CSSA-RELM resistivity inversion algorithm, method for monitoring seawater invasion interface by using CSSA-RELM resistivity inversion algorithm, and application of CSSA-RELM resistivity inversion algorithm

Abstract

The invention relates to the technical field of geophysical prospecting and computers, in particular to a CSSA-RELM resistivity inversion algorithm, a method for monitoring a seawater invasion interface through the CSSA-RELM resistivity inversion algorithm and application of the CSSA-RELM resistivity inversion algorithm. According to the CSSA-RELM resistivity inversion algorithm disclosed by the invention, a chaos sparrow search algorithm is utilized to optimize a regularization extreme learning machine, so that the CSSA-RELM resistivity inversion algorithm is formed; according to the characteristics of an inversion algorithm, a sample modeling mode is improved, sample data constraint conditions are added for specific problems, and the inversion precision of seawater intrusion test data is improved; the inversion algorithm is tested and verified by using the simulation data of the seawater intrusion test model in the inhomogeneous medium, and the application value of the extreme learning correlation inversion algorithm in the monitoring and research of the seawater intrusion interface position and the seawater wedge form is improved.

Description

Technical Field

[0001] The present invention relates to the field of geophysical exploration and computer technology, and in particular to a CSSA-RELM resistivity inversion algorithm and a method and application thereof for monitoring a seawater intrusion interface. Background Art

[0002] The phenomenon of seawater intrusion is mainly formed under the combined influence of natural conditions and human activities. On the one hand, there is a density difference between salt water and fresh water in the aquifer (the density of seawater is about 2.5% higher than that of fresh water), so seawater will seep into the fresh water on land, causing seawater intrusion; on the other hand, when the water level of underground fresh water in the land aquifer is higher than the seawater level, the fresh water will seep toward the seawater, thereby preventing the continued invasion of seawater, and the two will eventually reach a dynamic balance.

[0003] The commonly used methods for studying seawater intrusion include analytical methods, numerical simulation methods and physical test methods. When conducting physical simulation tests in the laboratory, it is usually limited by the scale of the model and requires more accurate monitoring methods. In practice, aquifers with pollution problems such as seawater intrusion may be highly heterogeneous, and seawater intrusion is a dynamic process. In actual monitoring, sampling and analysis are often performed through monitoring wells. The measurement process is slow and the accuracy is low. It is also impossible to identify the type and morphology of the salt-fresh water interface. Therefore, choosing a more accurate and convenient monitoring method is a key issue.

[0004] Electrical prospecting is a geophysical exploration method based on the electromagnetic and electrochemical differences between rocks (minerals). High-density electrical method, namely high-density resistivity tomography (ERT), is one of the most commonly used methods in geophysical methods. It has significant advantages in detecting geological structures. There are two types of non-destructive high-density electrical method and inter-well electrical method. It is a two-dimensional or three-dimensional visualization method of underground resistivity distribution. At present, high-density electrical method has been widely used in the seawater intrusion zone of aquifers in vertical two-dimensional images as a powerful means to monitor the interface between salt and fresh water. Some researchers designed indoor test devices for seawater intrusion and tried to use high-density electrical methods to monitor the resistivity changes of the seawater intrusion interface in the physical model of the sand trough, and then studied the migration laws of the salt-fresh water interface. For example, in 2012, Zhao Zhankun et al. simulated the seawater intrusion process in a physical sand trough indoor experiment, and used high-density electrical methods to monitor the salt-fresh water interface, and studied the evolution laws of the mutation interface and the transition zone interface; in 2019, Guo Longfeng used two-dimensional and three-dimensional high-density electrical data in an indoor test device for seawater intrusion to study the migration laws of the seawater intrusion interface under zero head difference and pumping conditions.

[0005] Extreme Learning Machine (ELM), proposed by Huang Guangbin et al. in 2006, is a new and efficient machine learning method. The application of extreme learning machine methods in geophysics, including the study of nonlinear inversion imaging of resistivity, is in its infancy and has been less studied. In 2015, Jiang Feibo et al. used the principal component analysis method to reduce the dimensionality of high-dimensional data and proposed a nonlinear inversion method of principal component-regularized extreme learning machine to invert the high-dimensional exploration data obtained by ultra-high density electrical method. The results show that this method can better solve the problem of nonlinear modeling of high-dimensional data inversion of ultra-high density electrical method, make up for the shortcomings of single device data inversion, and have more accurate inversion results than other nonlinear inversion methods.

[0006] At present, there are few developments and applications of extreme learning machines in resistivity inversion. However, previous studies have shown its advantages in complex models and large-scale data. However, complex optimization models will make the model too complex, which improves accuracy but loses computational efficiency or stability. At the same time, existing studies have confirmed the application value of extreme learning machines in ultra-high-density electrical inversion, but in practical applications, most of them still use high-density electrical methods, especially two-dimensional high-density electrical methods. Summary of the invention

[0007] In order to solve the above-mentioned prior art problems, the present invention provides a CSSA-RELM resistivity inversion algorithm;

[0008] Another object of the present invention is to provide a method for monitoring seawater intrusion interface using CSSA-RELM resistivity inversion algorithm.

[0009] Another object of the present invention is to provide an application of a CSSA-RELM resistivity inversion algorithm.

[0010] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0011] A CSSA-RELM resistivity inversion algorithm comprises the following steps:

[0012] (1) Design a seawater intrusion interface geoelectric model based on the target problem, use Res2dmod software to perform forward simulation, and obtain the extreme learning machine inversion training set ρ 训 With the test set ρ 测 , determine the input layer and output layer;

[0013] (2) Determine the number of hidden layer neurons L and the regularization parameter C;

[0014] (3) Initializing the chaotic sparrow algorithm, including the population size N, the number of discoverers Pnum, the number of sparrows warned Snum, the dimension D of the objective function, the connection weight between the input layer and the hidden layer and the upper and lower bounds lb and ub of the threshold of the hidden layer, and the maximum number of iterations or solution accuracy;

[0015] (4) Use the Tent chaotic sequence to initialize the population and generate N D-dimensional vectors Z i , and move each component carrier to the value range of the original problem space variable;

[0016] (5) Substitute the training sample ρ 训 , train the network to calculate the fitness of each sparrow, select the current optimal fitness and its corresponding position x b , as well as the current worst fitness and its corresponding position x w ;

[0017] (6) Select Pnum sparrows with the best fitness as discoverers and the remaining sparrows as joiners, and update the positions of discoverers and joiners;

[0018] (7) Randomly select Snum sparrows from the sparrow population to conduct reconnaissance and early warning, and update their positions;

[0019] (8) Recalculate the fitness value of each sparrow and the average fitness value of the population;

[0020] (9) If the fitness value of a sparrow is less than the average value, it means that the "aggregation" phenomenon has occurred and Gaussian mutation begins. If the individual after mutation is better than the individual before mutation, the individual after mutation is used to replace the individual before mutation, otherwise the original individual remains unchanged; if the fitness value of a sparrow is greater than or equal to the average value, it means that the "divergence" phenomenon has occurred and Tent chaotic perturbation begins. If the individual after perturbation is better, the individual after perturbation is used to replace the individual before perturbation, otherwise the original individual remains unchanged;

[0021] (10) Update the optimal and worst positions and fitness values ​​of the entire population;

[0022] (11) If the maximum number of iterations or the solution accuracy is reached, the optimization result is output to obtain the globally optimal connection weights between the input layer and the hidden layer and the threshold of the hidden layer; otherwise, return to (6) to continue the loop operation;

[0023] (12) Select the activation function and calculate the output matrix H of the hidden layer and its Moore-Penrose generalized inverse matrix H + ;

[0024] (13) Calculate the weight of the output layer;

[0025] (14) Optimize the parameters of RELM by cross-validation, including activation function, number of hidden layer neurons and regularization parameter. After obtaining the optimal parameters, proceed to the next step, otherwise return to step (2);

[0026] (15) Use the CSSA-RELM obtained after parameter optimization to train and save the trained network;

[0027] (16) Input the test set, use the saved CSSA-RELM to perform inversion test, and output the inverted resistivity results.

[0028] Furthermore, in step (1), according to the conditions of the test sand tank, a geoelectric forward model was designed under the model of the resistivity forward numerical simulation software Res2dmod: samples were collected to test the resistivity value of the saturated fine sand aquifer under different chloride ion concentrations, and a relationship curve between the resistivity of the aquifer and the chloride ion concentration was established; a geoelectric forward model was designed under the model of the resistivity forward numerical simulation software Res2dmod, and a geoelectric model of the seawater intrusion interface was established; and a training set and a test set of the geoelectric model inversion algorithm were constructed.

[0029] Furthermore, step (1) uses the resistivity forward numerical simulation software Res2dmod to perform modeling, and simultaneously generates input data for training the neural network, i.e., apparent resistivity data, and output data for training the neural network, i.e., actual resistivity data.

[0030] Furthermore, in step (1), before importing the sample data set for network training, the sample data should be normalized in advance; the generated apparent resistivity data corresponds one-to-one with the actual resistivity data, and a ten-fold cross-validation method is used in the training.

[0031] Furthermore, in step (2), the values ​​of the hidden layer nodes and the regularization parameter C are set within an appropriate range of values. Under the conditions of different activation functions, the cross-validation method is used to calculate the normalized errors of the training and prediction results of RELM under different L and C.

[0032] Preferably, the hidden layer nodes L are set in the range of [10, 15, 20, ..., 70, 75, 80], and the value of the regularization parameter C is set in the range of [2 -5 ,2 -4.5 ,…,2 2 ,2 2.5 ,2 3 ] within the range of ].

[0033] Furthermore, in step (14), a cross-validation method is used for training to obtain the hidden node set L and regularization parameter C with the minimum validation error as the best RELM parameters.

[0034] Preferably, the activation function includes a Sigmoid function, a Sine function, a hard limit transfer function, a triangular basis function, or a radial basis function.

[0035] Furthermore, the cross-validation method is used to optimize the activation function and the L and C parameters to obtain the optimal determination coefficient R 2 The activation function and L, C parameter values ​​under , and obtain the best modeling performance.

[0036] Preferably, the activation function is a Sigmoid function. When L = 75 and C = 2 -3.5 When ≈0.08839, the Sigmoid function obtains the best determination coefficient R of the cross-validation result. 2 , and obtain the best modeling performance.

[0037] Furthermore, the parameters of the CSSA mainly include the size of the sparrow population, the maximum number of iterations, and the maximum warning value when searching for predators, producers, and searchers.

[0038] A method for monitoring a seawater intrusion interface using a CSSA-RELM resistivity inversion algorithm comprises the following steps: monitoring a seawater intrusion interface and / or monitoring changes in the morphology and resistivity of a salt-fresh water interface according to the CSSA-RELM resistivity inversion algorithm.

[0039] An application of the CSSA-RELM resistivity inversion algorithm in monitoring seawater intrusion interfaces and / or monitoring changes in the morphology and resistivity of freshwater and saltwater interfaces.

[0040] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0041] The imaging result of the CSSA-RELM resistivity inversion algorithm of the present invention is more effective than the traditional least squares inversion method.

[0042] The extreme learning machine of the present invention has considerable research value in the optimization and application of the method for monitoring seawater intrusion interface, and can be used to solve relatively complex resistivity inversion problems with large amounts of data, improve the stability and applicability of the method, and expand its scope of application.

[0043] The present invention utilizes a chaotic sparrow search algorithm to optimize a regularized extreme learning machine to form a CSSA-RELM resistivity inversion algorithm; according to the characteristics of the inversion algorithm, the sample modeling method is improved, sample data constraints are added for specific problems, and the inversion accuracy of seawater intrusion test data is improved; the inversion algorithm is tested and verified using simulated data of a seawater intrusion test model in a non-uniform medium, thereby improving the application value of an extreme learning-related inversion algorithm in monitoring and studying the seawater intrusion interface position and the seawater wedge morphology. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the implementation mode will be briefly introduced below. Obviously, the drawings described below are only some implementation modes of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 It is a schematic diagram of the structure of the extreme learning machine;

[0046] Figure 2 It is a schematic diagram of the uniform medium sand tank test model;

[0047] Figure 3 Schematic diagram of two types of seawater intrusion interface geoelectric models and the corresponding apparent resistivity forward simulation results (a) Abrupt interface model (b) Apparent resistivity forward simulation results of abrupt interface (c) Wedge interface model (d) Apparent resistivity forward simulation results of wedge interface;

[0048] Figure 4 This is a photo of the test sand tank model;

[0049] Figure 5 is the RELM inversion imaging result;

[0050] Figure 6 It is the CSSA-RELM inversion imaging result. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the present application will be clearly and completely described below in conjunction with the drawings of the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the described embodiments, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0052] Unless otherwise defined, the technical terms or scientific terms used in this application should be understood by people with ordinary skills in the field to which this application belongs. "First", "second" and similar words used in this application do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0053] As a new machine learning method, Extreme Learning Machine (ELM) has unique advantages in solving complex models and large-scale data problems. With the subsequent introduction of regularization, the overfitting problem was solved.

[0054] Based on the sparrow search algorithm, the chaotic sparrow search algorithm improves the algorithm's global search capability, avoids the problem of reduced population diversity in the later stages of iteration, and has more advantages in solving complex problems.

[0055] The extreme learning machine uses a single-hidden layer feedforward neural network (SLFNs) as a model, randomly assigns input weights and biases (thresholds) to the network, and uses the Moore-Penrose generalized inverse to calculate output weights based on the least squares criterion. It has a fast convergence speed and is not prone to falling into local extreme values. Therefore, it is suitable for solving resistivity nonlinear inversion problems with complex models and large amounts of data.

[0056] 1. Extreme Learning Machine Algorithm

[0057] For a given training sample {(x i ,t i )i=1,2,...N}, where the input item x i =(x i1 ,x i2 ,...,x in ) T ∈R n , output item t i =(t i1 ,t i2 ,...,t im ) T ∈R mAssuming the number of hidden layer nodes of a single hidden layer feedforward neural network is L and the activation function is g(x), its mathematical model is:

[0058]

[0059] Where, j = 1, 2, ... N, w i =(w i1 ,w i2 ,...,w im ) T is the weight vector between the i-th hidden layer node and the input layer node, β i =(β i1 ,β i2 ,...,β im ) T is the weight vector between the i-th hidden layer node and the output layer node, b i is the threshold of the i-th hidden layer node.

[0060] The objective function of the extreme learning machine is:

[0061]

[0062] In order to find the minimum value of the objective function, the traditional gradient descent learning algorithm uses an iterative method to update the network parameters:

[0063]

[0064] Where W is the set of parameters (ω, β, b) and η is the learning rate.

[0065] The method of extreme learning machine seeks the optimal network parameters to obtain the minimum value of the objective function, avoiding the problem that the iterative method converges slowly and easily falls into local extreme values. The specific method is:

[0066]

[0067] In the formula, β is the output layer weight matrix, that is T is the target output layer matrix, that is

[0068] When the activation function is infinitely differentiable, the weights of the network's input layer and the thresholds of the hidden layer nodes can be randomly assigned, becoming:

[0069]

[0070] After the assignment, the learning of the extreme learning machine is equivalent to solving the least squares solution of Hβ=T If L = N, then the matrix H is a reversible square matrix, and the extreme learning machine can approximate the training samples with zero error; but in general, the number of hidden layer nodes L is much smaller than the number of training samples N. In this case, the minimum norm square solution of Hβ = T is:

[0071]

[0072] In the formula, H + is the generalized inverse Moore-Penrose matrix of H.

[0073] 2. Regularization of Extreme Learning Machine

[0074] A regularization parameter is introduced into the standard extreme learning machine to enhance its stability and generalization ability, forming a regularized extreme learning machine (RELM). The objective function formula is:

[0075]

[0076] Where C is the regularization parameter.

[0077] 3. Activation function of regularized extreme learning machine

[0078] In the process of regularized extreme learning machine learning, the activation function type, the number of hidden nodes and the regularization parameter mainly affect the training and inversion performance of the extreme learning machine.

[0079] Common activation functions:

[0080] (1) Sigmoid function:

[0081]

[0082] (2) Sine function:

[0083]

[0084] (3) Hard limit transfer function:

[0085]

[0086] (4) Triangular basis function:

[0087]

[0088] (5) Radial basis function:

[0089] g(x)=exp(-n 2 ) (12)

[0090] After determining the activation function, the method for selecting the number of hidden layer nodes L and the regularization parameter C is mainly the trial calculation method. L and C are selected within a certain range, and the cross validation (CV) method is used for training. The set of L and C with the lowest validation error or when it reaches the set value is taken as the optimal parameter of RELM.

[0091] 4. Chaotic sparrow search algorithm

[0092] The sparrow algorithm mainly simulates the foraging and anti-predator behavior of sparrows. Sparrows are gregarious birds that are widely distributed around the world and are omnivorous birds. Sparrows are highly gregarious, have strong memories, are very smart and alert, and usually use behavioral strategies flexibly, switching between production and foraging. In order to improve their predation efficiency, sparrows are generally divided into finders (Producers) and joiners (Scroungers). Finders are mainly responsible for finding food in the population and providing foraging directions and areas for the group; joiners are mainly responsible for obtaining food based on the information provided by finders. The sparrow algorithm idealizes and simplifies the behavior of sparrows and formulates corresponding rules, mainly including:

[0093] (1) Discoverers usually have a higher level of energy reserves, the level of which depends on the assessment of the individual's fitness value. They provide foraging directions and areas for all joiners.

[0094] (2) Some hungry joiners may fly to other places to find food to gain more energy. They will follow the finder that can provide the best food to find food. Some joiners may monitor the finder and compete for their food.

[0095] (3) Each sparrow can become a discoverer as long as it can find a better food source. However, in a population, they will keep the ratio of discoverers to joiners stable throughout the population.

[0096] (4) Sparrows’ anti-predator behavior. Once a sparrow discovers a predator, it will begin to make calls as an alarm signal. When the alarm value is greater than the safety threshold, the discoverer will guide all the participants to a safe area.

[0097] (5) When sparrows at the edge of the group sense danger, they will quickly move to a safer area to get a safer position, while sparrows in the middle of the group will walk randomly to get closer to other sparrows.

[0098] The Sparrow Algorithm updates the positions of the discoverer and joiner in each iteration. The expression for updating the discoverer position is:

[0099]

[0100] In the formula, t is the current iteration number, iter max is the maximum number of iterations, α∈(0,1] is a random number, R 2 is the warning value in the range of [0,1], ST is the safety value in the range of [0.5,1], Q is a random number that obeys the normal distribution, L represents a matrix of size 1×d with all elements being 1, and d is the dimension of the variable to be optimized.

[0101] In each iteration, the expression for the joiner position update is:

[0102]

[0103] In the formula, This is the best position for the discoverer at present. is the global worst position, A represents a 1×d matrix whose elements are randomly assigned -1 or 1, A + =A T (AA T ) -1 , n is the number of sparrows. When , it means that the participants with lower fitness have not obtained food and are in a hungry state, so they will fly to other places to find food and obtain energy.

[0104] In addition to the discoverer and joiner, the sparrow algorithm also includes anti-predator position updates. That is, when sparrows discover natural enemies, the sparrows that are aware of the danger will sound an alarm, and when the alarm value is greater than the safety threshold of the group, the sparrow population will produce anti-predator behavior. At this time, the expression for the position update of the sparrows that are aware of the danger is:

[0105]

[0106] In the formula, f is the fitness value, f g is the global optimal fitness value, f w is the global worst fitness value, is the global optimal position, β is the step size control parameter, K is a random number in [-1,1], and ε is a constant.

[0107] In the process of applying the algorithm, you first need to define parameters such as population size, maximum number of iterations, warning value, and the ratio of discoverers to joiners based on experience.

[0108] A Chaos Sparrow Search Optimization Algorithm (CSSA) was proposed. The algorithm firstly used Tent chaotic mapping to initialize the sparrow population so that the initial individuals were distributed as evenly as possible. When the population showed "aggregation" or "divergence" phenomenon, Gaussian mutation and Tent chaotic perturbation were used to adjust the individuals so that they could jump out of the local optimum.

[0109] (1) Initialize the population using Tent chaos map:

[0110] The chaotic variables in the chaotic system have the characteristics of randomness, ergodicity and regularity, and are often used in optimization search problems. In order to avoid the problem that the standard Tent chaotic sequence easily falls into small periodic points or unstable periodic points, random variables are added to the standard Tent mapping:

[0111]

[0112] In the formula, NT is the number of particles in the chaotic order, rand(0,1) is a random number between [0,1], The whole is a random variable term.

[0113] (2) Tent chaos disturbance:

[0114] For the chaos variable Z d , substitute it into the solution space of the problem:

[0115] newX d =min d +(max d -min d )·Z d (18)

[0116] In the formula, min d and max d is the d-th dimension variable newX d The minimum and maximum values ​​of .

[0117] Perform chaotic perturbation on individuals:

[0118]

[0119] X' represents the individual that needs to be disturbed, newX is the amount of chaotic disturbance generated, and newX' is the individual after chaotic disturbance.

[0120] (3) Gaussian variation:

[0121] Gaussian mutation refers to the process of using a mean of μ and a variance of σ in the mutation process. 2Normally distributed random numbers replace the original parameter values. The Gaussian mutation formula is:

[0122] mutation(x)=(1+N(0,1)) (20)

[0123] Where N(0,1) represents a normally distributed random number with an expected value of 0 and a standard deviation of 1.

[0124] Gaussian distribution has strong local search capabilities. In problems with many local minima, using Gaussian distribution to optimize them can better help the algorithm find the global minimum and improve the robustness of the algorithm.

[0125] Example 1

[0126] Design of indoor test model for evolution law of seawater intrusion

[0127] The purpose of the indoor simulation test of seawater intrusion is to reveal the mechanism of seawater intrusion, so as to provide a basis for the prevention and control of seawater intrusion and the rational use of water resources. The design of the sand tank physical model of this embodiment is reasonable and restored, and the parameters are proportional to the parameters of the actual seepage zone, which makes it easier to convert the indoor test results into actual data results through the proportional coefficient.

[0128] According to the boundary conditions, seawater intrusion is generally divided into two types: one is the constant head boundary condition, where the groundwater flow rate through the constant head boundary depends on the properties of the aquifer; the other is the constant flow condition, where the groundwater flow through the constant flow boundary is considered to be known. The constant head boundary condition is the most important factor affecting seawater intrusion. After generalization of the aquifer system, rivers, lakes, etc. are all considered to be constant head boundaries.

[0129] The physical model design of the sand tank in this embodiment meets the following rules:

[0130] (1) When designing the physical model of the sand trough, ensure that the length, width, aquifer thickness, and sea-land boundary head value of the trough are proportional to the various physical quantities in the actual seepage zone.

[0131] (2) It is assumed that the seepage in the aquifer in the model is consistent with that under natural conditions, that is, laminar flow, and that the seepage obeys Darcy’s law.

[0132] (3) Ensure that the trajectory of the liquid particles in the model is similar to that in the natural state, and the time it takes for the liquid particles to flow through the corresponding line segment is proportional to that in the natural state.

[0133] (4) The boundary conditions of the sand tank model should be consistent with those in the natural state, and the infiltration recharge / evaporation consumption of the model should conform to the ratio in nature:

[0134] α ε =α K (twenty one)

[0135] In the formula, α ε is the infiltration intensity proportionality coefficient, α K is the proportionality coefficient with permeability coefficient.

[0136] 1. Physical model of sand tank

[0137] In this embodiment, a physical model of a sand tank with a uniform medium is constructed. The device is mainly used to observe the morphology of the fresh-salt water interface of seawater intrusion in a uniform medium, and serves as the basis for designing a model data set for identifying the type of seawater intrusion interface. In the experiment, the high-density electrical method is used to monitor the resistivity of the sand tank interface.

[0138] like Figure 2 As shown in the figure, the main body of the test device is made of plexiglass. The formation and migration process of the salt-fresh water interface can be clearly seen from the front of the sand trough. The lower part of the trough is placed on a metal bracket for support and is equipped with four pulleys for easy movement.

[0139] The main body of the sand trough consists of three parts from left to right: the trough head (fresh water trough 6), the trough body (sand trough 5, 1.80m long, 0.60m high, 0.10m thick), and the trough tail (sea water trough 4).

[0140] The water troughs on both sides and the sand trough in the middle are evenly drilled with holes and separated by a filter to prevent sand from entering the water trough, but to allow water to flow smoothly into the sand trough.

[0141] The first water head constant device 3 and the second water head constant device 7 are arranged on both sides of the trough head and the trough tail. Water enters the water troughs on both sides, and the water levels of seawater and fresh water on both sides are adjusted through adjustable baffles.

[0142] Two large water barrels are used as the seawater pool 2 and the freshwater pool 1, which are used as water supply sources for the seawater tank 4 and the freshwater tank 6 respectively, and a peristaltic pump connects the pool with the seawater tank and the freshwater tank.

[0143] The peristaltic pump facilitates the uniform supply of water to the constant head water tank. The water level is controlled by the constant head device, so that seawater and fresh water can be evenly and controllably supplied to the sand tank.

[0144] When filling the device, fine sand with a particle size of 1 to 0.5 mm is selected, and fine sand and soil are filled layer by layer. During the filling process, each layer is ensured to be evenly compacted, and fresh water is filled and discharged for saturated sedimentation many times. The filled uniform sand medium area is 1.80m long and 0.55m high.

[0145] The seawater level is controlled by the constant head device on the right side of the seawater tank. Seawater is prepared using anhydrous sodium chloride to simulate the seawater part. A suitable dye is selected and prepared in a bucket in advance, and a peristaltic pump is used to supply water to the seawater tank.

[0146] During the experiment, in order to visually observe the migration and change of the seawater wedge during the seawater intrusion process from the sand tank, this embodiment adds a dye to the seawater for tracing. The dye meets the following requirements: (1) The dye and Cl - The migration rate in the aqueous medium is the same; (2) the dye does not react chemically with NaCl; (3) the dye is not absorbed by the aqueous medium. Therefore, this embodiment selects brilliant blue (bis[4-(N-ethyl-N-3-sulfonylbenzyl)aminophenyl]-2-sulfonyltoluene disodium salt) as the seawater dye, with a concentration of 2g / L. Fresh water is mainly simulated by tap water, and the water level is controlled by a constant head device, which also serves as a transition to reduce the impact of bubbles in the water.

[0147] During the test, the front of the sand trough was photographed to obtain a time-series image of the formation and migration process of the salt-fresh water interface, and the image was post-processed to facilitate the observation of the characteristic values ​​of the seawater wedge shape and area changing over time. In order to ensure the consistency of the image reflecting the salt-fresh water interface, the camera parameters, camera shooting angle and position must be fixed during the test, the curtains must be closed, the fluorescent lamp on the top is used as the light source, and a black cloth is set up between the camera and the front of the sand trough. The side of the sand trough facing the camera receives uniform light to avoid interference with the interface imaging caused by direct photography.

[0148] The top of the sand trough is open to facilitate the layout of high-density electrical electrode probes. The DUK-2A high-density electrical measurement system of Chongqing Geological Instrument Factory was used. According to the model size, 30 electrodes were arranged with a distance of 0.06m between electrodes. Since the size of the indoor test is small and the copper electrodes used in the field test are large, copper wire is used to connect the wires in each cable as a small probe, which is vertically inserted into the surface layer of fine sand in the device. The main instrument and battery are placed on the back of the device to avoid affecting the observation of interface migration. In the electrical measurement, 9 layers of collection and Wenner α device are uniformly set.

[0149] Since the two-dimensional high-density electrical instrument has a high acquisition efficiency and a small number of measurement points, when the interface resistivity in the seawater intrusion test is monitored by the high-density electrical method in this embodiment, the interface advancement and resistivity changes occurring during the measurement process are ignored by default, and the time point when the measurement starts is recorded, and the measurement result is used as the interface resistivity information at that moment.

[0150] A CSSA-RELM resistivity inversion algorithm comprises the following steps:

[0151] (1) Design a seawater intrusion interface geoelectric model based on the target problem, use Res2dmod software to perform forward simulation, and obtain the extreme learning machine inversion training set ρ 训 With the test set ρ 测 , determine the input layer and output layer;

[0152] (2) Determine the number of hidden layer neurons L and the regularization parameter C;

[0153] (3) Initializing the chaotic sparrow algorithm, including the population size N, the number of discoverers Pnum, the number of sparrows warned Snum, the dimension D of the objective function, the connection weight between the input layer and the hidden layer and the upper and lower bounds lb and ub of the threshold of the hidden layer, and the maximum number of iterations or solution accuracy;

[0154] (4) Use the Tent chaotic sequence to initialize the population and generate N D-dimensional vectors Z i , and move each component carrier to the value range of the original problem space variable;

[0155] (5) Substitute the training sample ρ 训 , train the network to calculate the fitness of each sparrow, select the current optimal fitness and its corresponding position x b , as well as the current worst fitness and its corresponding position x w ;

[0156] (6) Select Pnum sparrows with the best fitness as discoverers and the remaining sparrows as joiners, and update the positions of discoverers and joiners;

[0157] (7) Randomly select Snum sparrows from the sparrow population to conduct reconnaissance and early warning, and update their positions;

[0158] (8) Recalculate the fitness value of each sparrow and the average fitness value of the population;

[0159] (9) If the fitness value of a sparrow is less than the average value, it means that the "aggregation" phenomenon has occurred and Gaussian mutation begins. If the individual after mutation is better than the individual before mutation, the individual after mutation is used to replace the individual before mutation, otherwise the original individual remains unchanged; if the fitness value of a sparrow is greater than or equal to the average value, it means that the "divergence" phenomenon has occurred and Tent chaotic perturbation begins. If the individual after perturbation is better, the individual after perturbation is used to replace the individual before perturbation, otherwise the original individual remains unchanged;

[0160] (10) Update the optimal and worst positions and fitness values ​​of the entire population;

[0161] (11) If the maximum number of iterations or the solution accuracy is reached, the optimization result is output to obtain the globally optimal connection weights between the input layer and the hidden layer and the threshold of the hidden layer; otherwise, return to (6) to continue the loop operation;

[0162] (12) Select the activation function and calculate the output matrix H of the hidden layer and its Moore-Penrose generalized inverse matrix H + ;

[0163] (13) Calculate the weight of the output layer;

[0164] (14) Optimize the parameters of RELM by cross-validation, including activation function, number of hidden layer neurons and regularization parameter. After obtaining the optimal parameters, proceed to the next step, otherwise return to step (2);

[0165] (15) Use the CSSA-RELM obtained after parameter optimization to train and save the trained network;

[0166] (16) Input the test set, use the saved CSSA-RELM to perform inversion test, and output the inverted resistivity results.

[0167] In the CSSA-RELM resistivity inversion algorithm of this embodiment, ρ 视 is the apparent resistivity value directly measured by high-density electrical method; ρ 真 is the true resistivity value corresponding to the apparent resistivity value, that is, the final result sought by CSSA-RELM.

[0168] According to the extreme learning machine structure, for a given training sample {(ρ 视i ,ρ 真i )i=1,2,...N}, where the input term ρ 视i =(ρ 视i1 ,ρ 视i2 ,...,ρ 视in ) T ∈R n , the output term ρ 真i =(ρ 真i1 ,ρ 真i2 ,...,ρ 真im ) T ∈R m Assuming the number of hidden layer nodes of a single hidden layer feedforward neural network is L and the activation function is g(ρ), its mathematical model is:

[0169]

[0170] Where, j = 1, 2, ... N, ω i =(ω i1 ,ω i2 ,...,ω im ) T is the weight vector between the i-th hidden layer node and the input layer node, β i =(β i1 ,β i2 ,...,β im ) T is the weight vector between the i-th hidden layer node and the output layer node, b i is the threshold of the i-th hidden layer node.

[0171] The objective function of the extreme learning machine is:

[0172]

[0173] In order to find the minimum value of the objective function, the traditional gradient descent learning algorithm uses an iterative method to update the network parameters:

[0174]

[0175] Where W is the set of parameters (ω, β, b) and η is the learning rate.

[0176] The method of extreme learning machine seeks the optimal network parameters to obtain the minimum value of the objective function, avoiding the problem that the iterative method converges slowly and easily falls into local extreme values. The specific method is:

[0177]

[0178] In the formula, β is the output layer weight matrix, that is ρ true is the target output layer matrix, that is

[0179] When the activation function is infinitely differentiable, the weights of the network's input layer and the thresholds of the hidden layer nodes can be randomly assigned, becoming:

[0180]

[0181] After the assignment, the learning of the extreme learning machine is equivalent to solving Hβ=ρ true The least squares solution of If L = N, then the matrix H is a reversible square matrix, and the extreme learning machine can approximate the training samples with zero error; but in general, the number of hidden layer nodes L is much smaller than the number of training samples N. In this case, Hβ = ρ 真 The minimum norm square solution of is

[83] :

[0182]

[0183] In the formula, H + is the generalized inverse Moore-Penrose matrix of H.

[0184] However, the random assignment of the weights of the input layer and the thresholds of the hidden layer nodes also brings certain uncertainties to network training.

[0185] The chaotic sparrow algorithm is used to optimize the selection and calculation process of the weight vector ω of the input layer and the hidden layer and the hidden layer threshold b:

[0186] First, the conventional sparrow algorithm will update the positions of the discoverer and the joiner in each iteration. The expression for the discoverer position update is:

[0187]

[0188] In the formula, t is the current iteration number, iter max is the maximum number of iterations, α∈(0,1] is a random number, R 2 is the warning value in the range of [0,1], ST is the safety value in the range of [0.5,1], Q is a random number that obeys the normal distribution, L represents a matrix of size 1×d with all elements being 1, and d is the dimension of the variable to be optimized.

[0189] In each iteration, the expression for the joiner position update is:

[0190]

[0191] In the formula, This is the best position for the discoverer at present. is the global worst position, A represents a 1×d matrix whose elements are randomly assigned -1 or 1, A + =A T (AA T ) -1 , n is the number of sparrows. When , it means that the participants with lower fitness have not obtained food and are in a hungry state, so they will fly to other places to find food and obtain energy.

[0192] In addition to the discoverer and joiner, the sparrow algorithm also includes anti-predator position updates. That is, when sparrows discover natural enemies, the sparrows that are aware of the danger will sound an alarm, and when the alarm value is greater than the safety threshold of the group, the sparrow population will produce anti-predator behavior. At this time, the expression for the position update of the sparrows that are aware of the danger is:

[0193]

[0194] In the formula, f is the fitness value, f g is the global optimal fitness value, f w is the global worst fitness value, is the global optimal position, θ is the step size control parameter, K is a random number in [-1,1], and ε is a constant.

[0195] Among them, the fitness function is set to the sum of the mean square error of the training set and the test set:

[0196]

[0197] In the formula, N is the number of training sets, n is the number of test sets, and ρ训T is the expected output value of the training set, ρ 测t is the expected output value of the test set, ρ 训Y is the true output value of the training set, ρ 测y is the true output value of the test set.

[0198] In the process of applying the algorithm, we first need to define the initial value of the algorithm according to the empirical value, including the population size, the maximum number of iterations, the warning value, and the ratio of discoverers to joiners. The chaotic variables in the chaotic system have the characteristics of randomness, ergodicity and regularity, and are often used to optimize search problems. Adding a chaotic algorithm to SSA optimizes the stability and robustness of its search process, forming a chaotic sparrow search algorithm.

[0199] First, the population is initialized using the Tent chaotic map. At the same time, in order to avoid the problem that the standard Tent chaotic sequence easily falls into small periodic points or unstable periodic points, a random variable is added to the standard Tent map. [124,125] :

[0200]

[0201] In the formula, NT is the number of particles in the chaotic order, rand(0,1) is a random number between [0,1], The whole is a random variable term.

[0202] For the chaos variable Z d , Tent chaotic perturbation substitutes it into the solution space of the problem:

[0203] newX d =min d +(max d -min d )·Z d (33)

[0204] In the formula, min d and max d is the d-th dimension variable newX d The minimum and maximum values ​​of .

[0205] Perform chaotic perturbation on individuals:

[0206]

[0207] X' represents the individual that needs to be disturbed, newX is the amount of chaotic disturbance generated, and newX' is the individual after chaotic disturbance.

[0208] The final optimal position X bestThe corresponding weight vector ω between the hidden layer nodes and the output layer nodes and the threshold b of the hidden layer are obtained, and then substituted back into the extreme learning machine RELM for training.

[0209] 3. Model training

[0210] This embodiment establishes RELM and CSSA-RELM resistivity inversion models, and uses the trained network to invert the test results of high-density resistivity measurement results during the seawater intrusion experimental monitoring process.

[0211] (1) Training set and test set

[0212] According to the conditions of the test sand tank, a geoelectric forward model was designed under the model of Res2dmod software.

[0213] Fine sand samples were collected for the test, and the relationship curve between sand resistivity and chloride ion concentration was established based on the resistivity values ​​of the saturated aquifer under different chloride ion concentrations, thereby assisting in establishing the training set and test set of the geoelectric model of the seawater intrusion interface.

[0214] In this embodiment, a total of 402 data sets were established, of which 80% were used as training sets and 20% were used as test sets. In addition, during the modeling process, different conditions were set for the samples, including abrupt interfaces and wedge interfaces.

[0215] Forward modeling of the geoelectric model of seawater intrusion interface Figure 3 shown.

[0216] Output the results of apparent resistivity and true resistivity of the forward model, such as Figure 3 The resistivity forward numerical simulation software Res2dmod is used to build the model, and the input data (i.e., apparent resistivity data) and output data (i.e., actual resistivity data) of the neural network training are generated at the same time.

[0217] Before importing the sample data set for network training, the sample data should be normalized in advance. The generated apparent resistivity data corresponds to the actual resistivity data one by one, and the 10-fold cross-validation method is used to select the activation function and related parameters in the training.

[0218] (2) Training effect

[0219] Before training, the cross-validation method is first used to obtain the activation function, hidden node number set L and regularization parameter C with the smallest validation error as the optimal RELM parameters. By selecting a specific area with larger hidden nodes and smaller regularization parameters, a RELM model with better fitting accuracy and generalization ability can be obtained. In this experiment, the selection of hidden node L is set in the range of [10, 15, 20, ..., 70, 75, 80], and the value of regularization parameter C is set in the range of [2 -5 ,2 -4.5 ,…,2 2 ,2 2.5 ,2 3 ]. Using the cross-validation method under different activation functions, the normalized errors of RELM training and prediction results under different L and C are calculated.

[0220] In order to accurately evaluate the performance of the data set, when the number of hidden layer nodes increases from 10 to 80, the other parameters of each hidden layer node remain unchanged, the RELM network is trained 5 times, and the average of all results is calculated, including the determination coefficient R of training and testing. 2 The average value of .

[0221] Finally, the Sigmoid function was selected as the best activation function for the training network, and when L = 75 and C = 2 -3.5 When ≈0.08839, the Sigmoid function can obtain the best determination coefficient R of the cross-validation results. 2 , and obtain the best modeling performance.

[0222] The parameters of CSSA mainly include the size of the sparrow population, the maximum number of iterations, and the maximum warning value when searching for predators, producers, and searchers. The sparrow population size is set to 80, and the maximum number of iterations is set to 50. For the setting of other parameters, refer to the relevant literature, the lower limit of the weight and threshold is set to -5, the upper limit of the weight and threshold is set to 10, the warning value of the sparrow is set to 0.6, the proportion of producers is set to 0.7, and the rest are entrants. The proportion of sparrows aware of danger in the population is 0.2. Compared with the standard RELM, CSSA-RELM can avoid the randomness of parameter selection in the calculation process, make the model training results more accurate and stable, and improve the training and testing effects after parameter optimization.

[0223] Embodiment 2 Application Example

[0224] A method for monitoring a seawater intrusion interface using a CSSA-RELM resistivity inversion algorithm comprises the following steps: monitoring a seawater intrusion interface and / or monitoring changes in the morphology and resistivity of a salt-fresh water interface according to the CSSA-RELM resistivity inversion algorithm.

[0225] An application of the CSSA-RELM resistivity inversion algorithm in monitoring seawater intrusion interfaces and / or monitoring changes in the morphology and resistivity of freshwater and saltwater interfaces.

[0226] Based on Example 1, this example simulates the situation in the sand tank where the fresh water level on the left is 0.47m, the sea water level is 0.51m, and the head difference on both sides is 0.04m, simulating the invasion phenomenon after the sea water level suddenly rises. Figure 4 As shown in the figure, the high-density resistivity method was used to monitor the changes in the resistivity of the salt-fresh water interface during the experiment.

[0227] The well-trained RELM network and CSSA-RELM network were used to invert the apparent resistivity data and output the inverted resistivity results. The resistivity inversion results were imaged using Surfer11 software and the inversion imaging results were compared. In the inversion imaging map, the area with low resistivity indicates seawater intrusion, while the area with high resistivity indicates the area where seawater intrusion has not yet occurred.

[0228] The approximately wedge-shaped area in front of the low resistivity area represents the morphological characteristics of the seawater wedge, such as Figure 5 shown.

[0229] When the experiment lasted 300 minutes, the end of the seawater wedge in actual observation had crossed the freshwater boundary in the sand box. In the RELM inversion imaging results, the advancement of the seawater wedge in the aquifer can be reflected as the resistivity change of the interface, that is, the resistivity value of the seawater intrusion part on the right side decreases and the area increases. In the CSSA-RELM inversion results, it is also reflected that the resistivity value of the seawater intrusion area gradually decreases and the seawater wedge advances forward, which is consistent with the actual situation. At the same time, the uniformity of the seawater wedge resistivity imaging results is improved compared with the RELM method.

[0230] The application results show that all measured apparent resistivity points are used as input nodes and all model parameters are used as output nodes, which means that the neural network has a large number of input nodes and output nodes, as well as a complex hidden layer structure, so the real resistivity data will not be discarded in the sample modeling. Therefore, the training network of the inversion result can completely invert the real value and fully reflect the situation of uneven apparent resistivity. This embodiment shows that when there are fewer measured data points, the RELM and CSSA-RELM inversion imaging results are more effective than the traditional least squares inversion method. In addition, the RELM and CSSA-RELM inversion imaging results can reflect the morphology of the freshwater interface and the change trend of resistivity.

[0231] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A CSSA-RELM resistivity inversion algorithm, characterized in that: The following steps are involved: (1) Design a seawater intrusion interface geoelectric model based on the target problem, use Res2dmod software to perform forward simulation, and obtain the extreme learning machine inversion training set ρ 训 With the test set ρ 测 , determine the input layer and output layer; (2) Determine the number of hidden layer neurons L and the regularization parameter C; (3) Initializing the chaotic sparrow algorithm, including the population size N, the number of discoverers Pnum, the number of sparrows warned Snum, the dimension D of the objective function, the connection weight between the input layer and the hidden layer and the upper and lower bounds lb and ub of the threshold of the hidden layer, and the maximum number of iterations or solution accuracy; (4) Use the Tent chaotic sequence to initialize the population and generate N D-dimensional vectors Z i , and move each component carrier to the value range of the original problem space variable; (5) Substitute the training sample ρ 训 , train the network to calculate the fitness of each sparrow, select the current optimal fitness and its corresponding position x b , as well as the current worst fitness and its corresponding position x w ; (6) Select Pnum sparrows with the best fitness as discoverers and the remaining sparrows as joiners, and update the positions of discoverers and joiners; (7) Randomly select Snum sparrows from the sparrow population to conduct reconnaissance and early warning, and update their positions; (8) Recalculate the fitness value of each sparrow and the average fitness value of the population; (9) If the fitness value of a sparrow is less than the average value, it means that the "aggregation" phenomenon has occurred and Gaussian mutation begins. If the individual after mutation is better than the individual before mutation, the individual after mutation is used to replace the individual before mutation, otherwise the original individual remains unchanged. If the fitness value of a sparrow is greater than or equal to the average value, it means that the "divergence" phenomenon has occurred and Tent chaotic perturbation begins. If the individual after perturbation is better, the individual after perturbation is used to replace the individual before perturbation, otherwise the original individual remains unchanged. (10) Update the optimal and worst positions and fitness values ​​of the entire population; (11) If the maximum number of iterations or the solution accuracy is reached, the optimization result is output to obtain the globally optimal connection weights between the input layer and the hidden layer and the threshold of the hidden layer; otherwise, return to (6) to continue the loop operation; (12) Select the activation function and calculate the output matrix H of the hidden layer and its Moore-Penrose generalized inverse matrix H + ; (13) Calculate the weight of the output layer; (14) Optimize the parameters of RELM by cross-validation method, including activation function, number of hidden layer neurons and regularization parameter. After obtaining the optimal parameters, proceed to the next step, otherwise return to step (2); (15) Use the CSSA-RELM obtained after parameter optimization to train and save the trained network; (16) Input the test set, use the saved CSSA-RELM to perform inversion test, and output the inverted resistivity results.

2. The CSSA-RELM resistivity inversion algorithm according to claim 1, characterized in that: In step (1), according to the conditions of the test sand tank, the resistivity values ​​of the saturated fine sand aquifer under different chloride ion concentrations are tested, and a relationship curve between the resistivity of the aquifer and the chloride ion concentration is established; a geoelectric forward model is designed under the model of the resistivity forward numerical simulation software Res2dmod, and a geoelectric model of the seawater intrusion interface is established; and a training set and a test set of the geoelectric model inversion algorithm are constructed.

3. The CSSA-RELM resistivity inversion algorithm according to claim 1, characterized in that: Step (1) uses the resistivity forward numerical simulation software Res2dmod to build a model and generate input data for training the neural network, i.e., apparent resistivity data, and output data for training the neural network, i.e., actual resistivity data.

4. The CSSA-RELM resistivity inversion algorithm according to claim 1, characterized in that: In step (1), before importing the sample data set for network training, the sample data should be normalized in advance; the generated apparent resistivity data corresponds one-to-one with the actual resistivity data, and the cross-validation method is used in the training.

5. The CSSA-RELM resistivity inversion algorithm according to claim 1, characterized in that: In step (2), the values ​​of the hidden layer node L and the regularization parameter C are set within an appropriate range; under the conditions of different activation functions, the cross-validation method is used to calculate the normalized errors of the training and prediction results of RELM under different L and C.

6. The CSSA-RELM resistivity inversion algorithm according to claim 1, characterized in that: In step (14), the cross-validation method is used for training to obtain the hidden node set L and regularization parameter C with the smallest validation error as the best RELM parameters.

7. The CSSA-RELM resistivity inversion algorithm according to claim 6, characterized in that: Through the cross-validation method, the activation function and L and C parameters are optimized to obtain the best determination coefficient R 2 The activation function and L, C parameter values ​​under , and obtain the best modeling performance.

8. The CSSA-RELM resistivity inversion algorithm according to claim 5, characterized in that: The parameters of the CSSA mainly include the sparrow population size, the maximum number of iterations, and the maximum warning value when searching for predators, producers, and searchers.

9. A method for monitoring seawater intrusion interface using CSSA-RELM resistivity inversion algorithm, characterized in that: The method comprises the following steps: monitoring the seawater intrusion interface and / or monitoring the morphology and resistivity changes of the salt-fresh water interface according to the CSSA-RELM resistivity inversion algorithm described in any one of claims 1 to 8.

10. An application of the CSSA-RELM resistivity inversion algorithm in monitoring seawater intrusion interfaces and / or monitoring changes in the morphology and resistivity of fresh-salt water interfaces.

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