A method and system for landfill leakage detection considering stress wave propagation in non-uniform media

Abstract

The present invention proposes a method and system for landfill leakage detection considering stress wave propagation in non-uniform media. The method is to establish a stress wave propagation model for non-uniform media, decompose the actual wave velocity into a reference wave velocity and a variation; then use an adaptive algorithm to estimate and update the wave velocity in real time; finally, accurately locate the leakage source position through a weighted optimization method. The present invention also provides a system for implementing this method, including a sensor array, a signal acquisition and preprocessing module, an adaptive wave velocity estimation module, a leakage source location module, and a result display and alarm module. By considering the non-uniformity and time-varying characteristics of the medium, combining an adaptive algorithm and a weighted optimization strategy, the present invention effectively improves the leakage point location accuracy and has important practical value.

Description

Technical Field

[0001] The present invention relates to the technical field of environmental monitoring, and particularly to a method and system for leakage detection of landfills. Background Art

[0002] As an important facility for urban solid waste treatment, the leakage detection of landfills is directly related to the safety of groundwater environment and public health. In practical engineering, leakage detection faces unique technical challenges, which mainly stem from the complexity of landfill media. The landfill contains multiple anti-seepage systems inside. Due to the landfill process and natural settlement, complex spatial distributions will be formed among various media. At the same time, the biochemical degradation and compaction effects during the landfill process make the physical properties of media such as soil and garbage show significant non-uniformity. In the prior art, common leakage detection methods include the resistance method, the acoustic method, etc. However, these methods have the following problems in practical applications:

[0003] 1. Medium non-uniformity: Media such as landfill soil have complex non-uniformity, resulting in significant spatial variations in the stress wave propagation speed;

[0004] 2. Time-varying characteristics: The medium characteristics will change with environmental conditions (such as temperature, humidity, etc.), making it difficult for traditional fixed-parameter models to accurately describe the stress wave propagation characteristics;

[0005] 3. Positioning accuracy: Due to the influence of the above factors, existing methods often have problems with insufficient positioning accuracy in practical applications. Summary of the Invention

[0006] Aiming at the key technical problems in the leakage detection of landfills, the present invention proposes a method for leakage detection of landfills considering stress wave propagation in non-uniform media. Aiming at the problem of insufficient positioning accuracy caused by the non-uniformity and time-varying characteristics of landfill media, the present invention proposes an innovative solution from three aspects: the stress wave propagation model, the adaptive algorithm, and the system implementation.

[0007] The technical solution of the present invention: A method for leakage detection of landfills considering stress wave propagation in non-uniform media, in which a plurality of stress wave sensors are arranged around the landfill to form a distributed sensor array, a stress wave sensor position vector is established, the propagation speed of stress waves is collected, and the obtained data is processed. The steps are as follows:

[0008] (1) Establish a wave velocity model, representing the wave velocity at a spatial position as the superposition of a reference wave velocity and a wave velocity deviation. The reference wave velocity is calculated from the calibrated wave velocity values of multiple reference points, and the wave velocity deviation is represented by the expansion of spatial basis functions. Considering the time-varying characteristics of the medium, a time-varying term is introduced into the wave velocity model. The time-varying term includes an initial perturbation value, an attenuation coefficient, and a random perturbation term, thereby establishing a complete wave velocity model for non-uniform time-varying media. The model equation is as follows: , , , , where, is time, is the time-varying wave velocity at the spatial position , is the reference wave velocity, is the wave velocity deviation at the spatial position , is the wave velocity change term related to time, is the calibrated wave velocity value of the th reference point, is the number of calibration points, is the coefficient of the th spatial basis function, is the th spatial basis function, is the total number of spatial basis functions, is the initial perturbation value, is the attenuation coefficient, is the random perturbation term, is the natural constant of mathematics;

[0009] (2) Based on the above wave velocity model, establish a stress wave travel time equation. The theoretical travel time is obtained by dividing the Euclidean distance from the leakage source position to each stress wave sensor position by the wave velocity, where the Euclidean distance is calculated from three-dimensional coordinates. Then, define the wave velocity estimation error as the sum of the squares of the difference between the measured travel time and the theoretical travel time, and use the gradient descent method to iteratively update the wave velocity. , this equation represents the non-uniform attenuation characteristics of the wave velocity at the spatial position , where, is the update amount of the time-varying wave velocity at the spatial position at the th time step, is the coefficient of the th spatial basis function estimated at the th time step, is the change amount of the time-varying wave velocity estimated at the th time step, , are obtained through particle filtering;

[0010] (3) During the process of leakage source location, a weighted objective function is constructed. , , where is the weighted objective function, is the total number of stress wave sensors, is the weight of each stress wave sensor, is the th measured arrival time of the stress wave sensor, is the Euclidean distance from the leakage source to the stress wave sensor, is the th position vector of the stress wave sensor, is the three-dimensional coordinates of the leakage source, , is the theoretical stress wave propagation time, is the standard deviation parameter used to control the weight decay rate, and the gradient descent method is used to update the leakage source position. , where is the iteration step size, is the position estimate value at the th iteration, is the position estimate value at the th iteration, is the gradient of the objective function with respect to the position, and gradient descent is achieved by calculating the gradient of the objective function with respect to the position.

[0011] Preferably, a particle filter method is used to solve the wave speed model. Each particle is predicted and updated through the state transition equation, and the particle weights are calculated and updated based on the measured data. The relationship equation between the observed value and the state quantity is designed as: , where is the likelihood probability of the measurement value of the th stress wave sensor at the th time step corresponding to the th particle, represents the state vector of the th particle at the th time step, is twice the value of pi, represents the exponential function with as the base;

[0012] The stress wave arrival time equation is solved by the numerical integration method.

[0013] Furthermore, to avoid particle degeneracy, the effective number of particles is calculated. When the effective number of particles is less than a preset threshold, resampling is performed. A new set of particles is generated by calculating the cumulative weights and uniformly sampling within the interval. The system state estimation is calculated based on the current particle set, including the leakage source position estimation, medium parameter estimation, and time-varying term estimation. Iteration stops when the change in position estimation is less than the threshold or the maximum number of iterations is reached.

[0014] Preferably, the spatial basis function adopts a Gaussian radial basis function, and its expression is:

[0015] , which shows the non-uniform attenuation characteristics of the wave velocity at the spatial position . Among them, is the central coordinate of the th basis function, which is distributed in a uniform grid within the landfill area, and the grid spacing is ; is the characteristic length parameter; represents the Euclidean distance from the spatial position to ; The number of spatial basis functions and the characteristic length are determined according to the actual size of the landfill and the spatial distribution characteristics of the medium non-uniformity.

[0016] Preferably, in the initialization stage, the prior distributions of each parameter are set, including setting the initial distribution of the leakage source position as a uniform distribution on the effective area of the landfill, the initial distribution of the medium parameter as a normal distribution, its mean is a zero vector, and the covariance matrix is a constant multiple of the identity matrix, and the initial distribution of the time-varying term is also set as a normal distribution with a mean of zero;

[0017] The initial covariance matrix of the medium parameter is , where , is the identity matrix.

[0018] A leakage detection system for implementing a leakage detection method for landfills considering stress wave propagation in inhomogeneous media, comprising a plurality of stress wave sensors arranged around the landfill, a signal acquisition and preprocessing module, an adaptive wave speed estimation module, a leakage source location module, and a result display and alarm module. The stress wave sensors are arranged in a rectangular manner around the landfill area. The signal acquisition and preprocessing module real-time collects the stress wave speed and performs digital filtering, threshold detection, arrival time extraction, and wave speed estimation on the collected original signal. The adaptive wave speed estimation module estimates and dynamically updates the wave speed by calculating the difference between the theoretical propagation time and the measured time according to the preprocessed signal sent by the signal acquisition and preprocessing module, using the gradient descent method to adapt to the changes in the medium characteristics. The leakage source location module constructs an objective function considering the reliability of the stress wave sensors using the updated wave speed value and accurately estimates the leakage source location through the gradient descent algorithm until the preset convergence condition is met. The result display and alarm module displays the location result in a graphical manner on the monitoring interface in real time, determines whether to trigger an alarm according to the preset value, and saves the detection data in the database for subsequent analysis.

[0019] Preferably, low-pass filters are used for signal preprocessing to eliminate noise.

[0020] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, it is used to implement a leakage detection method for landfills considering stress wave propagation in inhomogeneous media and obtain the location of the leakage source.

[0021] The beneficial effects of the present invention: In terms of the stress wave propagation model, the present invention establishes a new stress wave propagation model. This model breaks through the limitations of traditional fixed-parameter models and creatively decomposes the actual wave speed into a reference wave speed and a variation. The variation is further divided into a spatial variation term and a temporal variation term. The spatial variation term is used to describe the spatial distribution characteristics of the wave speed caused by medium inhomogeneity, and the temporal variation term reflects the dynamic change of the wave speed caused by environmental condition changes. This model structure can comprehensively reflect the influence of medium characteristics on stress wave propagation and provides a theoretical basis for subsequent adaptive algorithms.

[0022] In terms of the adaptive algorithm, the present invention has developed a complete set of adaptive estimation methods. This method first constructs an error function for wave velocity estimation by comparing the differences between the theoretical travel time and the measured travel time in real time. Then, the wave velocity is iteratively updated using the principle of gradient descent, and the wave velocity estimation value is continuously optimized through multiple iterations. This adaptive mechanism enables the model to dynamically track changes in the medium characteristics and maintain a high estimation accuracy. To further improve the positioning accuracy, the present invention also adopts an innovative weighted optimization strategy for leak source positioning. This strategy constructs an objective function considering the reliability of stress wave sensors and introduces an adaptive weight mechanism, enabling the system to automatically adjust the weights of different stress wave sensors in the positioning calculation. When there is a large deviation between the measurement value of a certain stress wave sensor and the theoretical prediction value, the system will automatically reduce its weight, thereby significantly improving the robustness of the system to abnormal measurement values.

[0023] In terms of system implementation, the present invention designs a complete leak detection system. The distributed stress wave sensor array adopts an optimized spatial layout to ensure full coverage of the landfill area. The signal acquisition is responsible for high-precision digital acquisition of stress wave signals and preliminary noise elimination. The signal processing deeply processes the acquired signals, including digital filtering, feature extraction, and arrival time calculation, etc. The leak location calculation includes wave velocity adaptive estimation and leak source location calculation. The display output module then displays the detection results in real time and has data storage and analysis functions.

[0024] The method of the present invention not only proposes an innovative solution theoretically, but also shows significant technical advantages in practical applications. By establishing a non-uniform time-varying medium model, combining the adaptive estimation algorithm and the weighted optimization strategy, it can effectively overcome the influence brought by the medium characteristics and significantly improve the leak point positioning accuracy. At the same time, the complete system implementation solution provided by the present invention provides a reliable guarantee for the engineering application of this method. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The drawings are only for the purpose of illustrating the preferred embodiments and are not considered to be a limitation of the present invention. In the drawings:

[0026] Figure 1 is the overall framework diagram of the system of the present invention;

[0027] Figure 2 is the schematic diagram of the layout of stress wave sensors;

[0028] Figure 3 is the flowchart of the adaptive processing of non-uniform media; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] In the leak detection project of a landfill, it is first necessary to establish a stress wave propagation model for non-uniform media. Considering the complexity of the landfill media, in the spatial position The wave velocity at can be expressed as the superposition of a reference wave velocity and a wave velocity deviation: , where is the actual wave velocity at the spatial position , is the reference wave velocity (the average wave velocity of the medium), is the wave velocity deviation at the spatial position , is the three-dimensional spatial position vector . The calculation formula of is: is the calibrated wave velocity value of the th reference point, is the number of calibration points.

[0030] The expression of is: is the coefficient of the th spatial basis function, is the th spatial basis function, is the total number of spatial basis functions.

[0031] Considering the time-varying characteristics that the landfill medium properties change with environmental conditions (such as temperature, humidity, etc.), a non-uniform time-varying medium wave velocity model is introduced: , where is time, is the time-varying wave velocity at the spatial position , is the wave velocity change term related to time. This model can effectively describe the influence of the non-uniformity and time-varying characteristics of the landfill medium on the stress wave propagation.

[0032] The model of is: is the initial perturbation value, is the attenuation coefficient, is the random perturbation term, is the natural constant of mathematics.

[0033] Based on the above wave velocity model, a stress wave travel time equation is established. For the th stress wave sensor, the theoretical travel time for the stress wave to propagate from the leakage source position to the stress wave sensor position can be expressed as: , where is the theoretical stress wave propagation time, is the The position vector of a stress wave sensor, is the three-dimensional coordinates of the leakage source, , is the Euclidean distance from the leakage source to the stress wave sensor.

[0034] , where, is the coordinates of the th stress wave sensor,

[0035] is the three-dimensional coordinates of the leakage source.

[0036] , where is the total error, is the measured travel time of the th stress wave sensor, is the total number of stress wave sensors.

[0037] , , is the measurement noise, which follows a normal distribution with a mean of 0 and a variance of .

[0038] Based on the defined wave speed estimation error , the gradient descent method is used to iteratively update the wave speed parameter. In each iteration, calculate with respect to the coefficient of the th spatial basis function and the partial derivative of the time-dependent wave speed change term : , , where in the formula, is the measured travel time of the th stress wave sensor, is the theoretical travel time of the th stress wave sensor, is the propagation path from the leakage source to the th stress wave sensor, is the measured travel time of the th stress wave sensor, is the theoretical travel time of the th stress wave sensor, is the propagation path from the leakage source to the th stress wave sensor. is the path integral differential element. Update the parameter according to the gradient direction: , where, on the integral path, represents time The corresponding estimated leakage source location trajectory is the th iteration of the th spatial basis function coefficient, is the th iteration of the th spatial basis function coefficient, is the spatial parameter learning rate, represents the spatial gradient at location and time , is the time-varying term function after the th iteration, is the time-varying term function after the th iteration, is the time-varying parameter learning rate, and are the physical times corresponding to the th and th iterations. Until is less than the set threshold or the maximum number of iterations is reached. By minimizing , the adaptive optimization of the wave speed model is achieved.

[0039] For , where is included in the state vector of the particle filter, and the update of the wave speed is achieved through the state estimation of the particle filter:

[0040] , where is the updated amount of the time-varying wave speed at the spatial position at the th time step, is the th spatial basis function coefficient estimated at the th time step, is the estimated change amount of the time-varying wave speed at the th time step. These estimated values are all obtained through the particle filter.

[0041] During the leakage source location process, considering the reliability differences of the measured values of each stress wave sensor, a weighted objective function is constructed:

[0042] , where , , is the weighted objective function, represents the weights of each stress wave sensor and is calculated by the following formula:

[0043] , where is the standard deviation parameter used to control the weight decay rate, and exp is the exponential function with the natural constant e as the base.

[0044] Construct the objective function with weights The core purpose is to reduce the interference of abnormal stress wave sensor data on the positioning result through dynamic weight allocation, thereby improving the system robustness. The design basis is: when the measured travel time of the stress wave sensor has a large deviation from the theoretical travel time As the evaluation criterion for optimizing the leakage source location, its gradient descent solution drives the coordinate iterative update through the partial derivative to minimize the positioning error.

[0045] This weight calculation method ensures that the stress wave sensors with smaller deviations between the measured values and the theoretical predicted values have larger weights.

[0046] Use the gradient descent method to solve the leakage source location:

[0047] , where is the iteration step size, is the position estimate value at the -th iteration, is the position estimate value at the -th iteration, is the gradient of the objective function with respect to the position.

[0048] In order to effectively solve the non-uniform time-varying medium wave speed model and the stress wave travel time equation for leakage source location in practical engineering, the present invention adopts the particle filter method.

[0049] In the specific implementation process, first measure initial particles to form an initial particle set: , where the state vector is composed of the three-dimensional coordinates of the leakage source , the basis function coefficient vector and the time-varying term concatenated together and defined as: , where the symbol represents the vertical concatenation of column vectors, and the dimension of the final state vector is Explanation of the above definition: This definition method is a technical means adopted for the joint estimation of multiple parameters in particle filtering. The state vector is essentially a vertical concatenation of parameters in different dimensions. The purpose is to integrate all parameters to be optimized into a unified high-dimensional vector for joint iterative update through a probability framework. Therefore, although the above definition is not an equal-dimensional matrix in the strict mathematical sense, its adoption in particle filtering also falls within the scope that can be understood and implemented by those skilled in the art.

[0050] The initial weight of each particle is set to a uniform distribution: , where is the initial weight of the -th particle, and the initial state distribution is set based on prior knowledge. In practical applications, the initial distribution of the leakage source location can be limited within the landfill, and the medium parameters can take the statistical average of historical data. At each time step , the particle state vector is predicted and updated through the state transition equation:

[0051] , , , is the position estimate value at the -th iteration, is the basis function coefficient vector at the -th iteration, is the basis function coefficient vector at the -th iteration, is the time-dependent wave speed change term at the -th iteration, is the time-dependent wave speed change term at the -th iteration. The covariance matrix parameters of the perturbation terms are set according to actual engineering experience: the position perturbation , and the initial covariance matrix of the medium parameters is , where , is the identity matrix. The time-varying term noise , the time-varying term attenuation coefficient , is the position perturbation, which follows the distribution , is the parameter perturbation, which follows the distribution , is the time-varying term noise, which follows the distribution . In weight update, the standard deviation parameter Not only used to control the weight decay rate, but also reflects the confidence level in measurement noise. In this embodiment, its value is 0.001 s, which matches the measurement accuracy of the stress wave sensor. The reference wave velocity of the medium wave velocity Is set to 1500 m / s according to the average characteristics of the landfill medium, which is based on the statistical results of a large number of experimental data.

[0052] Based on the measured data, calculate and update the weight for each particle: , where, Represents the Weight of the th particle at the Time step, Is the weight of this particle at the previous time step, Is the total number of stress wave sensors. The symbol

[0053] The observation likelihood calculation for a single stress wave sensor is:

[0054] , where, Is the likelihood probability of the measurement value of the th stress wave sensor at the Time step corresponding to the th particle, Represents the State vector of the th particle at the Is twice the value of pi, Represents the exponential function with the natural constant As the base. The role of the observation likelihood calculation is to quantify the total number of sub-intervals of each particle state (including the leakage source location , basis function coefficients, and time-varying terms) and the measured data of the stress wave sensor . The exponential term in the formula corresponds to the product of the observation likelihood , indicating that the observation likelihood calculation directly determines the distribution of particle weights.

[0055] In a non-uniform medium, the theoretical travel time Needs to be solved by path integration. Assume that the stress wave propagates along the straight-line path From the leakage source to the th sensor. Discretize the path uniformly into Sub-intervals to ensure that the length of each segment . Based on the trapezoidal rule, the theoretical travel time is calculated as: , where, Is the step size of the path integration , , is the wave velocity value at the -th discrete point on the path, is the wave velocity value at the -th discrete point, calculated by the basis function expansion model .

[0056] Particle weight normalization:

[0057] Calculate the particle weights based on the error between the theoretical travel time and the measured travel time (i.e., the calculation involved in ), and then normalize the weights of all particles:

[0058] , where is the normalized weight of the -th particle, represents the weight of the -th particle at the -th time step, and the denominator represents the sum of the weights of these particles. The normalization operation ensures that the sum of the weights is 1, providing a probability distribution basis for the subsequent resampling step.

[0059] To avoid the particle degeneracy problem, resampling judgment is required. Calculate the effective number of particles:

[0060] , where represents the effective number of particles; in the summation term, is the particle number from 1 to ; represents the square value of the normalized weight of the -th particle at the -th time step. When is less than the threshold (set to in this embodiment), perform system resampling to generate a new particle set and reset the weights. During the resampling process of particle filtering, when the effective number of particles is less than the threshold , the system resampling method is used to generate a new particle set.

[0061] Specifically, first calculate the cumulative weight:

[0062] , and then uniformly sample points in the interval [0,1], , where follows a uniform distribution on the interval [0,1]. By comparing and the cumulative weight Determine the index of the new particle.

[0063] Based on the current particle set, calculate the system state estimation, including the estimation of the leakage source location:

[0064] , where, represents the leakage source location estimated at the time step; represents the position state of the time step and the th particle.

[0065] Estimation of medium parameters:

[0066] , where, represents the medium parameter vector estimated at the time step; represents the medium parameter state vector of the time step and the th particle.

[0067] Estimation of time-varying terms:

[0068] , where, represents the time-varying term value estimated at the time step; represents the time-varying term state value of the time step and the th particle.

[0069] The iteration termination condition of the algorithm is set to that the position estimation change threshold is 0.01 m and the maximum number of iterations . When either of these conditions is met, the iteration stops.

[0070] In actual engineering applications, the method of the present invention has been verified in a certain landfill. Eight stress wave sensors are arranged around the landfill area, as Figure 2 shown. The spatial layout of the stress wave sensors in the landfill area is as follows: 3 on the upper boundary (S1 - S3), 3 on the lower boundary (S4 - S6), and 1 each on the left and right boundaries (S7 and S8). The sampling frequency of the stress wave sensors is set to 1000 Hz, and the signal preprocessing uses a low-pass filter with a cut-off frequency of 200 Hz.

[0071] To construct the spatial basis function of the non-uniform wave velocity model, the Gaussian radial basis function form is adopted:

[0072] , where, is the center coordinate of the th basis function ( , (the total number of basis functions), represents the spatial position to of the Euclidean distance, is the coverage radius of the basis function (default = 0.5 m). According to the preset grid point distribution (such as uniform grid or adaptive clustering), it is independent of the stress wave sensor position ( ). By adjusting the basis function coefficient , the spatial non-uniform characteristics of the wave speed field can be characterized.

[0073] The prior of the medium parameters follows a normal distribution: , where is the basis function index, represents the medium parameter vector at the initial time; represents the mean vector, with a dimension of ; represents the covariance matrix, with a dimension of . Specifically, represents a zero vector of dimension, representing the identity matrix of dimension multiplied by 0.1.

[0074] The prior of the time-varying term also follows a normal distribution: , where represents the initial perturbation value; the first parameter 0 represents the mean, and 0.01 represents the variance.

[0075] Corresponding to the above method, the present invention proposes a non-uniform medium leakage detection system for landfills, including a plurality of stress wave sensors arranged around the landfill, a signal acquisition and preprocessing module, an adaptive wave speed estimation module, a leakage source location module, and a result display and alarm module. The stress wave sensors are arranged in a rectangular manner around the landfill area. The signal acquisition and preprocessing module collects the stress wave speed in real time and performs digital filtering, threshold detection, arrival time extraction, and wave speed estimation on the collected original signal. The adaptive wave speed estimation module estimates and dynamically updates the wave speed by calculating the difference between the theoretical propagation time and the measured time according to the preprocessed signal sent by the signal acquisition and preprocessing module, so as to adapt to the change of the medium characteristics. The leakage source location module constructs an objective function considering the reliability of the stress wave sensors by using the updated wave speed value, and accurately estimates the leakage source location through the gradient descent algorithm until the preset convergence condition is met. The result display and alarm module displays the location result in a graphical manner on the monitoring interface in real time, judges whether to trigger an alarm according to the preset value, and saves the detection data in the database for subsequent analysis. The signal preprocessing uses a low-pass filter to eliminate noise.

[0076] For the convenience of popularization and use, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, it is used to implement the above-mentioned landfill non-uniform medium leakage detection method to obtain the location of the leakage source. The readable storage medium can be a read-only memory (ROM), a programmable ROM, a flash memory, etc. Any memory with a storage function and capable of installing or calling the stored program in the current technology can be used in the method and system of the present invention.

Claims

1. A landfill leakage detection method considering the propagation of stress waves in non-uniform media, wherein a plurality of stress wave sensors are arranged around the landfill to form a distributed stress wave sensor array, a stress wave sensor position vector is established, the propagation velocity of the stress wave is collected, and the obtained data is processed, wherein: (1) A wave velocity model is established, and the wave velocity at a spatial position is expressed as the superposition of a reference wave velocity and a wave velocity deviation, wherein the reference wave velocity is calculated by calibrating the wave velocity values ​​of multiple reference points, and the wave velocity deviation is expressed by expanding the spatial basis function. Meanwhile, the time-varying characteristics of the medium are considered, and a time-varying term is introduced into the wave velocity model. The time-varying term includes an initial disturbance value, an attenuation coefficient, and a random disturbance term. A complete wave velocity model for non-uniform time-varying media is established. The model equation is as follows: , , , ,in, For time, For the spatial position The time-varying wave velocity at is the reference wave speed, It is the spatial location The wave velocity deviation, is the time-dependent wave velocity variation term, For the The calibrated wave velocity value of the reference point, is the number of calibration points, For the The coefficients of the spatial basis functions, For the The spatial basis functions, is the total number of spatial basis functions, is the initial disturbance value, is the attenuation coefficient, is the random disturbance term, is a natural constant in mathematics; (2) Based on the above wave velocity model, the stress wave travel time equation is established. The theoretical travel time is obtained by calculating the Euclidean distance from the leakage source to each stress wave sensor and dividing it by the wave velocity. The Euclidean distance is calculated by the three-dimensional coordinates. Then, the wave velocity estimation error is defined as the square sum of the difference between the measured travel time and the theoretical travel time. The wave velocity is iteratively updated using the gradient descent method. ,in, For the The time step is the spatial position The time-varying wave velocity update at , For the The time step estimation The spatial basis function coefficients, For the The time-varying wave velocity change estimated by the time step, , It is obtained through particle filtering; (3) In the process of locating the leakage source, a weighted objective function is constructed. , ,in, is the objective function with weights, is the total number of stress wave sensors, is the weight of each stress wave sensor, For the The measured travel time of a stress wave sensor, is the Euclidean distance from the leakage source to the stress wave sensor, It is The position vector of the stress wave sensor, is the three-dimensional coordinate of the leakage source, , is the theoretical stress wave propagation time, is the standard deviation parameter, which is used to control the weight decay speed. The gradient descent method is used to update the leakage source position. ,in, is the iteration step length, For the The position estimate of the iteration, For the The position estimate of the iteration, is the gradient of the objective function with respect to the position, and gradient descent is achieved by calculating the gradient of the objective function with respect to the position.

2. The landfill leakage detection method considering the propagation of stress waves in non-uniform media according to claim 1 is characterized in that: The particle filter method is used to solve the wave velocity model, and each particle is predicted and updated through the state transfer equation. The particle weight is calculated and updated based on the measured data, and the relationship equation between the observation value and the state quantity is designed: ,in, For the Time step The stress wave sensor measurement value corresponds to The likelihood probability of a particle is Indicates Time step The state vector of a particle, is twice pi, Represents a natural constant An exponential function with base ; The stress wave travel time equation is solved by numerical integration method.

3. The landfill leakage detection method considering the propagation of stress waves in non-uniform media according to claim 1 is characterized in that: To avoid particle degradation, the number of valid particles is calculated. When the number of valid particles is less than the preset threshold, resampling is performed. A new particle set is generated by calculating the cumulative weight and uniformly sampling within the interval. The system state estimation is calculated based on the current particle set, including the leakage source location estimation, medium parameter estimation and time-varying term estimation. The iteration is stopped when the position estimation change is less than the threshold or the maximum number of iterations is reached.

4. The landfill leakage detection method considering the propagation of stress waves in non-uniform media according to any one of claims 1 to 3, characterized in that: The spatial basis function adopts Gaussian radial basis function, and its expression is: , which expresses the spatial position The non-uniform attenuation characteristics of the wave velocity at For the The center coordinates of the basis functions are distributed in a uniform grid in the landfill area with a grid spacing of ; is the characteristic length parameter; Indicates spatial location arrive Euclidean distance of; number of spatial basis functions and characteristic length The value of is determined based on the actual size of the landfill and the spatial distribution characteristics of the medium heterogeneity.

5. The landfill leakage detection method considering the propagation of stress waves in non-uniform media according to claim 4 is characterized in that: In the initialization stage, the prior distribution of each parameter is set, including setting the initial distribution of the leakage source location to a uniform distribution on the effective area of ​​the landfill, setting the initial distribution of the medium parameter to a normal distribution with a mean of zero vector, and setting the covariance matrix to a constant multiple of the unit matrix. The initial distribution of the time-varying term is also set to a normal distribution with a mean of zero. The initial covariance matrix of the medium parameters is ,in , for Identity matrix.

6. A leakage detection system for implementing the method of claim 5, characterized in that: The invention comprises a plurality of stress wave sensors arranged around the landfill, a signal acquisition and preprocessing module, an adaptive wave velocity estimation module, a leakage source positioning module, and a result display and alarm module, wherein the stress wave sensors are arranged in a rectangular manner around the landfill area, the signal acquisition and preprocessing module collects the stress wave velocity in real time, and performs digital filtering, threshold detection, arrival time extraction and wave velocity estimation on the collected original signal; the adaptive wave velocity estimation module estimates and dynamically updates the wave velocity by calculating the difference between the theoretical propagation time and the measured time according to the preprocessed signal sent by the signal acquisition and preprocessing module, so as to adapt to the change of the medium characteristics; the leakage source positioning module constructs an objective function considering the reliability of the stress wave sensor by using the updated wave velocity value, and accurately estimates the leakage source position by using the gradient descent algorithm until the preset convergence condition is met; the result display and alarm module displays the positioning result in real time on the monitoring interface in a graphical manner, judges whether to trigger an alarm according to the preset value, and saves the detection data in a database for subsequent analysis.

7. The leakage detection system according to claim 6, characterized in that: Signal preprocessing uses a low-pass filter to eliminate noise.

8. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, it is used to implement the method of one of claims 1, 2, 3, and 5 to obtain the location of the leakage source.

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