Method and device for determining dam displacement monitoring index

Abstract

The present disclosure provides a method and device for formulating a dam displacement monitoring index, relating to the technical field of dam safety monitoring. The method includes: establishing a finite element model of the dam to be monitored, and determining target material parameters based on the finite element model; performing a random field simulation on the target material parameters, and conducting a stochastic finite element analysis on the simulated parameter random field to obtain the probability density distribution of the dam body displacement at different water levels; determining the displacement statistical value and displacement confidence interval at each water level according to the probability density distribution of each dam body displacement; fitting to obtain the water pressure component and its interval value based on the displacement statistical value and displacement confidence interval, constructing a dam displacement monitoring hybrid model in combination with the temperature component and the aging component, and calculating the dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value. By considering the uncertainty of the dam body material, the present disclosure formulates the dam displacement monitoring index, and can accurately achieve the dynamic monitoring and early warning of the dam.

Description

Technical Field

[0001] The present disclosure relates to the technical field of dam safety monitoring. Specifically, it relates to a method and device for formulating dam displacement monitoring indexes. Background Technique

[0002] With the gradual acceleration of dam construction, how to deeply carry out dam safety monitoring work, fully explore the hidden information contained in safety monitoring data, and quickly and accurately grasp the operational behavior of the dam has become particularly important. Among them, dam displacement monitoring can more intuitively and accurately reflect the safety state of the dam body structure. Therefore, displacement monitoring is one of the most important monitoring items in dam safety monitoring.

[0003] When conducting dam displacement monitoring, the ability of the dam to resist possible loads can be evaluated and predicted by formulating monitoring indexes, so as to determine the warning value and extreme value of the effect quantity under this load combination. At present, the commonly used methods for formulating dam displacement monitoring indexes include the confidence interval method, the typical small probability method, etc. Among them, the confidence interval method and the typical small probability method belong to mathematical statistics methods, which are based on statistical probability theory and evaluate dam monitoring indexes based on existing monitoring data, and have the advantages of simple method and easy operation. However, in the initial stage of project operation, when the dam displacement monitoring data is scarce and has not experienced the most unfavorable load conditions, the monitoring indexes formulated by using the confidence interval method and the typical small probability method are not the extreme states in reality. At the same time, the monitoring indexes established based on mathematical statistics methods do not connect the mechanical characteristics and deformation mechanism of the dam structure, and their physical concepts are not clear, so they are not suitable for formulating dam monitoring indexes in the initial operation stage.

[0004] Therefore, there is an urgent need to provide a new scheme for formulating dam displacement monitoring indexes to accurately and comprehensively reflect the true operational behavior of the dam.

[0005] It should be noted that the information disclosed in the above background technique section is only used to strengthen the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The purpose of the embodiments of the present disclosure is to provide a method and device for formulating dam displacement monitoring indexes, so as to at least to a certain extent solve the problem in the related art that it is difficult to accurately and comprehensively reflect the true operational behavior of the rockfill dam due to the deviation of the formulated dam displacement monitoring indexes.

[0007] According to the first aspect of the embodiments of the present disclosure, a method for formulating dam displacement monitoring indexes is provided, including:

[0008] Establish a finite element model of the dam to be monitored, and determine the target material parameters based on the finite element model;

[0009] Perform a random field simulation on the target material parameters, and conduct a stochastic finite element analysis of the simulated parameter random field at different water levels to obtain the probability density distribution of the dam displacement at each water level;

[0010] Determine the displacement statistical values and displacement confidence intervals at each water level according to the probability density distributions of the dam displacements;

[0011] Fit the water pressure component and the water pressure component interval value based on the displacement statistical values and the displacement confidence intervals;

[0012] Construct a hybrid model for dam displacement monitoring by combining the temperature component, the aging component and the water pressure component, and calculate the dam displacement monitoring index based on the hybrid model for dam displacement monitoring and the water pressure component interval value.

[0013] In an exemplary embodiment of the present disclosure, the performing a random field simulation on the target material parameters, and conducting a stochastic finite element analysis of the simulated parameter random field at different water levels to obtain the probability density distribution of the dam displacement at each water level includes:

[0014] Perform a random field simulation on the target material parameters of each material zone in the dam to be monitored to obtain the corresponding simulated random field;

[0015] Assign each simulated random field to the corresponding dam element in the finite element model to obtain the parameter random field of the dam to be monitored;

[0016] Conduct a stochastic finite element analysis of the parameter random field at different water levels to obtain the dam measuring point displacements at each water level, and obtain the probability density distribution of the dam displacement at each water level by statistically analyzing the dam measuring point displacements.

[0017] In an exemplary embodiment of the present disclosure, the simulated random field includes a correlated lognormal random field;

[0018] The performing a random field simulation on the target material parameters of each material zone in the dam to be monitored to obtain the corresponding simulated random field includes:

[0019] Generate a standard Gaussian random field according to the statistical distribution characteristics of the target material parameters and the spatial correlation defined by the Gaussian autocorrelation function;

[0020] Decompose the correlation coefficient matrix of the random variables in the standard Gaussian random field, calculate the correlated standard Gaussian random field according to the decomposition result and the correlated standard normal random sample matrix, and perform an equiprobability transformation on the correlated standard Gaussian random field to generate the correlated lognormal random field.

[0021] In an exemplary embodiment of the present disclosure, the displacements of the dam body measurement points include the first dam body measurement point displacement, the second dam body measurement point displacement, the third dam body measurement point displacement, and the fourth dam body measurement point displacement;

[0022] Performing stochastic finite element analysis on the parameter random field at different water levels to obtain the displacements of the dam body measurement points at each water level, and obtaining the probability density distribution of the dam body displacements at each water level by statistically analyzing the displacements of the dam body measurement points, includes:

[0023] Performing stochastic finite element analysis on the parameter random field at different water levels to obtain the first dam body measurement point displacement at each water level;

[0024] Establishing a stochastic simulation surrogate model using the target material parameters and the first dam body measurement point displacement, and fitting the second dam body measurement point displacement at each water level using the stochastic simulation surrogate model;

[0025] Comparing the statistical eigenvalue errors between the first dam body measurement point displacement and the second dam body measurement point displacement;

[0026] If the statistical eigenvalue error is greater than a preset difference, increasing the number of the parameter random fields, and performing stochastic finite element analysis on the adjusted number of parameter random fields at different water levels to obtain the third dam body measurement point displacement;

[0027] Reconstructing and fitting the stochastic simulation surrogate model based on the third dam body measurement point displacement to obtain the fourth dam body measurement point displacement;

[0028] If the statistical eigenvalue error between the third dam body measurement point displacement and the fourth dam body measurement point displacement is less than or equal to the preset difference, obtaining the probability density distribution of the dam body displacements at each water level by statistically analyzing the third dam body measurement point displacement and the fourth dam body measurement point displacement.

[0029] In an exemplary embodiment of the present disclosure, the obtaining the probability density distribution of the dam body displacements at each water level by statistically analyzing the third dam body measurement point displacement and the fourth dam body measurement point displacement, includes:

[0030] Performing stability detection using the third dam body measurement point displacement and the fourth dam body measurement point displacement at each water level to obtain the target random field simulation times when the dam body measurement point displacement is in a stable state;

[0031] Statistically analyzing the dam body measurement point displacements corresponding to the target random field simulation times to obtain the probability density distribution of the dam body displacements at each water level.

[0032] In an exemplary embodiment of the present disclosure, the displacement statistical values include displacement mean and displacement standard deviation;

[0033] Determining the displacement statistical value and displacement confidence interval at each water level according to the probability density distribution of each dam body displacement includes:

[0034] Performing statistical analysis on the probability density distribution of each dam body displacement, and calculating the corresponding displacement mean and displacement standard deviation;

[0035] Determining the boundary values of the displacement confidence interval according to the displacement mean and displacement standard deviation, and in combination with the significance level.

[0036] In an exemplary embodiment of the present disclosure, fitting the water pressure component and the water pressure component interval value based on the displacement statistical value and the displacement confidence interval includes:

[0037] Performing polynomial fitting on the displacement means at different water levels to generate a water pressure component related to the water level;

[0038] Performing polynomial fitting on the boundary values of the displacement confidence intervals at different water levels to generate the corresponding water pressure component interval values.

[0039] In an exemplary embodiment of the present disclosure, the dam displacement monitoring hybrid model includes an original dam displacement monitoring hybrid model and a target dam displacement monitoring hybrid model;

[0040] Combining the temperature component, the aging component and the water pressure component to construct a dam displacement monitoring hybrid model, and calculating the dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value includes:

[0041] Taking the environmental quantities corresponding to the temperature component, the aging component and the water pressure component as independent variables, and taking the dam body measuring point displacement as the dependent variable, to construct the original dam displacement monitoring hybrid model;

[0042] Performing fitting analysis on each component in the original dam displacement monitoring hybrid model by using the displacement monitoring data and environmental quantity monitoring data of the dam to be monitored, to obtain the undetermined coefficients in the original dam displacement monitoring hybrid model;

[0043] Based on the undetermined coefficients, obtaining the target dam displacement monitoring hybrid model, and substituting the water pressure component interval value into the target dam displacement monitoring hybrid model to obtain the dam displacement monitoring index of the dam to be monitored at a preset significance level.

[0044] In an exemplary embodiment of the present disclosure, establishing a finite element model of the dam to be monitored, and determining the target material parameters based on the finite element model includes:

[0045] Obtaining the engineering data of the dam to be monitored, and establishing the finite element model of the dam to be monitored according to the engineering data;

[0046] Determine the constitutive models adopted for each material partition divided in the finite element model, and select target material parameters from the constitutive models.

[0047] According to the second aspect of the embodiments of the present disclosure, there is provided a device for formulating a dam displacement monitoring index, including:

[0048] A material parameter determination module, configured to establish a finite element model of a dam to be monitored, and determine target material parameters based on the finite element model;

[0049] A parameter stochastic simulation module, configured to perform a random field simulation on the target material parameters, and perform a stochastic finite element analysis on the simulated parameter random field at different water levels to obtain the probability density distribution of the dam displacement at each water level;

[0050] A probability density statistics module, configured to determine the displacement statistical value and the displacement confidence interval at each water level according to each of the probability density distributions of the dam displacement;

[0051] A water pressure component determination module, configured to fit a water pressure component and a water pressure component interval value based on the displacement statistical value and the displacement confidence interval;

[0052] A monitoring index determination module, configured to construct a dam displacement monitoring hybrid model by combining a temperature component, an aging component and the water pressure component, and calculate a dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value.

[0053] According to the third aspect of the present disclosure, there is provided a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, any step of the method for formulating a dam displacement monitoring index described in the first aspect is implemented.

[0054] According to the fourth aspect of the present disclosure, there is provided an electronic device, including:

[0055] A processor and a memory, on which computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, any step of the method for formulating a dam displacement monitoring index described in the first aspect is implemented.

[0056] The technical solutions provided by the embodiments of the present disclosure may include the following beneficial effects:

[0057] In the exemplary embodiments of the present disclosure, the method for formulating the dam displacement monitoring index first uses a finite element model and random field simulation to consider the spatial uncertainty of the dam body material, obtains the displacement distribution under different water levels, can effectively capture the random characteristics of the dam body displacement, and thus more accurately predict the displacement behavior of the dam. Secondly, by analyzing the displacement probability density distribution under each water level, the displacement mean value and confidence interval are obtained, which dynamically reflects the influence of different water levels on the dam body displacement, and can provide an accurate displacement range and uncertainty assessment for real-time monitoring. Further, the water pressure component is obtained by fitting the displacement statistical value and the confidence interval, and combined with temperature and aging factors, a hybrid model for dam displacement monitoring is constructed. The monitoring index calculated based on this model and the water pressure component interval can accurately and comprehensively reflect the true operation state of the dam, provide a reliable early warning index, and timely identify abnormal dam body displacement.

[0058] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. Brief Description of the Drawings

[0059] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0060] Figure 1 The system architecture diagram of a method for formulating the dam displacement monitoring index according to an embodiment of the present disclosure is shown.

[0061] Figure 2 The flow schematic diagram of a method for formulating the dam displacement monitoring index according to an embodiment of the present disclosure is shown.

[0062] Figure 3 The schematic diagram of the cross-section and material zoning of the finite element model of a rockfill dam according to an embodiment of the present disclosure is shown.

[0063] Figure 4 The flow schematic diagram of a method for statistically analyzing the probability density distribution of the dam body displacement under each water level according to an embodiment of the present disclosure is shown.

[0064] Figure 5 The flow schematic diagram of another method for statistically analyzing the probability density distribution of the dam body displacement under each water level according to an embodiment of the present disclosure is shown.

[0065] Figure 6 The flow schematic diagram of a method for determining the dam displacement monitoring index according to an embodiment of the present disclosure is shown.

[0066] Figure 7 The flowchart of another method for formulating the dam displacement monitoring index in the embodiments of the present disclosure is shown.

[0067] Figure 8 The schematic diagram of a device for formulating the dam displacement monitoring index in the embodiments of the present disclosure is shown.

[0068] Figure 9 The schematic diagram of the structure of an electronic device suitable for implementing the embodiments of the present disclosure is shown.

[0069] In the drawings, the same or corresponding reference numerals indicate the same or corresponding parts. Detailed implementation manners

[0070] The terms used in this specification are for the purpose of describing specific embodiments only and are not intended to limit this specification. The singular forms "a", "said" and "the" used in this specification and the appended claims are also intended to include the plural forms unless the context clearly dictates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0071] It should be understood that although the terms first, second, third, etc. may be used in this specification to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of this specification, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "when" or "while" or "in response to determining".

[0072] Figure 1 The schematic diagram of the system architecture of a method for formulating the dam displacement monitoring index to which the embodiments of the present disclosure can be applied is shown.

[0073] As Figure 1 shown, the system architecture 100 may include one or more of terminal devices such as a smart phone 101, a portable computer 102, a desktop computer 103, etc., a network 104, and a server 105. The network 104 is a medium for providing a communication link between the terminal device and the server 105. The network 104 may include various connection types, such as wired, wireless communication links, or fiber optic cables, etc.

[0074] The terminal device can be various electronic devices with data processing functions. There is a display screen on the electronic device, which is used to show the user the finite element model of the dam to be monitored, the distribution of dam body displacement monitoring points, the results of random field simulation, the water pressure components and the intervals of water pressure components, as well as the dam displacement monitoring indicators, etc. The electronic device includes, but is not limited to, the above-mentioned desktop computers, portable computers, smart phones, tablet computers, and so on.

[0075] It should be understood that Figure 1 the numbers of the terminal devices, networks and servers in

[0076] The method for formulating the dam displacement monitoring index provided by the embodiments of the present disclosure can be executed by the terminal device. Correspondingly, the device for formulating the dam displacement monitoring index can be set in the terminal device. However, it is easy for those skilled in the art to understand that the method for formulating the dam displacement monitoring index provided by the embodiments of the present disclosure can also be executed by the server 105. Correspondingly, the device for formulating the dam displacement monitoring index can also be set in the server 105. No special limitation is made in this exemplary embodiment.

[0077] It should be noted that the method for formulating the dam displacement monitoring index also includes a structural analysis method. This method uses the finite element method to establish a model, simulates the stress characteristics of the dam, has clear physical concepts, can calculate the deformation and stress changes of the dam body under various working conditions, and then simulates the load conditions that have never been encountered. Therefore, it is more suitable for formulating the dam displacement monitoring index in the initial operation stage of the dam.

[0078] Taking a rockfill dam as an example, the displacement monitoring index can be determined by using the mechanical parameters of the rockfill body material. For example, indoor geotechnical test parameters are used for structural calculation, and the water pressure component is determined accordingly. However, in actual engineering, affected by factors such as geological exploration, geotechnical tests, design assumptions, construction techniques and construction conditions, there are certain uncertainties and random distribution characteristics in the physical properties (density, void ratio, average particle size, etc.) and mechanical parameters of the rockfill body material. If these uncertainties are ignored in safety monitoring and evaluation, it will have a serious impact on the prediction of dam deformation and the analysis of dam safety, resulting in deviations in the dam displacement monitoring index, and thus it is difficult to accurately and comprehensively reflect the true operating state of the dam.

[0079] Based on the above one or more problems, the embodiments of the present disclosure provide a method for formulating a dam displacement monitoring index. By considering the uncertainty of the dam body material, the dam displacement monitoring index can be accurately formulated, and the dynamic monitoring and early warning of the dam can be realized. Taking the execution by the server as an example below, this method will be described. Refer to Figure 2As shown, the method may include steps S210 to S250:

[0080] Step S210, establish a finite element model of the dam to be monitored, and determine the target material parameters based on the finite element model;

[0081] Step S220, perform a random field simulation on the target material parameters, and conduct a stochastic finite element analysis of the simulated parameter random field at different water levels to obtain the probability density distribution of the dam body displacement at each water level;

[0082] Step S230, determine the displacement statistical value and displacement confidence interval at each water level according to the probability density distribution of each dam body displacement;

[0083] Step S240, fit the water pressure component and the water pressure component interval value based on the displacement statistical value and the displacement confidence interval;

[0084] Step S250, construct a dam displacement monitoring hybrid model by combining the temperature component, the aging component and the water pressure component, and calculate the dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value.

[0085] When implementing the method for formulating the dam displacement monitoring index provided by the present disclosure, first, by using the finite element model and random field simulation, considering the spatial uncertainty of the dam body material, the displacement distribution at different water levels is obtained, which can effectively capture the random characteristics of the dam body displacement, thereby more accurately predicting the displacement behavior of the dam. Second, by analyzing the probability density distribution of the displacement at each water level, the displacement mean value and confidence interval are obtained, which can dynamically reflect the influence of different water levels on the dam body displacement, and can provide an accurate displacement range and uncertainty assessment for real-time monitoring. Further, the water pressure component is obtained by fitting the displacement statistical value and the confidence interval, and combined with the temperature and aging factors, a dam displacement monitoring hybrid model is constructed. The monitoring index calculated based on this model and the water pressure component interval can accurately and comprehensively reflect the true operation state of the dam, and provide a reliable early warning index to timely identify abnormal dam body displacement.

[0086] Next, the method for formulating the dam displacement monitoring index in this exemplary embodiment will be described in detail.

[0087] In step S210, a finite element model of the dam to be monitored is established, and the target material parameters are determined based on the finite element model.

[0088] In the exemplary embodiment of the present disclosure, the dam to be detected may be a homogeneous earth dam, a clay core earth dam, a clay inclined wall dam, an asphalt concrete core wall, a rockfill dam, etc., and the present disclosure does not limit the type of the dam to be detected.

[0089] Exemplarily, engineering data of a dam to be monitored can be obtained, and a finite element model of the dam to be monitored can be established based on the engineering data. Then, the constitutive models adopted for each material zone divided in the finite element model are determined, and target material parameters are selected from the constitutive models. Among them, the constitutive models include linear elastic constitutive model, non-linear elastic constitutive model, plastic constitutive model, viscoelastic constitutive model, elastoplastic constitutive model, damage constitutive model, etc.

[0090] Taking the concrete face rockfill dam (abbreviated as rockfill dam) to be detected as an example for illustration. Among them, the engineering data of the rockfill dam includes engineering plane layout drawings, dam profile design drawings, dam body deformation monitoring layout drawings, dam construction progress reports, etc. According to the engineering data of the rockfill dam, the zoning of different materials inside the dam, the layered rolling construction conditions, and the layout and installation conditions of dam body displacement monitoring points can be determined, and thus a finite element model of the rockfill dam that conforms to the engineering reality can be established.

[0091] The calculation units in the finite element model of the dam to be monitored can adopt quadrilateral units or hexahedron units. For example, the size of the unit mesh is 1 / 20 - 1 / 30 of the dam height, and it should not exceed 10m. A fixed boundary is set at the bottom of the finite element model, a water pressure boundary is set on the upstream face slab, and at the same time, the layered filling method is set by simulating the construction steps, and the water pressure load loading method is set by simulating the staged impoundment.

[0092] Reference Figure 3 As shown, a schematic cross-section of a finite element model of a rockfill dam is given. The inside of the dam body is zoned according to the actual project. The material zones of this finite element model include concrete face slab, toe slab, extrusion wall, cushion layer, transition layer, upstream rockfill zone, main rockfill zone, and downstream rockfill zone. It can be understood that a plurality of dam body displacement monitoring points corresponding to the layout positions of the dam body displacement monitoring points on the rockfill dam are provided on the finite element model to facilitate the screening of monitoring data.

[0093] In an exemplary embodiment, the constitutive model adopted for each material zone selects the Duncan-Chang EB model in the non-linear elastic constitutive model. Specifically, the material parameters in the Duncan-Chang EB model include cohesion C , initial internal friction angle φ 0 , internal friction angle increment △ φ , initial tangent modulus intercept K , initial tangent modulus slope n , tangent bulk modulus intercept K b , tangent bulk modulus slope m , unloading modulus intercept K ur and failure ratio R f . Among them, the cohesion of the rockfill bodyC Generally, it is 0. For the remaining material parameters except the cohesion C the intercept of the tangent bulk modulus K b the initial internal friction angle φ 0 and the slope of the initial tangent modulus n have significant effects on the dam displacement. These three material parameters are the target material parameters. Therefore, to improve the analysis efficiency, in the exemplary embodiments of the present disclosure, only the target material parameters K b , φ 0 , n of each material zone of the dam are subjected to random field simulation, and the test values are used for the remaining material parameters.

[0094] In step S220, a random field simulation is performed on the target material parameters, and a stochastic finite element analysis is performed on the obtained parameter random field under different water levels to obtain the probability density distribution of the dam displacement at each water level.

[0095] It should be noted that since the change in the dam displacement mainly comes from the displacement of the rockfill, in the exemplary embodiments of the present disclosure, only the target material parameters K b , φ 0 , n of the three material zones of the upstream rockfill zone, the main rockfill zone, and the downstream rockfill zone are respectively subjected to random field simulation. Among them, the random field simulation refers to generating a variable distribution with randomness and spatial correlation within a spatial or temporal range by using probability and statistics methods to simulate the physical parameters with uncertainty and spatial variability in the real world. In the embodiments of the present disclosure, it is used to simulate the parameter variability and correlation of soil and rock materials within a spatial range.

[0096] In one exemplary embodiment, as shown in Figure 4 step S220 may further include steps S410 to S430:

[0097] Step S410, performing a random field simulation on the target material parameters of each material zone of the dam to be monitored to obtain the corresponding simulated random field.

[0098] For the three material zones of the upstream rockfill zone, the main rockfill zone, and the downstream rockfill zone, it is assumed that the numerical distributions of the target material parameters K b , φ 0 , n all follow the lognormal distribution ln X ~ N (μ 1 , σ 1 2 ). For example, under the standard normal distribution space, the mean value of the material parameters μ 1 Adopting the values of the indoor geotechnical test parameters of each material, the coefficient of variation of the material parameters in the upstream rockfill area and the main rockfill area is 0.1, and the coefficient of variation of the material parameters in the downstream rockfill area is 0.2. The standard deviation σ 1 = μ 1 C v , C v where is the coefficient of variation of the material parameters. Among them, the autocorrelation distance of the rockfill material is 10 m (vertical) and 100 m (horizontal, transverse river direction).

[0099] In an exemplary embodiment, the simulated random field obtained by random field simulation includes a correlated lognormal random field. Exemplarily, a standard Gaussian random field can be generated according to the statistical distribution characteristics of the target material parameters and the spatial correlation defined by the Gaussian autocorrelation function, and then the correlation coefficient matrix of the random variables in the standard Gaussian random field is decomposed. According to the decomposition result and the correlated standard normal random sample matrix, a correlated standard Gaussian random field is calculated, and an equiprobability transformation process is performed on the correlated standard Gaussian random field to generate a correlated lognormal random field. Among them, the statistical distribution characteristics of the target material parameters can correspondingly include the mean value of the material parameters μ 1 , standard deviation σ 1 and the coefficient of variation of the material parameters C v . It should be noted that these three physical quantities are also the eigenvalue parameters of the target material parameter random field at the same time.

[0100] Specifically, the random field simulation method based on Cholesky decomposition (square root method) can be used to perform U times of random field simulation on the target material parameters in each material zone respectively. Among them, in order to simulate the parameter uncertainty and correlation of the rockfill material within the spatial range, the correlation degree between two points in space of a soil parameter is represented by the autocorrelation coefficient ρ to describe the autocorrelation between soil parameters at different spatial positions within the random field:

[0101] (1)

[0102] where , are the central point coordinates , The eigenvalues of the random field unit grid parameter distribution, COV( ) is the covariance of the grid parameter distribution, and Var( ) is the variance of the grid parameter distribution.

[0103] It should be noted that the autocorrelation function shown in formula (1) assumes that the random field follows the stationary hypothesis or the quasi-stationary hypothesis, that is, the mean and variance of the soil parameters are independent of the spatial position of the random field, and the autocorrelation function is only related to the relative distance between two spatial points. Since the on-site measured data is relatively scarce, the theoretical correlation function can be used to describe the autocorrelation between material parameters. Among them, the Gaussian correlation function has good stationarity. Therefore, the autocorrelation coefficient ρ can be expressed as:

[0104] (2)

[0105] Where is the horizontal relative distance, , is the vertical relative distance, , is the horizontal transverse relative distance, , , , are the fluctuation ranges in three directions respectively.

[0106] In addition to the autocorrelation of the same soil parameter, there is also cross-correlation between different soil parameters, which can also be calculated by the Gaussian correlation function shown in formula (2), so as to obtain the autocorrelation coefficient matrix and the cross-correlation coefficient matrix.

[0107] It should be noted that when using the lognormal distribution to describe the distribution of geotechnical mechanical parameters, it is necessary to generate the relevant lognormal random field through the Nataf transformation on the basis of the standard Gaussian random field to show the autocorrelation and cross-correlation between soil parameters. Among them, the Nataf transformation refers to converting the original random variable into a standard normal random variable. The decomposition of the autocorrelation coefficient matrix and the cross-correlation coefficient matrix in the random field transformation process are both carried out in the standard normal space. Since the equiprobability transformation is a non-linear transformation process in different spaces, the correlation coefficient between soil parameters will change during the transformation process. Therefore, it is necessary to calculate the equivalent correlation coefficient in the standard normal space:

[0108] (3)

[0109] Where is the equivalent autocorrelation coefficient of the standard normal random variable, SN (Standard Normal) represents the standard normal space, is the autocorrelation coefficient of the original random variable, is the equivalent cross - correlation coefficient of the standard normal random variable, is the cross - correlation coefficient of the original random variable, and are the eigenvalues of the distribution of the random field cell grid parameters of the center point coordinates and respectively, and are the simulated values of the cell parameter Gaussian random field with the center point coordinates being and respectively, is the equivalent cross - correlation coefficient 's two - dimensional joint probability density function, μ H and σ H are the mean and standard deviation of the random field respectively, k i,j is the autocorrelation correction coefficient. Since the difference between the equivalent autocorrelation coefficient and the original autocorrelation coefficient has little impact on the calculation results and can be ignored, we can set k i,j = 1.

[0110] Based on the equivalent correlation coefficient in the standard normal space, the equivalent cross - correlation coefficient matrix and the equivalent autocorrelation coefficient matrix can be obtained respectively. Then, perform Cholesky decomposition on the two, that is: and , and the lower triangular matrix L 1 and L 2 can be obtained. Further, establish the independent standard normal random sample matrix of soil parameters ξ . Multiply the lower triangular matrix L 1 and L 2 by ξ respectively, and the correlated standard Gaussian random field can be obtained, that is:

[0111] (4)

[0112] where is the correlated standard normal random sample matrix.

[0113] Finally, through the equal - probability transformation method, take the exponential of the correlated standard Gaussian random field to obtain the correlated log - normal random field:

[0114] (5)

[0115] Among them, is the standard deviation of the normal variable , , is the mean of the normal variable . , is the lognormal variable X i 's standard deviation, is the mean of the lognormal variable X i .

[0116] Step S420: Assign each of the simulated random fields to the corresponding dam body elements in the finite element model to obtain the parameter random field of the dam to be monitored.

[0117] Among them, the material parameters generated in the simulated random field are assigned to each dam body element of the finite element model, so that the material parameters of each element are no longer fixed values but have spatial randomness, in order to more realistically reflect the uncertainty and spatial variability of the dam materials.

[0118] Exemplarily, first identify the dam body elements in the finite element model, and correspond the random field coordinates with the finite element mesh coordinates to ensure that each element can receive the correct material parameter values. Then, assign the material parameter values at the corresponding positions in the simulated random field to the finite element mesh elements, so that the material parameters of each element (such as the initial internal friction angle, the slope of the initial tangent modulus, etc.) conform to the statistical distribution characteristics of the random field. After the assignment, the finite element model of the entire dam is no longer a deterministic model but a parameter random field with spatial random characteristics, which can be used for subsequent stochastic finite element analysis.

[0119] Step S430: Conduct stochastic finite element analysis on the parameter random field under different water levels to obtain the displacements of the dam body measurement points at each water level, and obtain the probability density distribution of the dam body displacements at each water level by statistically analyzing the displacements of the dam body measurement points.

[0120] Taking the horizontal displacement at the vertex of the maximum cross-section of the concrete face rockfill dam (denoted as measurement point B for example) as the displacement of the dam body measurement point for illustration. In one exemplary implementation, the displacements of the dam body measurement points include the first displacement of the dam body measurement point, the second displacement of the dam body measurement point, the third displacement of the dam body measurement point, and the fourth displacement of the dam body measurement point. Among them, the first displacement of the dam body measurement point, the second displacement of the dam body measurement point, the third displacement of the dam body measurement point, and the fourth displacement of the dam body measurement point are respectively the horizontal displacement values of different measurement points calculated at measurement point B.

[0121] Refer to Figure 5As shown, the process for determining the probability density distribution of the dam displacement at each water level for this measuring point specifically includes steps S510 to S560:

[0122] Step S510: Conduct stochastic finite element analysis of the parameter random field at different water levels to obtain the displacement of the first dam measuring point at each water level.

[0123] In this step, through stochastic finite element calculation, the displacement of the first dam measuring point corresponding to different water levels under U groups of parameter random fields is obtained. By statistically analyzing the displacement of the first dam measuring point, the probability density distribution of the dam displacement can be preliminarily obtained. The stochastic finite element method adopted in the embodiments of the present disclosure separates the traditional deterministic finite element analysis from the stochastic analysis process. While simplifying the computational amount, accurate and reliable structural numerical simulation results can be obtained. In addition, to make the finite element meshing of the dam match the random field element meshes, the random field elements in the embodiments of the present disclosure adopt the same quantity and size as the finite element meshes.

[0124] Step S520: Establish a stochastic simulation surrogate model using the target material parameters and the displacement of the first dam measuring point, and use the stochastic simulation surrogate model to fit and obtain the displacement of the second dam measuring point at each water level.

[0125] Regard the stochastic finite element analysis in step S510 as a stochastic simulator. The input variable of this stochastic simulator is the eigenvalue of the random field parameters of the target material parameters, and the output variable is the displacement of the dam measuring point. In the exemplary implementation manner of the present disclosure, the stochastic polynomial chaos expansion method can be used to simulate the non-linear relationship and displacement probability density distribution between the target material parameters and the displacement of the first dam measuring point. That is, the stochastic polynomial chaos expansion method is used to establish a surrogate model of the stochastic simulator, namely, a stochastic simulation surrogate model is obtained. In this example, by establishing an approximate calculation model to replace the high-cost stochastic finite element analysis, the calculation efficiency is improved while ensuring the accuracy.

[0126] Specifically, the process of establishing a stochastic simulation surrogate model is as follows:

[0127] For a random variable that can be described by a probability density function f X and has independent components the random variable denotes M the set of real numbers in dimension , then M ( X )The polynomial chaos expansion of is:

[0128] (6)

[0129] Where It is about the probability density function f X is the orthogonal multivariate polynomial is the multivariate index to label the components of the multivariate polynomial , is the coefficient corresponding to the polynomial represents the set of real numbers. In the embodiments of the present disclosure, the polynomial in formula (6) can be truncated, so as to be converted into the sum of finite terms to improve the feasibility of analysis. Therefore, formula (6) can be written as:

[0130] (7)

[0131] wherein is the truncated polynomial chaos expansion is the selected multivariate index set of the multivariate polynomial represents M d-dimensional non-negative integer set.

[0132] From a probability perspective Y x can be regarded as a conditional random variable . Suppose represents the relevant cumulative distribution function. By using the probability integral transformation, any continuous random variable Z can be transformed into the required distribution , that is:

[0133] (8)

[0134] wherein is the cumulative distribution function of the random variable Z . The symbol " " represents the distribution form, that is, the random variables on both sides of formula (8) follow the same distribution, and the right side of the formula is x and Z 's deterministic function. Therefore, when it is assumed that Y has a finite variance, based on the random polynomial chaos expansion method, the distribution equality as shown in formula (9) can be achieved in the ( X , Z ) variable space:

[0135] (9)

[0136] In addition, to improve the numerical stability, an additional noise variable ε is introduced, and the random substitution term is defined ( is the truncation set, represents M +1-dimensional non-negative integer set), then formula (8) can be expressed as:

[0137] (10)

[0138] Among them, the noise variable ε is a central Gaussian random variable with a standard deviation of σ 2 , that is .

[0139] Next, estimate the coefficient c α and the standard deviation ε of the noise variable σ 2 .

[0140] Based on the material parameters, water level and dam body measurement point displacement data , the maximum likelihood estimation can be used to fit and solve the coefficient matrix c = { c α}:

[0141] (11)

[0142] Among them, is the estimated value of the coefficient matrix c , l is the likelihood function with respect to the coefficient matrix c , is the numerical approximation of this one-dimensional integral, N is the number of polynomial terms after truncation, x and y are the input data and output data respectively, that is, the material parameters, water level height and measurement point displacement, σ 3 is the displacement standard deviation.

[0143] The likelihood function in formula (11) is:[[]]

[0144] (12)

[0145] The likelihood function in formula (11) can be obtained by analytical calculation. Among them, y is the actual value of the dam body measurement point displacement, is the approximation of the dam body measurement point displacement after polynomial truncation, σ 3 is the displacement standard deviation, D Z represents the domain of the variable Z , f ( z ) is ZThe distribution function. Therefore, the BFGS quasi-Newton method based on derivatives can be used to solve this optimization problem.

[0146] Standard deviation σ 2 It can be adopted N cv -fold cross-validation (nested cross-validation) to select σ 2 the best value, that is, to maximize the cross-validation score of Equation (11), and this maximum score is calculated by derivative-free Bayesian optimization. Among them, σ 2 the search interval of If σ 2 the optimal

[0147] In the exemplary embodiment of the present disclosure, the eigenvalue of the random field parameter of the target material parameter is used as the input variable and the displacement of the first dam body measurement point corresponding to different water levels under the U groups of parameter random fields obtained is used as the output variable According to Formulas (6) to (12), the construction and fitting of the stochastic simulation surrogate model are carried out, and the fitting value of the stochastic simulation surrogate model is obtained , which is the displacement of the second dam body measurement point at each water level.

[0148] Subsequently, the fitting accuracy of the stochastic simulation surrogate model can be verified. When the accuracy meets the simulation requirements, the stochastic simulation surrogate model is used to output the displacement values of multiple dam body measurement points.

[0149] Step S530, comparing the statistical eigenvalue error between the displacement of the first dam body measurement point and the displacement of the second dam body measurement point.

[0150] Among them, the statistical eigenvalues include but are not limited to the mean value and the standard deviation. For example, the mean value of the displacement of the first dam body measurement point can be compared with the mean value of the displacement of the second dam body measurement point to determine the fitting accuracy of the stochastic simulation surrogate model according to the error between the two. Of course, the fitting accuracy of the stochastic simulation surrogate model can also be determined by comparing the standard deviation of the displacement of the first dam body measurement point with the standard deviation of the displacement of the second dam body measurement point , and the present disclosure does not limit this.

[0151] Step S540, if the statistical eigenvalue error is greater than the preset difference, increase the number of the parameter random fields, and perform stochastic finite element analysis under different water levels on the parameter random fields after the number adjustment to obtain the displacement of the third dam body measurement point.

[0152] For example, the preset difference is set to 5%. Of course, the specific value of the preset difference can also be set according to actual application needs, which is not limited here. The mean value of the displacement of the second dam body measuring point If the relative error between the means of is less than or equal to 5%, it indicates that the fitting accuracy of the random simulation proxy model is high, and the next step of analysis can be carried out, that is, the probability density distribution of the dam body displacement under each water level is obtained by statistically analyzing the displacement of the first dam body measuring point and the displacement of the second dam body measuring point, and step S230 is directly executed.

[0153] If the displacement of the first dam measuring point The mean value of the displacement of the second dam body measuring point If the relative error between the means of is greater than 5%, the number of parameter random fields in step S410 is increased. In fact, the number of parameter random fields is increased by increasing the number of random field simulations U, and random finite element calculations are performed again to obtain larger-scale dam displacement data, that is, to obtain the displacement of the third dam body measuring point.

[0154] Step S550: reconstructing and fitting a random simulation proxy model based on the displacement of the third dam body measuring point to obtain the displacement of the fourth dam body measuring point.

[0155] In this step, the random simulation proxy model is recalculated and optimized using the new calculation data. Specifically, the displacement of the third dam body measuring point is used as the output variable to reconstruct and fit the random simulation proxy model to obtain the displacement of the fourth dam body measuring point.

[0156] Step S560: if the statistical characteristic value error between the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point is less than or equal to a preset difference, the probability density distribution of the dam body displacement under each water level is obtained by statistically calculating the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point.

[0157] Among them, if the statistical characteristic value error between the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point is less than the preset difference, such as the relative error between the mean of the displacement of the third dam body measuring point and the mean of the displacement of the fourth dam body measuring point is less than or equal to 5%, the error between the two meets the requirement. The random simulation agent model is used to output multiple dam body measuring point displacement values, such as generating the displacement of the fourth dam body measuring point corresponding to each water level under the random field of the U' group parameters.

[0158] Finally, the probability density distribution of dam displacement under different water levels is obtained by statistically analyzing the displacement of the third and fourth dam measuring points, that is, the probability density distribution of horizontal displacement of measuring point B under different water levels is formed. Among them, since the calculated value of dam displacement under parameter random field has a certain randomness, the stability of the calculation result needs to be tested.

[0159] Exemplarily, the stability detection is carried out by using the displacement of the third dam body measurement point and the displacement of the fourth dam body measurement point at each water level, and the number of target random field simulations in which the displacement of the dam body measurement point is in a stable state is obtained. Specifically, the horizontal displacement of the measurement point B at a certain water level is statistically analyzed, and the change of the sliding mean value of the horizontal displacement with the number of random field simulations is obtained. When the displacement mean value basically tends to be stable, the corresponding number of target random field simulations is determined. For example, when the number of random field simulations reaches 400 times, the displacement calculation result is in a stable state, that is, under 400 random field simulations, the displacement calculation result already has good stability and representativeness. Therefore, the first 400 groups of displacement calculation results can be used to construct the water pressure component subsequently.

[0160] Then, by selecting the sample size corresponding to the stable displacement mean value, the probability density distribution of the displacement of the dam body measurement point under this sample size is sorted out. Specifically, by statistically analyzing the displacement of the dam body measurement point in the first 400 groups under the number of target random field simulations, the probability density distribution of the dam body displacement at this water level can be obtained. By analogy, the probability density distributions of the dam body displacements at each water level are obtained.

[0161] It can be understood that if the statistical eigenvalue error between the displacement of the third dam body measurement point and the displacement of the fourth dam body measurement point is still greater than the preset difference value, steps S540 and S550 can be continuously repeated until the statistical eigenvalue error between the latest dam body measurement point obtained by random finite element calculation and the latest dam body measurement point obtained by fitting with the random simulation surrogate model meets the requirements. Finally, the probability density distributions of the dam body displacements at each water level are statistically obtained based on the two.

[0162] In step S230, the displacement statistical value and the displacement confidence interval at each water level are determined according to each of the probability density distributions of the dam body displacements.

[0163] Among them, the displacement statistical value includes the displacement mean value and the displacement standard deviation. Exemplarily, statistical analysis is carried out on each probability density distribution of the dam body displacement, and the corresponding displacement mean value and displacement standard deviation are calculated. Further, according to the displacement mean value and the displacement standard deviation, and combined with the significance level, the boundary values of the displacement confidence interval are determined.

[0164] For example, for the first 400 groups of displacement calculation results, by analyzing the corresponding probability density distribution of the dam body displacement, the displacement mean value at each water level is statistically analyzed and the significance level α = 5% boundary values of the displacement confidence interval 、 , there are:

[0165] (13)

[0166] Among them, 、 The upper and lower limit values of the displacement confidence interval at each water level respectively, μ 2 、 σ 2 The mean value and standard deviation of the probability density distribution of the dam displacement at each water level respectively, is the standard score, and the significance level α = 5% 。

[0167] In step S240, based on the displacement statistical value and the displacement confidence interval, the water pressure component and the water pressure component interval value are fitted.

[0168] In this step, the displacement statistical value is the displacement mean value. Specifically, polynomial fitting is performed on the displacement mean values at different water levels to generate the water pressure component related to the water level. Similarly, polynomial fitting is performed on the boundary values of the displacement confidence intervals at different water levels to generate the corresponding water pressure component interval values.

[0169] Exemplarily, the expressions of the obtained water pressure component and the water pressure component interval value are:

[0170] (14)

[0171] Among them, is the water pressure component based on the displacement mean value , and are respectively the upper limit of the water pressure component and the lower limit of the water pressure component based on the boundary values of the confidence interval 、 , H m is the upstream water depth, m represents the power exponent of the water level, M is the number of polynomial terms, generally taking 3 or 4, a m 、a’ m 、a’’ m are undetermined coefficients.

[0172] In step S250, a dam displacement monitoring hybrid model is constructed by combining the temperature component, the aging component and the water pressure component, and a dam displacement monitoring index is calculated based on the dam displacement monitoring hybrid model and the water pressure component interval value.

[0173] Among them, the dam displacement monitoring hybrid model includes the original dam displacement monitoring hybrid model and the target dam displacement monitoring hybrid model. Referring to Figure 6 shown, step S250 can further include steps S610 to S630:

[0174] Step S610: Construct the original dam displacement monitoring hybrid model with the environmental quantities corresponding to the temperature component, aging component, and water pressure component as independent variables and the dam body measuring point displacement as the dependent variable.

[0175] In the exemplary embodiment of the present disclosure, when constructing the original dam displacement monitoring hybrid model with the environmental quantities corresponding to the temperature component, aging component, and water pressure component as independent variables and the dam body measuring point displacement as the dependent variable, there is:

[0176] (15)

[0177] Wherein, is the dam body measuring point displacement, such as the horizontal displacement of measuring point B. are the displacement components in three directions of the dam body. δ H is the water pressure component, that is, the dam body displacement caused by the change in the upstream water depth. δ H The corresponding environmental quantity is the upstream water depth. δ T is the temperature component, that is, the dam body displacement caused by the temperature change. δ T The corresponding environmental quantity is the temperature. δ θ is the aging component, that is, the dam body displacement caused by the time change. δ θ The corresponding environmental quantity is the time.

[0178] The temperature component δ T and the aging component δ θ in formula (15) are determined according to formula (16):

[0179] (16)

[0180] Wherein, T p is the average temperature within p days before the observation date. t is the time (days) counted from a certain day. m 1 , m 2 are respectively the air temperature factor coefficient and the period coefficient, generally taking 9 - 10. θ is the project operation time (days) / 100. b p , b 1p , b 2p、c 1 and c 2 are all undetermined coefficients.

[0181] In actual engineering, due to the influence of fault replacement, installation time, earthquake or human factors on the monitoring equipment, the monitoring reference does not match the initial displacement value of the dam, resulting in a certain difference between the measured displacement data and the displacement value obtained by finite element calculation. Therefore, when establishing the original dam displacement monitoring hybrid model in the embodiments of the present disclosure, a correction parameter can be added to the deterministic component (i.e., the water pressure component) obtained by finite element calculation L for appropriate adjustment. At this time, formula (15) can be adjusted to:

[0182] (17)

[0183] Step S620: Use the displacement monitoring data and environmental quantity monitoring data of the dam to be monitored to perform fitting analysis on each component in the original dam displacement monitoring hybrid model to obtain the undetermined coefficients in the original dam displacement monitoring hybrid model;

[0184] Still taking the measured horizontal displacement of the measuring point B at the top of the maximum cross-section of the concrete face rockfill dam as an example, when establishing the displacement monitoring index of this measuring point, the horizontal displacement of this measuring point and the environmental quantity monitoring data can be sorted out, where the environmental quantity monitoring data includes the upstream water depth, air temperature, etc.

[0185] For example, a total of 1700 groups of "displacement - environmental quantity" monitoring data are obtained, and the "displacement - environmental quantity" monitoring data is divided into a fitting sample set and a test sample set, where the fitting sample set contains 1600 groups of monitoring data and the test sample set contains 100 groups of monitoring data. Then, substitute the fitting sample set into the original dam displacement monitoring hybrid model for partial least squares fitting, and calculate the undetermined coefficients in each component, including all the undetermined coefficients shown in formulas (14) and (16).

[0186] Step S630: Obtain the target dam displacement monitoring hybrid model based on the undetermined coefficients, and substitute the water pressure component interval value into the target dam displacement monitoring hybrid model to obtain the dam displacement monitoring index of the dam to be monitored at a preset significance level.

[0187] It can be understood that if all the undetermined coefficients shown in formulas (14) and (16) are determined, the fitted target dam displacement monitoring hybrid model can be obtained. Then, substitute the upper limit of the water pressure component and the lower limit expression obtained in step S240 into the target dam displacement monitoring hybrid model to obtain the dam displacement monitoring index at a preset significance level such as α = 5%.

[0188] In this embodiment, the target dam displacement monitoring hybrid model has advantages such as small prediction residuals, high prediction accuracy, and good prediction stability. At the same time, the correlation between the predicted value and the measured value is relatively high, and the distribution form similarity is relatively high. Therefore, the target dam displacement monitoring hybrid model has high feasibility and superiority in dam displacement prediction analysis.

[0189] In the embodiment of the present disclosure, by relating the structural mechanics and deformation characteristics of the dam body, and adopting the stochastic finite element method and the corresponding surrogate model to simulate the water pressure component on the basis of the traditional structural analysis method to consider the uncertainty of the dam body material parameters, the deformation mechanism of the dam body is more truly and accurately reflected. When there is less monitoring data in the initial operation period, the present disclosure combines the displacement statistical characteristics at different water levels, and can directly determine the corresponding monitoring indexes according to the target dam displacement monitoring hybrid model. At the same time, the monitoring indexes are dynamically adjusted with the change of the input environmental quantity, and the theoretical basis is more sufficient and has higher rationality.

[0190] In an exemplary embodiment, referring to Figure 7 as shown, a flow schematic diagram of another method for formulating the dam displacement monitoring index is given. This process includes steps S701 to S712:

[0191] Step S701, determining the stochastic parameter eigenvalue of the target material parameter: establishing a finite element model of the dam to be monitored, determining the constitutive model adopted for each material zone divided in the finite element model, and selecting the target material parameter from the constitutive model, and then determining the stochastic parameter eigenvalue of the target material parameter;

[0192] Step S702, performing a random field simulation on the target material parameter to obtain a parameter random field;

[0193] Step S703, performing a stochastic finite element analysis to obtain the dam body measuring point displacement;

[0194] Step S704, establishing a stochastic simulation surrogate model to replace the stochastic finite element analysis and outputting the new dam body measuring point displacement;

[0195] Step S705, determining whether the fitting accuracy requirement is satisfied. If the fitting accuracy requirement is satisfied, execute step S706. Otherwise, increase the number of random field simulations and repeat steps S702 to S705 until the stochastic simulation surrogate model satisfies the fitting accuracy requirement;

[0196] Step S706, obtaining the displacement probability density distribution at each water level according to the dam body measuring point displacement;

[0197] Step S707, statistically calculating the displacement mean value at each water level;

[0198] Step S708: Statistically calculate the displacement confidence interval at each water level;

[0199] Step S709: Perform polynomial fitting on the displacement mean values at each water level to obtain the water pressure component;

[0200] Step S710: Perform polynomial fitting on the displacement confidence intervals at each water level to obtain the boundary values of the water pressure component interval;

[0201] Step S711: Construct a hybrid model for dam displacement monitoring: Use the environmental quantities corresponding to the temperature component, aging component, and water pressure component as independent variables, and the dam body measuring point displacement as the dependent variable to construct a hybrid model for dam displacement monitoring;

[0202] Step S712: Determine the undetermined coefficients of the model to obtain the fitted hybrid model for dam displacement monitoring: Use the displacement monitoring data and environmental quantity monitoring data of the dam to be monitored to perform fitting analysis on the hybrid model for dam displacement monitoring, calculate each undetermined coefficient in the model, and obtain the hybrid model for dam displacement monitoring with all undetermined coefficients determined in each component. Then, substitute the boundary values of the water pressure component interval obtained in Step S710 into the fitted hybrid model for dam displacement monitoring to finally obtain the dam displacement monitoring index.

[0203] In this exemplary embodiment, the random field is used to simulate the uncertainty of the mechanical parameters of the dam body material, and based on the stochastic simulation surrogate model, the water pressure component is determined, and then a hybrid model for dam displacement monitoring is established. Further, based on the probability density distribution of the dam body displacement at each water level, the boundary values of the displacement confidence interval are calculated, and then the dam displacement monitoring index is formulated. In this process, the physical factors of the monitoring model are clearly defined, the prediction error of different measuring point displacements changes little, the prediction stability is strong, and it has high accuracy and applicability. Moreover, by relating the structural mechanics and deformation characteristics of the dam body, and using the stochastic finite element method combined with the stochastic simulation surrogate model to simulate the water pressure component to consider the uncertainty of the dam body material parameters, it more truly and accurately reflects the deformation mechanism of the dam body. Therefore, the displacement monitoring index formulated in this disclosure has higher accuracy and adaptability, sufficient theoretical basis, and better warning effect.

[0204] In this exemplary embodiment, a device for formulating the dam displacement monitoring index is also provided. Referring to Figure 8 As shown, the device may include a material parameter determination module 810, a parameter stochastic simulation module 820, a probability density statistics module 830, a water pressure component determination module 840, and a monitoring index determination module 850, where:

[0205] The material parameter determination module 810 is configured to establish a finite element model of the dam to be monitored and determine the target material parameters based on the finite element model;

[0206] A parameter random simulation module 820, configured to perform a random field simulation on the target material parameters, and perform a stochastic finite element analysis on the simulated parameter random field under different water levels to obtain the probability density distribution of the dam displacement under each water level;

[0207] A probability density statistics module 830, configured to determine the displacement statistical value and the displacement confidence interval under each water level according to the probability density distribution of each dam displacement;

[0208] A water pressure component determination module 840, configured to fit a water pressure component and a water pressure component interval value based on the displacement statistical value and the displacement confidence interval;

[0209] A monitoring index determination module 850, configured to construct a dam displacement monitoring hybrid model by combining the temperature component, the aging component and the water pressure component, and calculate a dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value.

[0210] In an exemplary embodiment of the present disclosure, when the parameter random simulation module 820 performs a random field simulation on the target material parameters, and performs a stochastic finite element analysis on the simulated parameter random field under different water levels to obtain the probability density distribution of the dam displacement under each water level, specifically, it is used for:

[0211] Perform a random field simulation on the target material parameters of each material partition in the dam to be monitored to obtain a corresponding simulated random field;

[0212] Assign each of the simulated random fields to the corresponding dam element in the finite element model to obtain the parameter random field of the dam to be monitored;

[0213] Perform a stochastic finite element analysis on the parameter random field under different water levels to obtain the dam measurement point displacements under each water level, and obtain the probability density distribution of the dam displacement under each water level by statistically analyzing the dam measurement point displacements.

[0214] In an exemplary embodiment of the present disclosure, the simulated random field includes a correlated lognormal random field; when the parameter random simulation module 820 performs a random field simulation on the target material parameters of each material partition in the dam to be monitored to obtain a corresponding simulated random field, specifically, it is used for:

[0215] Generate a standard Gaussian random field according to the statistical distribution characteristics of the target material parameters and the spatial correlation defined by the Gaussian autocorrelation function;

[0216] Decompose the correlation coefficient matrix of the random variables in the standard Gaussian random field, calculate the correlated standard Gaussian random field based on the decomposition result and the correlated standard normal random sample matrix, and perform an equal-probability transformation on the correlated standard Gaussian random field to generate the correlated lognormal random field.

[0217] In an exemplary embodiment of the present disclosure, the dam body measurement point displacements include the first dam body measurement point displacement, the second dam body measurement point displacement, the third dam body measurement point displacement, and the fourth dam body measurement point displacement; when the parameter random simulation module 820 performs a stochastic finite element analysis of the parameter random field at different water levels to obtain the dam body measurement point displacements at each water level and obtains the probability density distribution of the dam body displacements at each water level by statistically analyzing the dam body measurement point displacements, it is specifically used for:

[0218] Perform a stochastic finite element analysis of the parameter random field at different water levels to obtain the first dam body measurement point displacement at each water level;

[0219] Establish a stochastic simulation surrogate model using the target material parameters and the first dam body measurement point displacement, and use the stochastic simulation surrogate model to fit and obtain the second dam body measurement point displacement at each water level;

[0220] Compare the statistical eigenvalue errors between the first dam body measurement point displacement and the second dam body measurement point displacement;

[0221] If the statistical eigenvalue error is greater than a preset difference, increase the number of the parameter random fields, and perform a stochastic finite element analysis of the adjusted number of parameter random fields at different water levels to obtain the third dam body measurement point displacement;

[0222] Reconstruct and fit the stochastic simulation surrogate model based on the third dam body measurement point displacement to obtain the fourth dam body measurement point displacement;

[0223] If the statistical eigenvalue error between the third dam body measurement point displacement and the fourth dam body measurement point displacement is less than or equal to the preset difference, obtain the probability density distribution of the dam body displacements at each water level by statistically analyzing the third dam body measurement point displacement and the fourth dam body measurement point displacement.

[0224] In an exemplary embodiment of the present disclosure, when the parameter random simulation module 820 performs obtaining the probability density distribution of the dam body displacements at each water level by statistically analyzing the third dam body measurement point displacement and the fourth dam body measurement point displacement, it is specifically used for:

[0225] Perform stability detection using the third dam body measurement point displacement and the fourth dam body measurement point displacement at each water level to obtain the target random field simulation times when the dam body measurement point displacement is in a stable state;

[0226] Statistically analyze the displacements of the dam body measurement points corresponding to the simulated times of the target random field, and obtain the probability density distributions of the dam body displacements at each water level.

[0227] In an exemplary embodiment of the present disclosure, the displacement statistical values include the displacement mean and the displacement standard deviation; when the probability density statistical module 830 executes to determine the displacement statistical values and the displacement confidence intervals at each water level according to the probability density distributions of the dam body displacements, specifically, it is used for:

[0228] Perform statistical analysis on the probability density distributions of the dam body displacements, and calculate the corresponding displacement mean and displacement standard deviation;

[0229] According to the displacement mean and the displacement standard deviation, and in combination with the significance level, determine the boundary values of the displacement confidence interval.

[0230] In an exemplary embodiment of the present disclosure, when the water pressure component determination module 840 executes to fit the water pressure component and the water pressure component interval value based on the displacement statistical value and the displacement confidence interval, specifically, it is used for:

[0231] Perform polynomial fitting on the displacement means at different water levels to generate a water pressure component related to the water level;

[0232] Perform polynomial fitting on the boundary values of the displacement confidence intervals at different water levels to generate the corresponding water pressure component interval values.

[0233] In an exemplary embodiment of the present disclosure, the dam displacement monitoring hybrid model includes an original dam displacement monitoring hybrid model and a target dam displacement monitoring hybrid model;

[0234] When the monitoring index determination module 850 executes to construct a dam displacement monitoring hybrid model by combining the temperature component, the aging component and the water pressure component, and calculate the dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value, specifically, it is used for:

[0235] Taking the environmental quantities corresponding to the temperature component, the aging component and the water pressure component as independent variables, and the dam body measurement point displacement as the dependent variable, construct the original dam displacement monitoring hybrid model;

[0236] Use the displacement monitoring data and the environmental quantity monitoring data of the dam to be monitored to perform fitting analysis on each component in the original dam displacement monitoring hybrid model, and obtain the undetermined coefficients in the original dam displacement monitoring hybrid model;

[0237] Based on the undetermined coefficients, obtain the target dam displacement monitoring hybrid model, and substitute the water pressure component interval value into the target dam displacement monitoring hybrid model to obtain the dam displacement monitoring index of the dam to be monitored at the preset significance level.

[0238] In an exemplary embodiment of the present disclosure, when the material parameter determination module 810 executes to establish a finite element model of the dam to be monitored and determine the target material parameters based on the finite element model, specifically, it is used for:

[0239] Obtain the engineering data of the dam to be monitored, and establish a finite element model of the dam to be monitored according to the engineering data;

[0240] Determine the constitutive models adopted by the material zones divided in the finite element model, and select the target material parameters from the constitutive models.

[0241] The specific details of each module of the above dam displacement monitoring index formulation device have been described in detail in the corresponding dam displacement monitoring index formulation method, so they will not be elaborated here.

[0242] The exemplary embodiments of the present disclosure further provide a computer-readable storage medium, on which a program product capable of implementing the above methods of this specification is stored. In some possible embodiments, various aspects of the present disclosure can also be implemented in the form of a program product, which includes program code. When the program product runs on an electronic device, the program code is used to cause the electronic device to execute the steps according to various exemplary embodiments of the present disclosure described in the above "Exemplary Method" section of this specification.

[0243] The program product can be a portable compact disc read-only memory (CD-ROM) and includes program code, and can run on an electronic device, such as a personal computer. However, the program product of the present disclosure is not limited to this. In this document, the readable storage medium can be any tangible medium that contains or stores a program, and the program can be used by or in combination with an instruction execution system, apparatus, or device.

[0244] The program product can adopt any combination of one or more readable media. The readable media can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0245] A computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries readable program code. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the foregoing. The readable signal medium may also be any readable medium other than a readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device.

[0246] The program code contained on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0247] The program code for performing the operations of the present disclosure may be written in any combination of one or more programming languages, including object-oriented programming languages such as Java, C#, C++, etc., and also including conventional procedural programming languages such as the "C" language or similar programming languages. The program code may be executed entirely on the user's computing device, partially on the user's device, executed as a stand-alone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., by connecting through the Internet using an Internet service provider).

[0248] In addition, an exemplary embodiment of the present disclosure further provides an electronic device capable of implementing the above-described method for formulating dam displacement monitoring indicators.

[0249] The following refers to Figure 9 to describe the electronic device 900 according to such an embodiment of the present disclosure. Figure 9 The illustrated electronic device 900 is merely an example and should not impose any limitation on the functions and scope of use of the embodiments of the present disclosure.

[0250] As Figure 9 shown, the electronic device 900 is presented in the form of a general-purpose computing device. The components of the electronic device 900 may include but are not limited to: the at least one processing unit 910 described above, the at least one storage unit 920 described above, a bus 930 connecting different system components (including the storage unit 920 and the processing unit 910), and a display unit 940.

[0251] The storage unit 920 stores program code, which can be executed by the processing unit 910, enabling the processing unit 910 to execute the steps according to various exemplary embodiments of the present disclosure described in the "Exemplary Method" section above in this specification. For example, the processing unit 910 can execute the method steps in the exemplary embodiments of the present disclosure.

[0252] The storage unit 920 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 921 and / or a cache storage unit (Cache) 922, and may further include a read-only storage unit (ROM) 923.

[0253] The storage unit 920 may also include a program / utilities 924 having a set (at least one) of program modules 925. Such program modules 925 include, but are not limited to: an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment.

[0254] The bus 930 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus structures.

[0255] The electronic device 900 may also communicate with one or more external devices 970 (such as a keyboard, a pointing device, a Bluetooth device, etc.), and may also communicate with one or more devices that enable a user to interact with the electronic device 900, and / or communicate with any device that enables the electronic device 900 to communicate with one or more other computing devices (such as a router, a modem, etc.). Such communication may be carried out through an input / output (I / O) interface 950. Also, the electronic device 900 may communicate with one or more networks (such as a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) through a network adapter 960. As shown in the figure, the network adapter 960 communicates with other modules of the electronic device 900 through the bus 930. It should be understood that although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 900, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0256] Through the description of the above embodiments, those skilled in the art can easily understand that the exemplary embodiments described herein can be implemented by software or by a combination of software and necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

[0257] In addition, the above drawings are only schematic illustrations of the processes included in the method according to the exemplary embodiments of the present disclosure, rather than for limiting purposes. It is easy to understand that the processes shown in the above drawings do not indicate or limit the chronological order of these processes. Additionally, it is also easy to understand that these processes can be executed synchronously or asynchronously in, for example, multiple modules.

[0258] Through the description of the above embodiments, those skilled in the art can easily understand that the exemplary embodiments described herein can be implemented by software or by a combination of software and necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

[0259] After considering the specification and practicing the invention disclosed herein, those skilled in the art will readily conceive of other embodiments of the present disclosure. This application is intended to cover any variations, uses, or adaptations of the present disclosure, which follow the general principles of the present disclosure and include known common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and embodiments are only regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the claims.

[0260] It should be understood that the present disclosure is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present disclosure is only limited by the appended claims.

Claims

1. A method for formulating dam displacement monitoring indicators, characterized in that: include: Establishing a finite element model of the dam to be monitored, and determining target material parameters based on the finite element model; Performing random field simulation on the target material parameters, and performing random finite element analysis on the simulated parameter random fields at different water levels to obtain probability density distribution of dam body displacement at each water level; Determining the displacement statistics and displacement confidence interval at each water level according to the probability density distribution of the dam body displacement; Fitting the water pressure component and the water pressure component interval value based on the displacement statistical value and the displacement confidence interval; A dam displacement monitoring hybrid model is constructed by combining the temperature component, the time-effect component and the water pressure component, and a dam displacement monitoring index is calculated based on the dam displacement monitoring hybrid model and the water pressure component interval value.

2. The method for formulating dam displacement monitoring indicators according to claim 1 is characterized in that: The random field simulation of the target material parameters is performed, and the random finite element analysis of the simulated parameter random field is performed at different water levels to obtain the probability density distribution of the dam body displacement at each water level, including: Performing random field simulation on target material parameters of each material partition in the dam to be monitored to obtain a corresponding simulated random field; Assigning each of the simulated random fields to the corresponding dam body unit in the finite element model to obtain a parameter random field of the dam to be monitored; The parameter random field is subjected to random finite element analysis at different water levels to obtain the displacement of the dam body measuring points at each water level, and the probability density distribution of the dam body displacement at each water level is obtained by statistically analyzing the displacement of the dam body measuring points.

3. The method for formulating dam displacement monitoring indicators according to claim 2 is characterized in that: The simulated random field includes a correlated log-normal random field; The random field simulation of the target material parameters of each material partition in the dam to be monitored to obtain the corresponding simulated random field includes: generating a standard Gaussian random field according to the statistical distribution characteristics of the target material parameters and the spatial correlation defined by the Gaussian autocorrelation function; The random variable correlation coefficient matrix in the standard Gaussian random field is decomposed, and the relevant standard Gaussian random field is calculated according to the decomposition result and the relevant standard normal random sample matrix, and the relevant standard Gaussian random field is subjected to equal probability transformation processing to generate the relevant log-normal random field.

4. The method for formulating dam displacement monitoring indicators according to claim 2 is characterized in that: The dam body measuring point displacement includes the first dam body measuring point displacement, the second dam body measuring point displacement, the third dam body measuring point displacement and the fourth dam body measuring point displacement; The random finite element analysis of the parameter random field under different water levels is performed to obtain the displacement of the dam body measuring points under each water level, and the probability density distribution of the dam body displacement under each water level is obtained by statistically analyzing the displacement of the dam body measuring points, including: Performing random finite element analysis on the parameter random field at different water levels to obtain the displacement of the first dam body measuring point at each water level; A random simulation proxy model is established using the target material parameters and the first dam body measurement point displacement, and the random simulation proxy model is used to fit the second dam body measurement point displacement at each water level; comparing the statistical characteristic value error between the displacement of the first dam body measuring point and the displacement of the second dam body measuring point; If the statistical characteristic value error is greater than the preset difference, the number of the parameter random fields is increased, and random finite element analysis is performed on the parameter random fields after the adjustment under different water levels to obtain the displacement of the third dam body measuring point; Reconstructing and fitting a random simulation proxy model based on the displacement of the third dam body measuring point to obtain the displacement of the fourth dam body measuring point; If the statistical characteristic value error between the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point is less than or equal to the preset difference, the probability density distribution of the dam body displacement at each water level is obtained by statistically analyzing the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point.

5. The method for formulating dam displacement monitoring indicators according to claim 4 is characterized in that: The method of obtaining the probability density distribution of the dam body displacement at each water level by counting the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point includes: Using the displacement of the third dam body measuring point and the displacement of the fourth dam body measuring point at each water level to perform stability detection, and obtain the target random field simulation number of the dam body measuring point displacement being in a stable state; The displacements of the dam body measuring points corresponding to the target random field simulation times are counted to obtain the probability density distribution of the dam body displacements at each water level.

6. The method for formulating dam displacement monitoring indicators according to claim 1, characterized in that: The displacement statistics include a displacement mean and a displacement standard deviation; Determining the displacement statistics and displacement confidence interval at each water level according to the probability density distribution of the dam body displacements includes: Performing statistical analysis on the probability density distribution of the displacement of each dam body, and calculating the corresponding displacement mean and displacement standard deviation; The limit values ​​of the displacement confidence interval are determined based on the displacement mean and displacement standard deviation and combined with the significance level.

7. The method for formulating dam displacement monitoring indicators according to claim 6, characterized in that: The fitting based on the displacement statistics and the displacement confidence interval to obtain the water pressure component and the water pressure component interval value includes: The displacement mean under different water levels is fitted with a polynomial to generate the water pressure component related to the water level; Polynomial fitting is used to fit the limit values ​​of the displacement confidence interval under different water levels to generate the corresponding water pressure component interval values.

8. The method for formulating dam displacement monitoring indicators according to claim 1, characterized in that: The dam displacement monitoring hybrid model includes an original dam displacement monitoring hybrid model and a target dam displacement monitoring hybrid model; The dam displacement monitoring hybrid model is constructed by combining the temperature component, the time-effect component and the water pressure component, and the dam displacement monitoring index is calculated based on the dam displacement monitoring hybrid model and the water pressure component interval value, including: The original dam displacement monitoring hybrid model is constructed by taking the environmental quantities corresponding to the temperature component, the time-effect component and the water pressure component as independent variables and the displacement of the dam body measuring point as the dependent variable; Using the displacement monitoring data of the dam to be monitored and the environmental monitoring data, fitting and analyzing each component in the original dam displacement monitoring hybrid model is performed to obtain the undetermined coefficients in the original dam displacement monitoring hybrid model; A target dam displacement monitoring hybrid model is obtained based on the undetermined coefficients, and the water pressure component interval value is substituted into the target dam displacement monitoring hybrid model to obtain the dam displacement monitoring index of the dam to be monitored at a preset significance level.

9. The method for formulating dam displacement monitoring indicators according to claim 1, characterized in that: The step of establishing a finite element model of the dam to be monitored and determining target material parameters based on the finite element model includes: Acquiring engineering data of the dam to be monitored, and establishing a finite element model of the dam to be monitored according to the engineering data; The constitutive model used for each material partition divided in the finite element model is determined, and target material parameters are selected from the constitutive model.

10. A dam displacement monitoring index formulation device, characterized in that: include: A material parameter determination module, used to establish a finite element model of the dam to be monitored and determine target material parameters based on the finite element model; A parameter random simulation module is used to perform random field simulation on the target material parameters, and perform random finite element analysis on the simulated parameter random field at different water levels to obtain the probability density distribution of dam body displacement at each water level; A probability density statistics module, used to determine the displacement statistics and displacement confidence interval at each water level according to the probability density distribution of the dam body displacement; A water pressure component determination module, used for obtaining a water pressure component and a water pressure component interval value based on the displacement statistics and the displacement confidence interval fitting; The monitoring index determination module is used to construct a dam displacement monitoring hybrid model by combining the temperature component, the time-effect component and the water pressure component, and calculate the dam displacement monitoring index based on the dam displacement monitoring hybrid model and the water pressure component interval value.

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