessible side of the diaphragm wall, implement at least two rounds of controlled hydraulic excitation, record the hydraulic excitation data, and collect raw head observation data to obtain the raw dataset; S2. Extract the raw head observation data during the non-excitation period from the raw dataset as the background observation sequence, and use the hydraulic excitation data as known input to obtain the background head estimation data and its background uncertainty data through recursive estimation; S3. Based on the background head estimation data, perform background subtraction on the raw head observation data to obtain the background-corrected head response data, and then compare the background uncertainty data with the measured head response data. S4. Construct the observation error covariance matrix using noise statistical parameters; S5. Establish a three-dimensional transient seepage forward model of the detection area based on hydraulic excitation data, represent the outer boundary conditions of the detection area as boundary parameter vectors in a low-dimensional parameterized manner, represent the seepage channels as seepage parameter vectors, and concatenate the two to construct the parameter vector to be inverted; S6. Based on the background-corrected head response data, the observation error covariance matrix, and the three-dimensional transient seepage forward model, use iterative inversion based on ensemble statistics to jointly update the parameter vector to be inverted, and obtain the three-dimensional spatial distribution of the seepage channels and the seepage intensity and / or equivalent permeability parameters.

[0059] In this specific embodiment, S1 includes:

[0060] The detection area is defined as a three-dimensional area including the underground continuous wall and the horizontal influence range of 15m on both sides of the wall, and the strata within a depth of 5m below the bottom of the wall from the ground surface. The accessible side of the underground continuous wall is defined as the inside of the foundation pit.

[0061] A hydraulic excitation point is set at a distance of 1.0m from the inner side of the wall along the length of the wall on the accessible side. The hydraulic excitation point is formed by an excitation well with a diameter of 100mm. The well pipe is made of PVC pipe, and a screen pipe is installed in the target aquifer section. The screen pipe is backfilled with graded gravel to form a filter layer, and bentonite-cement grout is used to seal the upper and lower ends of the screen pipe to limit the hydraulic excitation effect in the well on the target aquifer section. At the same time, six observation points are set on the same side. The six observation points are arranged along the depth direction of the underground continuous wall and are located at a distance from the ground surface. At the depth location, after each observation point is drilled through an independent observation hole, a pressure measuring pipe with a filter head is lowered in, and filter material is backfilled on the outside of the pressure measuring pipe. Separation sections are set at the upper and lower ends of the filter material to achieve layered pressure measurement. Each observation point is equipped with a pressure-type water level gauge to output the water head observation value. The water level gauge range covers the static water level to the maximum excitation disturbance water head range, and the water head resolution is 1mm. All water level gauges, excitation wellhead flow meters, and wellhead pressure sensors use a unified time reference and record synchronously with a 1s sampling interval.

[0062] Two rounds of controlled hydraulic excitation were implemented, with each round of excitation executed in the sequence of "static background section - excitation section - recovery section". The static background section lasted for 1800s and was used to record the original head observation data when no excitation was applied. The excitation section achieved constant target flow control through a variable frequency pump and a PID closed-loop controller and simultaneously recorded the actual flow time series and wellhead pressure time series as hydraulic excitation data. The recovery section lasted for 3600s and was used to record the fallback process after the excitation stopped to enhance the tomographic identification information.

[0063] The first round of controlled hydraulic excitation used water injection and lasted for 1800 seconds, with a target flow rate of [missing information]. The second round of controlled hydraulic excitation was determined by adaptive excitation design and adopted a pumping method with an excitation duration of 2400s and a target flow rate of [missing information]. This ensures that at least one of the requirements for different controlled hydraulic excitation methods, target flow rates, and excitation durations is met between two adjacent cycles.

[0064] The adaptive excitation design is executed after the first round of data acquisition. First, a three-dimensional transient seepage forward model is established for excitation scheme evaluation. The layered permeability coefficient and specific water storage capacity obtained from field exploration are used as initial formation parameters. The observed hydraulic head at the end of the first round of static background section is used as the initial head field. The excitation well screen section is used as the excitation boundary position, and candidate excitation schemes are applied as specified flux boundary conditions at this boundary position. The candidate excitation scheme set consists of six fixed schemes, each uniquely determined by three excitation control parameters: excitation method, target flow rate, and excitation duration. Then, based on the current parameter set, a sensitivity index is calculated for each candidate excitation scheme, and a scheme satisfying a preset optimal criterion is selected as the excitation control parameter for the second round. The preset optimal criterion is set as maximizing the sensitivity index corresponding to the determinant of the Fisher information matrix, and this sensitivity index is defined as:

[0065] ;

[0066] in This represents a candidate incentive scheme. Indicating and candidate incentive schemes The corresponding sensitivity index value, Represents the determinant operator. Indicating in candidate incentive schemes The sensitivity matrix is ​​obtained by numerical difference of the three-dimensional transient seepage forward model, with its rows corresponding to the head response vector components formed by splicing six observation points at all sampling times, and its columns corresponding to the leakage parameter vector components divided according to the diaphragm wall area and depth layer. This represents the transpose operator. This represents the observation error covariance matrix used for scheme evaluation, constructed using a diagonal matrix and derived from the measurement noise variance obtained through level gauge calibration. express The inverse matrix is ​​obtained according to the above criteria. The largest candidate incentive scheme was selected and adopted as the second round of controlled hydraulic incentive implementation scheme.

[0067] The hydraulic excitation data corresponding to the two rounds of controlled hydraulic excitation and the original head observation data of the six observation points were aligned by timestamps and then aggregated to form the original dataset.

[0068] In this specific embodiment, S2 includes:

[0069] It consists of four parts: data extraction, state-space model construction, noise statistical parameter setting, and unscented Kalman filter recursion.

[0070] The original head observation sequence of six observation points was read from the original dataset, and a sampling time sequence was constructed. The sampling interval was set to [missing information]. And the sampling time is based on Indicates the first Each sampling time;

[0071] Simultaneously, the actual flow time series recorded by the excitation well is read and used as a known input, denoted as . Furthermore, water injection is considered positive, water pumping is considered negative, and pump stoppage is considered zero, and the timestamps are aligned with the observation points.

[0072] Subsequently, raw head observations during non-excitation periods were extracted as background observation sequences based on "the static background period before each round of controlled hydraulic excitation" and "the end of the recovery period after each round of controlled hydraulic excitation". The first static background period corresponds to sampling data from 0 to 1800 s, and the end of the first recovery period corresponds to sampling data from 2400 to 3600 s after pump shutdown. The second static background period corresponds to sampling data for 1800 s consecutively before the start of the second round of excitation, and the end of the second recovery period corresponds to sampling data from 2400 to 3600 s after pump shutdown. Outlier removal was performed on this background observation sequence to prevent sensor spikes from entering the recursive estimation. The outlier removal rule was set so that if the absolute value of the head jump between two adjacent sampling times at the same observation point exceeded 0.05 m, the sampling point was replaced with the median within each adjacent 30 s window. After extracting the background observation sequences, a discrete state-space model was independently established for each observation point to characterize the changes in the background hydraulic field, and known inputs were explicitly introduced into the model. To separate the head response component caused by controlled hydraulic excitation from the background head component unaffected by controlled hydraulic excitation, the state-space model comprises a two-dimensional state vector consisting of the background head state and the excitation response state, satisfying the following relationship:

[0073] ;

[0074] Where i represents the observation point number and K represents the sampling time number. Indicates the first The observation point at the ... The original water head observation values ​​at each sampling time, with units of Indicates and The corresponding background head component, in meters. Indicates and The corresponding controlled hydraulic excitation response components and their units are Indicates the first Known input flow rate at each sampling time, and in units of The attenuation coefficient represents the excitation response state and is a fixed value. Used to characterize the slow decay characteristics of the aquifer head response. Indicates the first The flow-head coupling coefficient at each observation point, with units of _ The determination was made using measured data from the first excitation phase. The method involved linearly interpolating the first static background phase and the end of the first recovery phase on the time axis to obtain the [number missing]. The initial background head sequence at each observation point is used to obtain the excitation response observation sequence by subtracting the initial background head sequence from the original head observation values. Finally, at a fixed point... Under the condition of least squares fitting of the second row of the above relation, we obtain The only solution;

[0075] The process noise representing the background water head state is used to characterize the slow random drift caused by foundation pit dewatering and regional groundwater level fluctuations. It represents the process noise of the excitation response state and is used to characterize the response deviation caused by formation heterogeneity. The above three types of noise are all set as white noise with a mean of zero and are independent of each other, representing the observation noise and used to characterize the water level gauge measurement error.

[0076] Regarding the setting of noise statistical parameters, the standard deviation of the background head state process noise is set as follows: The standard deviation of the excitation-response state process noise is set to . The standard deviation of the observed noise was set to And with the same resolution as the water level gauge;

[0077] Regarding the initial state settings, the average value of the original water head observations within the first 600 seconds of the first round of static background period was set for each observation point as follows: ,Will Set to 0 to indicate that there was no controlled hydraulic excitation response before the start of the experiment;

[0078] Subsequently, an unscented Kalman filter recursive estimation was performed on the above state-space model according to the sampling time sequence, with the filter parameters taken as follows: Cholesky decomposition is used to generate sigma points, and a time update is performed at each sampling time to obtain the sigma points. The prior estimate is obtained by performing measurement updates at sampling times covered by the background observation sequence to correct the prior estimate, while only the time update results are retained at sampling times not covered by the background observation sequence, thus obtaining background head estimation data covering all sampling times. and the filtering process The corresponding posterior variance output is the background uncertainty data. .

[0079] In this specific embodiment, S3 includes:

[0080] Read background head estimation data and its background uncertainty data And read the raw head observation data. and its sampling time sequence, the observation point numbering adopts The sampling time sequence number adopts and This represents the total number of sampling points throughout the entire testing period;

[0081] The time alignment process is set to direct alignment based on a one-to-one correspondence of timestamps. However, if individual sampling times are missing, this will cause issues. and When timestamps are inconsistent, the missing time will be... The background head estimates at two adjacent time points are interpolated linearly over time to complete the data, thus obtaining the data for each... One-to-one corresponding background head estimates;

[0082] Subsequently, background subtraction is performed at each sampling time for each observation point to form background-corrected head response data for inversion. At the same time, the observation error covariance matrix is ​​constructed based on the background uncertainty and measurement noise statistical parameters. The calculation and construction rules are as follows:

[0083] ;

[0084] in Indicates the first The observation point at the ... The background-corrected head response value at each sampling time, with units of (the value is missing from the original text). Indicates the first The observation point at the ... The original water head observations at each sampling time, in meters. Indicates and Background head estimate after timestamp alignment, in units of Indicates and The corresponding observation error variance and its unit is This represents the variance of the background head estimation error and is expressed by... The posterior variance of the unscented Kalman filter is given directly and in units of . This indicates the variance of the water level gauge measurement noise, and it is taken as a fixed value. This represents the observation error covariance matrix and is constructed as a diagonal matrix. express The One diagonal element, Indicates a two-dimensional index The index number mapped to the one-dimensional observation vector index. Indicates the number of observation points and takes a fixed value. ;

[0085] To avoid The presence of ill-conditioned condition numbers leads to unstable numerical updates in subsequent iterations; therefore, each... Apply lower bound constraints and all According to the index The sequential splicing forms the background-corrected head response data vector to be combined with... The diagonal elements correspond one-to-one.

[0086] In this specific embodiment, S4 includes:

[0087] The parameter vector to be inverted is formed by constructing a three-dimensional transient seepage forward model of the detection area and completing the low-dimensional parameterization of the outer boundary conditions and the discretization of the equivalent seepage parameters.

[0088] Establish a spatial coordinate system and define the computational domain, taking The axis is perpendicular to the normal of the diaphragm wall surface and points outward from the excavation pit. The axis is along the length of the wall, and is taken as... The axis is vertically downward and centered on the ground surface. The detection area was determined as The three-dimensional region is defined, and the geometry of the underground continuous wall is explicitly modeled within it. The wall thickness is 1m, and the bottom of the wall is located at... ;

[0089] The three-dimensional transient seepage forward model adopts the saturated seepage control equations and uses the head as the state variable. Its control equations are written as follows:

[0090] ;

[0091] in Represents a spatial position vector with units of 1. Indicates time and the unit is Indicates position At any time water head and the unit is Indicates position The permeability tensor at the location and its unit is And take isotropic form within the soil element Within the wall unit, the equivalent permeability parameter is assigned a value. express identity matrix Represents the scalar value of soil permeability coefficient and its unit is . Indicates specific water storage capacity and the unit is Represents the volumetric source and its unit is In this embodiment, the value is 0 except for the area affected by the excitation well;

[0092] The soil is divided into four layers according to depth, and its hydraulic parameters are fixed. Layering Layering , Layering Layering ;

[0093] Initial conditions are taken The initial head field at time is The interpolation field of the background head estimate at the end of the first static background segment in the three-dimensional domain is calculated using inverse distance weighting with depth-layered interpolation and six observation points. As a hard constraint point;

[0094] Boundary conditions are divided into two categories: excitation boundary terms and external boundary conditions. Excitation boundary terms are determined by the steps... Recorded known input flow time series The excitation is determined and applied to the wellbore boundary corresponding to the excitation screen section, specifically at each sampling time. Convert the flux to a wellbore normal and take piecewise constant values ​​between adjacent sampling times to drive transient calculations;

[0095] External boundary conditions are represented as boundary parameter vectors in a low-dimensional parameterized manner. The four lateral outer boundaries of the computational domain are divided according to The direction is divided into 6 segments, and each segment is along The direction is further divided into two segments, resulting in 24 boundary segments, and the boundary head of each boundary segment is set to a constant boundary parameter. and Thus obtain and This indicates the transpose operator, while setting the bottom boundary of the computational domain to an impermeable boundary to eliminate the non-uniqueness of the deep boundary for inversion, and setting the surface boundary to an impermeable boundary to match the condition of no surface infiltration during the test.

[0096] To make the boundary parameter vector represented in a low-dimensional parameterized manner To satisfy the smoothness constraint, the discrete form of the smoothness constraint is defined as the second-order difference constraint of the segmented parameters of adjacent boundary segments on the same side during the boundary parameter vector construction stage. In the subsequent ensemble Kalman inversion iterative update, the smoothness constraint is achieved by introducing a virtual observation term. The observation value of the virtual observation term is set to zero and its covariance is taken as a diagonal matrix, and the allowable boundary fluctuation amplitude is characterized by a standard deviation of 0.05m. Thus, the smoothness requirement is incorporated into the joint inversion in a calculable way without adding additional field measurements.

[0097] The leakage channels within the wall are represented by an equivalent permeability parameter distribution, forming a leakage parameter vector. Along the wall The wall is divided into 12 wall segments, each 5m long, along the direction of width and 7 layers, each 5m thick. Thus obtain The first leakage unit and the first The equivalent permeability parameter of each leakage unit is denoted as And the unit is ,Will And for each Apply range constraints To ensure physical feasibility and that the wall is non-leaky, the background value is taken as follows: ;

[0098] Boundary parameter vector With leakage parameter vector Construct the parameter vector to be inverted by splicing them together in a fixed order. And agreed The first 24 components correspond Then the 84 components correspond to This ensures that the parameter index is unique during subsequent set statistics updates;

[0099] To facilitate subsequent covariance localization processing, in step Synchronous generation of localized matrices The planar partitioning is based on the segmentation information of 12 wall segments, and the vertical partitioning is based on 7 depth levels, with the hydraulic influence radius set to a fixed value. It is also used to determine the relevant cutoff range between different partitions, and the localization matrix. Elements are categorized as follows: elements within the same partition are 1, elements spanning different partitions and whose centroids are more than [value missing]. Take 0, spanning multiple partitions and the distance between the centroids of the two units is not greater than 0. By assigning a rule value of 0.2", the long-distance spurious correlation under the condition of few measurement points is truncated at the matrix level and a definite input is provided for Schur element-wise product localization;

[0100] The numerical discretization of the three-dimensional transient seepage forward model adopts a tetrahedral finite element mesh with a maximum element side length of 0.5m within a 3m range on both sides of the wall and a maximum element side length of 2m in other areas. The time discretization adopts an implicit backward Euler scheme with a time step of 5s. The simulated head at six observation points is output at each time step and mapped to the 1s sampling time through linear interpolation to be consistent with the timestamp of the head response data after background correction.

[0101] In this specific embodiment, S5 includes:

[0102] The three-dimensional distribution of leakage channels and the output of equivalent permeability parameters are achieved through parameter set generation, forward simulation, observation residual weighting, ensemble Kalman inversion iterative update, covariance localization, and sparsity projection processing.

[0103] Based on the parameter vector to be inverted Generate a parameter set and set the size of the set to be . ,in Let be a boundary parameter vector and its components be Let be the leakage parameter vector and its components be... This represents the transpose operator, initializing the first... The members of a set are denoted as and The initial mean is taken as The initial head field is the head value at the centroid of the corresponding outer boundary segment, denoted as . And generate disturbances with a standard deviation of 0.2m for each Apply range constraints The initial mean is taken as the non-leaking background value of the wall. And record it as and in Space with mean A disturbance is generated with a standard deviation of 0.6 and for each Apply range constraints To ensure physical feasibility;

[0104] Then, the background-corrected head response data were indexed. splicing to form observation vector ,in Number the observation points and , The number of observation points. The sampling time number. The total number of observations participating in the inversion was determined by sampling points at 10-second intervals throughout the entire time period to reduce computational complexity. Before sampling, each observation point was... Perform a 10-second window moving average to avoid aliasing errors introduced during sampling;

[0105] Simultaneously read the observation error covariance matrix And its diagonal matrix structure remains unchanged;

[0106] To achieve the boundary parameter vector Smoothness constraints are applied to incorporate virtual observations into the inversion and construct augmented observation vectors. ,in A vector is a set of zeros whose dimension is equal to the total number of second-order differences calculated along the segment index within the same depth band for each lateral boundary. The second-order difference operator is denoted as a matrix. and Each row takes the coefficient at the positions of the three adjacent boundary parameters. The boundary parameter sequence within the same depth band of the same lateral boundary is applied to obtain the corresponding second-order difference value, thus defining the forward output of the virtual observation as... And require it to approach ;

[0107] The augmented observation error covariance matrix is ​​denoted as And take the diagonal form of the blocks blkdiag This represents the block diagonal concatenation operator. The virtual observation covariance matrix is ​​a diagonal matrix, and each diagonal element is set to 1. To limit the permissible range of fluctuations at the boundary;

[0108] The three-dimensional transient seepage forward model is defined as the forward operator. And let its input be a parameter vector of any set member. The output is the simulated head response vector corresponding to the six observation points on the extracted sampling time sequence. ,in The number of iterations and And construct the augmented forward operator. With One-to-one correspondence;

[0109] For each iteration Each set member Call Obtain analog output and use Construct the observation residuals, and simultaneously calculate the parameter-observation cross-covariance matrix based on ensemble statistics. With observation-observation covariance matrix ;

[0110] To implement covariance localization, the localization matrix is... Extended to a parameter-observation localization matrix The elements are constructed according to defined rules, so that each observation component corresponds to the wall segment parcel unit and depth layer unit with its nearest spatial location to form an observation belonging unit index, and the observation belonging unit is linked to the unit to which any parameter component belongs. Weight copying in The corresponding position to obtain and Consistent dimensions;

[0111] Subsequently, the parameter set is iteratively and jointly updated using the perturbation observation update form of ensemble Kalman inversion, and Schur element-wise product localization is performed on the cross-covariance during the update. The update formula is as follows:

[0112] ;

[0113] in This represents the Schur element-wise product operator. Indicates the first The second iteration The observed perturbation vectors of each set member satisfy zero mean and have covariance. Generate to achieve consistency in perturbation observations. This represents the matrix inversion operation, and in the numerical implementation, Cholesky decomposition is used to solve the linear equation system to avoid numerical instability caused by explicit inversion;

[0114] After each iteration update, a sparsification projection process is performed on the leakage parameter vector of each set member to conform to the sparse prior of the leakage channels. The processing order is to first calculate the set mean for each leakage unit. with set standard deviation And set the leakage threshold to And its value is equal to all Five times the arithmetic mean, then satisfying The update amount of the leakage unit is set to zero and the unit is updated in all set members. The uniform projection is based on the non-leaky background value of the wall. Subsequently, only the ensemble mean was retained in the remaining leak cells that were not projected back. The largest The leaking unit is not the background and the remaining leaking units are in all set members. The uniform back projection is used to obtain a spatially continuous but controlled number of leakage channels by using the non-leaking background value of the wall.

[0115] The iteration termination condition is set to simultaneously check the observation fit and parameter stability and then take... As an upper limit on the number of iterations, when the augmented observation residual vector is in The weighted root mean square is less than 0.005m, or the Euclidean norm of the change in the set mean parameter vector between two consecutive iterations is less than... The iteration terminates at the specified time and outputs the leakage parameter vector corresponding to the final set mean. The three-dimensional spatial distribution of leakage channels and the quantitative results of equivalent permeability parameters are used as the output, and the ensemble standard deviation corresponding to each leakage unit is used as an uncertainty characterization.

[0116] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0117] This invention integrates a unified computational framework by combining controlled hydraulic excitation and multi-point response acquisition, background recursive estimation and subtraction, three-dimensional transient seepage forward calculation, and ensemble statistics iterative joint inversion. This framework addresses the issues of limited measurement points due to inaccessibility at the site, continuous fluctuations in the background hydraulic field, and difficulty in accurately obtaining boundary conditions. Specifically, controlled excitation provides identifiable time-varying hydraulic disturbance sources, and multi-point synchronous observation generates multi-source, multi-response data required for tomography. Unscented Kalman filtering or particle filtering algorithms are used to recursively estimate the background head during non-excitation periods and output uncertainty, achieving separation and correction of background disturbances such as drainage and groundwater level fluctuations. Based on this, an observation error covariance matrix is ​​constructed and used as the inversion weighting basis, enabling the inversion update to adaptively suppress background drift and noise effects. This allows for the acquisition of stable head response information even under limited point distribution conditions and improves the reliability of three-dimensional localization and quantitative intensity characterization of seepage channels.

[0118] This invention addresses the key challenge of "strong boundary uncertainty that is easily confused with leakage effects" in this case by making improvements to the algorithm structure for engineering practice: First, the boundary conditions outside the detection area are parameterized in a low-dimensional manner using piecewise constants, piecewise linearity, or basis function expansion to form a boundary parameter vector, which is then concatenated with the leakage parameter vector. This enables joint estimation of boundary and leakage parameters during ensemble Kalman inversion iteration, reducing the risk of misjudging boundary errors as leakage. Second, the uncertainty of the background recursive estimation output is incorporated into the construction of the observation error covariance matrix, creating a closed-loop coupling between the background estimation module and the inversion module in error modeling, thereby improving adaptability to changes in background disturbances. Third, covariance localization is performed based on wall segment partitioning, depth stratification, and hydraulic influence radius to weaken spurious correlations generated by ensemble statistics under conditions of few measurement points, improving inversion convergence stability and spatial resolution, and thus better achieving three-dimensional accurate positioning of leakage channels and quantitative assessment of leakage intensity.

Claims

1. A method for detecting leakage in diaphragm walls based on hydraulic chromatography, characterized in that, include: S1. Deploy at least one hydraulic excitation point and multiple observation points on the accessible side of the diaphragm wall, implement at least two rounds of controlled hydraulic excitation, record the hydraulic excitation data and collect raw head observation data to obtain the raw dataset; S2. Extract the raw head observation data during non-excitation periods from the raw dataset as the background observation sequence, and use the hydraulic excitation data as known input to obtain the background head estimation data and its background uncertainty data through recursive estimation; S3. Perform background subtraction on the raw head observation data based on the background head estimation data to obtain the background-corrected head response data, and construct the observation error covariance matrix based on the background uncertainty data and measurement noise statistical parameters; S4. Based on the hydraulic excitation data, establish a three-dimensional transient seepage forward model of the detection area. Represent the outer boundary conditions of the detection area as a boundary parameter vector in a low-dimensional parameterized manner, and represent the seepage channel as a seepage parameter vector. Then, concatenate the two to construct the parameter vector to be inverted. S5. Based on the background-corrected head response data, the observation error covariance matrix, and the three-dimensional transient seepage forward model, use ensemble Kalman inversion to jointly update the parameter vector to be inverted, and obtain the three-dimensional spatial distribution of the seepage channel and the seepage intensity and / or equivalent permeability parameters.

2. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 1, characterized in that, S1 includes: The detection area is a three-dimensional area consisting of the underground continuous wall and the strata on both sides of the wall within a preset horizontal influence range and a preset depth range. Within the detection area, determine the location of the accessible side of the underground continuous wall, wherein the accessible side is the inside of the foundation pit, or the side that meets the construction conditions for setting up the hydraulic excitation point and the observation point; At least one hydraulic excitation point and multiple observation points are set at the location of the observation points, and the multiple observation points are distributed along the depth direction of the underground continuous wall to cover at least two different depth intervals. For each round of controlled hydraulic excitation, the excitation control parameters for that round of controlled hydraulic excitation are determined. The excitation control parameters include the excitation method, the excitation duration, and the target flow rate or target pressure. Based on the excitation control parameters, water injection or pumping is performed at the hydraulic excitation point to form controlled hydraulic excitation for the vessel, and the actual execution value of the excitation control parameters is recorded during the execution process to obtain hydraulic excitation data; While performing the controlled hydraulic excitation, the multiple observation points are simultaneously collected using a unified time reference to obtain raw head observation data; The original dataset is obtained by collecting hydraulic excitation data corresponding to at least two rounds of controlled hydraulic excitation and raw head observation data. In the at least two rounds of controlled hydraulic excitation, the two adjacent rounds of controlled hydraulic excitation differ in at least one of the following: the location of the hydraulic excitation point, the excitation method, the target flow rate, the target pressure, the excitation duration, and the excitation sequence.

3. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 1, characterized in that, S2 includes: The original head observation data and their corresponding sampling time sequences of the multiple observation points are extracted from the original dataset, and the original head observation data of the non-excitation period before and after the start of each round of controlled hydraulic excitation are extracted as background observation sequences. A state-space model is established to characterize the changes in the background hydraulic field. The state-space model includes a state equation for describing the evolution of the background hydraulic field over time and an observation equation for mapping the state variables to the background observation sequence. At least one of the state equation and the observation equation contains an input term with the hydraulic excitation data as a known input term, which is used to estimate the background head component that is not affected by the controlled hydraulic excitation. The initial state and noise statistics parameters are set for the state-space model; The state-space model is recursively estimated using an unscented Kalman filter or a particle filter algorithm according to the sampling time sequence to obtain background head estimation data corresponding to the multiple observation points. The state estimation uncertainty obtained during the recursive estimation process is output as background uncertainty data corresponding to the background head estimation data.

4. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 1, characterized in that, S3 includes: Based on the sampling time sequence of the original head observation data, the background head estimation data is time-aligned to obtain the background head estimation value corresponding to each sampling time. For each observation point, at each sampling time, the estimated background head value is subtracted from the original head observation data to obtain the background-corrected head response data; The background uncertainty variance of each observation point at each sampling time is determined based on the background uncertainty data, and the background uncertainty variance is superimposed with the preset or calibrated sensor measurement noise variance, or weighted superimposed according to the preset weight, to obtain the observation error variance of each observation point at each sampling time. An observation error covariance matrix is ​​constructed based on the observation error variance, such that the diagonal elements of the observation error covariance matrix correspond to the observation error variance of each observation point at each sampling time in the background-corrected head response data.

5. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 1, characterized in that, S4 includes: The excitation boundary terms of the three-dimensional transient seepage forward model are determined based on hydraulic excitation data; In the three-dimensional transient seepage forward model, the outer boundary of the detection area is divided into a preset number of boundary segments, and the boundary conditions of each boundary segment are represented by piecewise constants, piecewise linear representations, or expansions of preset basis functions. The boundary head or boundary flux of each boundary segment is used as the boundary parameters to form a boundary parameter vector. The preset basis functions include at least one of Fourier basis functions, polynomial basis functions, spline basis functions, and radial basis functions; in the three-dimensional transient seepage forward model, the seepage channel is represented as an equivalent permeability parameter distribution or an equivalent seepage source term distribution located within the underground continuous wall, and the parameters of the equivalent permeability parameter distribution or the equivalent seepage source term distribution are used as the seepage parameter vector; The leakage channel is divided into multiple units according to the diaphragm wall section and depth layer. The leakage parameter vector includes the equivalent permeability parameter or equivalent leakage source term intensity of each unit. The boundary parameter vector and the leakage parameter vector are concatenated to construct the parameter vector to be inverted. The detection area is divided into planar partitions based on the diaphragm wall sectional information, and into vertical partitions based on the depth stratification information. The relevant cutoff range between different partitions is determined based on the hydraulic influence radius, thereby generating a localization matrix for set covariance localization. The hydraulic influence radius is determined by empirical parameters, or by field tests, or by calculation using the three-dimensional transient seepage forward model combined with formation parameters.

6. The method for detecting leakage in diaphragm walls based on hydraulic tomography according to claim 1, characterized in that, S5 include: A parameter set is generated based on the parameter vector to be inverted, and each set of parameters in the parameter set is substituted into the three-dimensional transient seepage forward model to obtain the simulated head response corresponding to each set of parameters. The observation residuals are constructed using the deviation between the background-corrected head response data and the simulated head response, and the observation error covariance matrix is ​​used to weight the observation residuals. The parameter set is iteratively updated by ensemble Kalman inversion based on the observed residuals. In each iteration, the ensemble covariance used for updating is localized using a localization matrix. The localization process includes performing Schur element-wise product of the localization matrix and the set covariance; terminating the iterative update when a preset convergence condition is met, the preset convergence condition includes one or a combination of the following: the norm of the observation residual is less than a first threshold, the norm of the change in the parameter vector to be inverted in two adjacent iterations is less than a second threshold, and the number of iterations reaches the upper limit. The output is a three-dimensional spatial distribution of the leakage channels determined by the parameter set, and at least one of the leakage intensity and equivalent permeability parameters corresponding to the leakage channels.

7. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 2, characterized in that, The process for determining that at least one of the excitation control parameters differs between two adjacent rounds of controlled hydraulic excitation includes adaptive excitation design: after completing the data acquisition for the previous round of controlled hydraulic excitation, the sensitivity index corresponding to the candidate excitation scheme is calculated based on the three-dimensional transient seepage forward model and the current parameter set, and the candidate excitation scheme that makes the sensitivity index satisfy the preset optimal criterion is selected as the excitation control parameter for the next round of controlled hydraulic excitation; the sensitivity index includes at least one of the determinant of the Fisher information matrix, the trace of the Fisher information matrix, or the gradient norm of the observation residual with respect to the leakage parameter vector.

8. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 5, characterized in that, The boundary parameter vector represented in a low-dimensional parameterized manner satisfies either a continuity constraint or a smoothness constraint. The continuity constraint includes the boundary head or boundary flux of adjacent boundary segments being equal at the segment boundaries. The smoothness constraint includes the second-order difference of the boundary head or boundary flux of adjacent boundary segments being less than a preset threshold. Furthermore, the continuity constraint or the smoothness constraint is achieved by introducing a virtual observation term or a penalty term in the ensemble Kalman inversion iterative update.

9. The method for detecting leakage in diaphragm walls based on hydraulic chromatography according to claim 6, characterized in that, After each iteration update, a sparsification projection process is performed on the leakage parameter vector. The sparsification projection process includes at least one of the following: setting the update amount of the equivalent permeation parameter less than the leakage threshold to zero, setting the intensity of the equivalent leakage source term less than the leakage threshold to zero, retaining only a preset number of leakage units as non-zero and setting the remaining leakage units as background values; the leakage threshold is determined by the set variance, set mean, or preset empirical threshold of the parameter set.

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