Rockfill dam material parameter uncertainty inversion method based on bayesian inference

Abstract

The application discloses a rockfill dam material parameter uncertainty inversion method based on Bayesian inference, and particularly relates to the following steps: establishing a rockfill dam finite element model, determining the prior distribution of the to-be-inverted parameters; constructing an sPCE surrogate model based on the prior distribution of the to-be-inverted parameters; establishing a rockfill dam displacement statistical model, separating the measured displacement water pressure component; constructing a rockfill dam material likelihood function; rockfill dam material parameter uncertainty inversion; and rockfill dam material parameter uncertainty updating inversion. The application uses the Bayesian inference method to obtain the uncertainty distribution characteristics of the material parameters of different partitions of the dam body through the measured displacement data of the dam, the prior distribution of the parameters and the likelihood function. The method solves the shortcoming that the traditional inversion method cannot consider the parameter uncertainty, and the obtained parameter value is closer to the engineering practice; compared with the traditional inversion method, the parameter updating inversion can be carried out through the monitoring data in different periods, and the continuous tracking of the time-effectiveness evolution of the parameters is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hydraulic engineering material parameter analysis, and particularly relates to a rockfill dam material parameter uncertainty inversion method based on Bayesian inference. BACKGROUND

[0002] With the continuous development of water conservancy projects, the height of the rockfill dam under construction is constantly breaking through, and dam safety is also increasingly valued. Based on the actual material parameters of the dam body, structural analysis is an important way to understand the safety of the dam structure, evaluate the health state of the dam operation, etc. As a method based on numerical simulation analysis, the inversion analysis obtains the mechanical properties or initial stress conditions according to the changes in the properties of rock and soil under actual engineering loads. It has become one of the important means to determine the material parameter values of the dam body. At present, the traditional deterministic inversion method has been rapidly developed and widely applied in the inversion analysis of rock and soil problems. It seeks the optimal parameter group that satisfies the objective function through optimization algorithm, so as to make the calculation results as close to the measured data as possible. However, in actual engineering, due to the influence of geological exploration, soil test, design assumption, construction technology, construction condition and material time evolution, there are certain differences and random distribution characteristics between the actual mechanical parameters of rockfill and the design parameters. When using the traditional inversion method for analysis, the uncertainty of the parameters is ignored, and the incorrect cognition and assumption of the parameters cannot be corrected through monitoring data, which often leads to certain errors in the results of dam structure analysis, and further cannot effectively understand the actual operation state of the dam.

[0003] Bayesian inference is a kind of inference statistical method, which can use existing information to correct the prior distribution of the original parameters, so as to update it to the posterior distribution close to the actual engineering. Therefore, using Bayesian inference for parameter inversion analysis can effectively obtain the distribution information of the material mechanical parameters close to the actual dam, and accurately describe the parameter uncertainty. However, the analysis results of this method are affected by many factors such as prior distribution, proxy model, sampling method and likelihood function. Random determination will greatly reduce the accuracy of Bayesian analysis. Therefore, the above influencing factors need to be determined according to the actual engineering characteristics, and an efficient and reasonable rockfill dam material parameter uncertainty inversion method based on Bayesian inference is established. SUMMARY

[0004] The purpose of the present application is to provide a rockfill dam material parameter uncertainty inversion method based on Bayesian inference, so as to realize the material parameter updating inversion under different monitoring data.

[0005] The technical solution adopted by the present application is a rockfill dam material parameter uncertainty inversion method based on Bayesian inference, which is implemented according to the following steps:

[0006] Step 1, establish a finite element model of the rockfill dam, and determine the prior distribution of the parameters to be inverted;

[0007] Step 2, constructing sPCE surrogate model based on prior distribution of inversion parameters;

[0008] Step 3, establishing rockfill dam displacement statistical model, separating measured displacement water pressure component;

[0009] Step 4, constructing rockfill dam material likelihood function;

[0010] Step 5, rockfill dam material parameter uncertainty inversion;

[0011] Step 6, rockfill dam material parameter uncertainty updating inversion.

[0012] The application also has the characteristics that,

[0013] In step 1, specifically,

[0014] Step 1.1, based on the obtained rockfill dam engineering design data, including: rockfill dam plane layout, rockfill dam section design drawing, dam body deformation monitoring design drawing, establishing a rockfill dam finite element model;

[0015] Step 1.2, in order to describe the stress-strain relationship of each material unit in the rockfill dam finite element model, the parameter inversion analysis is carried out on the main rockfill area and the downstream rockfill area, that is, the initial internal friction angle The initial tangent modulus slope n, the tangent volume modulus intercept K b Three parameters are the research objects for uncertainty inversion; set n, K b The prior distribution of parameters obeys normal distribution N(mu, sigma 2 ).

[0016] In step 2, specifically,

[0017] Step 2.1, based on the prior distribution of material parameters n, K b of the main rockfill area and the downstream rockfill area respectively, Latin hypercube is used for sampling to generate m sets of material parameter combination sample set X={X1, X2,..., X m}, each element X i in the sample is a random combination of parameter n, K b sample value, that is Put the parameter sample into the finite element calculation to obtain the rockfill dam displacement response value sample set Y={Y1, Y2,..., Y m} corresponding to the parameter sample; integrate each sample to form the “parameter-displacement” sample set Z={X, Y}={ [X1, Y1], [X2, Y2],..., [Xm ,Y m ]};

[0018] Step 2.2, divide the "parameter-displacement" sample set Z into a training set and a test set, i.e. the training set Z = {X, Y} = {[X i ,Y i ]} = {[X1, Y1], [X2, Y2],..., [X 3m / 4 ,Y 3m / 4 ]}, and the test set Z' = {X', Y'} = {[X' i ,Y i ]} = {[X1, Y1], [X2, Y2],..., [X m / 4 ,Y m / 4 ]}; take {X i} as the input variable and {Y i} as the output variable in the training set, establish the sPCE proxy model and perform fitting analysis to obtain the trained sPCE proxy model;

[0019] According to the distribution form of the to-be-inverted parameters, Hermite orthogonal polynomials are selected as the basis functions to construct the PCE proxy model as follows:

[0020]

[0021] In the formula, y is the output variable; a0, ,... are polynomial coefficients to be solved; are random variables independent of each other and subject to normal distribution, which are input variables in uncertainty analysis; x(·) is the basis function of PCE;

[0022] The solution of the PCE expansion term coefficient is expressed as:

[0023]

[0024] In the formula, is the to-be-solved coefficient; ||a||0 is the number of non-zero elements in the to-be-determined expansion coefficient vector; ξ (i) is the i-th sampling sample of the input random variable vector ξ; Ψ(·) is the abbreviation of ;

[0025] The orthogonal matching pursuit method is adopted as the calculation strategy of the optimal term set of the adaptive complete PCE proxy model, and the expansion coefficients of the number of each term in the optimal order of the initial proxy model of the complete PCE are calculated Only the PCE basis function terms that have a greater impact on the output variable are retained, the basis function is reconstructed to form the sPCE model, and the non-zero term coefficients of the sPCE are obtained through formula (2), thereby completing the training of the sPCE proxy model, and obtaining the trained sPCE proxy model.

[0026] Step 2.3, with the input variable {X i ′} in the test set, the calculated displacement value {y i ′} is obtained after substituting the sPCE surrogate model, and the calculated displacement value {y i ′} is compared with the test set {Y i ′} to check the calculation error of the sPCE surrogate model. If it does not meet the accuracy requirement, repeat step 2.2; if it meets the accuracy requirement, output the obtained sPCE surrogate model.

[0027] In step 2.3, the error checking indicators are root mean square error RMSE, root mean square relative error RMSPE, mean error MAE, mean relative error MAPE, and correlation coefficient R, and the calculation formulas are as follows:

[0028]

[0029]

[0030] In step 3, the specific steps are as follows:

[0031] The statistical model of the rock-fill dam displacement is:

[0032] δ = δ H + δ T + δ θ (4)

[0033] In the formula, δ is the dam displacement; δ H is the water pressure component; δ T is the temperature component; and δ θ is the time-dependent component.

[0034] The expressions of each displacement component are selected as follows:

[0035]

[0036] In the formula, H is the upstream water depth; H is the average upstream water depth of the previous i days; T i is the average air temperature of the previous i days before the observation day; t is the time from the observation day to the starting day; m1 is 3, and m2 and m3 are 9 or 10; θ is the time-dependent displacement factor; a, b, and c are regression coefficients.

[0037] The environmental monitoring data of water depth H, air temperature T, and observation time t are substituted into the statistical model, and the least squares method is used to fit to obtain each regression coefficient; then the obtained regression coefficient a and H, are substituted into the water pressure component expression in formula (5) to obtain the water pressure component value δ H separated from the measured displacement.

[0038] Step 4 specifically involves:

[0039] Step 4.1: Based on the initial prior distribution of parameters in the main rockfill area and downstream rockfill area of ​​the dam body in Step 1.2, the sampling range of each parameter value in different inversion stages is set to [μ-3σ, μ+3σ]. The number of Markov chains is set to p=4 and the number of samples per chain is set to q=20000. The DREAM method is used to sample the parameter sets, generating parameter samples for the main rockfill area. Parameter samples of downstream rockfill area

[0040] Substitute the parameter samples S and S′ into the sPCE surrogate model in step 2 to simulate finite element analysis, and obtain the vertical displacement value h corresponding to the sample parameters. i (θ);

[0041] Step 4.2, set the mean error value μ of the monitoring data. wi =0, standard deviation of error distribution σ wi =1mm; Based on the prior distribution of the parameters, select the corresponding likelihood function form:

[0042]

[0043] In the formula, y i The water pressure component separated from the measured value; h i (θ) represents the displacement response value of the dam body calculated by the finite element method; μ wi The mean measurement error of the monitoring project; σ wi The standard deviation of the measurement error for the monitoring project;

[0044] The water pressure component y separated from the measured value i =δ Hi Finite element method for calculating the displacement response value h of the dam body i (θ), mean measurement error μ wi With standard deviation σ wi Substitute into equation (6) to construct the likelihood function of the material parameters of the rockfill dam.

[0045] Step 5 specifically involves:

[0046] Based on Bayesian theory, establish a Bayesian inference model:

[0047]

[0048] In the formula, θ represents the value belonging to... Parameters to be inverted in space; In order to be in Actual observation data in space Here is the measured value of the separated water pressure component; p(θ) is the prior distribution; is the likelihood function; is the posterior distribution of the parameter to be inverted; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function:

[0049]

[0050] The prior distribution of each parameter obtained in steps 1-4, the water pressure component, the likelihood function are substituted into equation (7) to calculate the posterior distribution N(μ',σ' of the material parameter to be inverted 2 to determine the inversion value of the parameter.

[0051] In step 6, specifically:

[0052] Based on the parameter inversion result obtained in step 5, select the new measured displacement value of the subsequent time sequence for parameter updating inversion; the posterior distribution of the parameter obtained by the previous measured displacement inversion is used as the prior distribution of the parameter in the next inversion, and the updating inversion ability of Bayesian inference is used. Repeat steps 3-5, substitute the water pressure component separated from the new measured value, the prior distribution, and the likelihood function into equation (6) to perform Bayesian inference updating inversion, and obtain the posterior distribution information of the parameter in different periods corresponding to different time sequence measured data to realize continuous tracking and updating of the material parameters of the rockfill dam.

[0053] The beneficial effects of the present application are:

[0054] (1) The present application uses the sparse chaotic polynomial expansion (sPCE) method to simulate the nonlinear relationship between the parameter to be inverted and the deformation of the dam, so as to construct a forward proxy model for the finite element analysis of the rockfill dam. Therefore, the displacement value of the dam can be obtained through the parameter to be inverted without the need for a large number of finite element analysis calculations, which ensures high inversion accuracy and greatly improves the inversion efficiency.

[0055] (2) The present application uses the Bayesian inference method to obtain the uncertainty distribution characteristics of the material parameters of different partitions of the dam through the measured displacement data of the dam, the prior distribution of the parameter, and the likelihood function. This method solves the problem that the traditional inversion method cannot consider the uncertainty of the parameter, and the obtained parameter value is closer to the engineering practice. Compared with the traditional inversion method, the parameter updating inversion can be performed through the monitoring data of different periods to realize the continuous tracking of the time-dependent evolution of the parameter.

[0056] (3) The method of the present application selects the strongly sensitive parameters in the constitutive model as the parameters to be inverted according to the actual material characteristics of the rockfill dam, and sets the likelihood function and error distribution parameters that conform to the engineering practice, so that the parameter inversion result is more accurate and the authenticity of the parameter inversion value is improved. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 This is a flowchart of the uncertainty inversion method for material parameters of rockfill dams based on Bayesian inference according to the present invention;

[0058] Figure 2 This is a schematic diagram of the cross-sectional structure of the finite element model of a rockfill dam in the Bayesian inference-based uncertainty inversion method for material parameters of rockfill dams of this invention.

[0059] Figure 3 This is a schematic diagram of a three-dimensional finite element model of a rockfill dam in the Bayesian inference-based uncertainty inversion method for material parameters of rockfill dams of this invention.

[0060] Figure 4 This is a schematic diagram of the displacement monitoring location of a rockfill dam in the Bayesian inference-based uncertainty inversion method for rockfill dam material parameters of the present invention.

[0061] Figure 5 This is a comparison chart of calculation errors for different proxy models in embodiments of the present invention;

[0062] Figure 6 Parameters of the main rockfill area and the downstream rockfill area at different times in this embodiment of the invention. Inversion result diagram;

[0063] Figure 7 The parameter K represents the parameters K for the main rockfill area and the downstream rockfill area at different times in this embodiment of the invention. b Inversion result diagram;

[0064] Figure 8 Parameters of the main rockfill area and the downstream rockfill area at different times in this embodiment of the invention. n Inversion result diagram;

[0065] Figure 9 This is a comparison chart of the prediction effects of different models on the measured displacement in an embodiment of the present invention;

[0066] Figure 10 This is a comparison chart of the prediction effects of different models on the measured displacement in the second period of this invention. Detailed Implementation

[0067] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] This invention relates to a Bayesian inference-based method for inverting uncertainties in the material parameters of rockfill dams, specifically as follows:

[0070] Step 1: Establish a finite element model of the rockfill dam and determine the prior distribution of the parameters to be inverted;

[0071] Step 2, constructing the sPCE surrogate model based on the prior distribution of inversion parameters;

[0072] Step 3, establishing a statistical model of the displacement of the rock-fill dam to separate the water pressure component of the measured displacement;

[0073] Step 4, constructing a rock-fill dam material likelihood function;

[0074] Step 5, rock-fill dam material parameter uncertainty inversion;

[0075] Step 6, rock-fill dam material parameter uncertainty updating inversion.

[0076] Embodiment 2

[0077] The rock-fill dam material parameter uncertainty inversion method based on Bayesian inference is implemented according to the following steps:

[0078] Step 1, establishing a rock-fill dam finite element model to determine the prior distribution of the rock-fill dam material constitutive model and the inversion parameters; specifically:

[0079] Step 1.1, based on the obtained rock-fill dam engineering design data, a rock-fill dam finite element model is established;

[0080] (1) The obtained engineering design data includes: rock-fill dam plan layout, rock-fill dam section design drawing, and dam body deformation monitoring design drawing. Among them, the rock-fill dam plan layout and the rock-fill dam section design drawing are used to establish the rock-fill dam finite element model; the dam body deformation monitoring design drawing is used to consider setting nodes at (or near) the monitoring point positions during model mesh division.

[0081] (2) Based on the rock-fill dam plan layout and the rock-fill dam section design drawing, considering the different material zoning conditions inside the dam body, different dam body cross sections are connected to generate a three-dimensional entity model in the computer aided design (CAD) software, and the three-dimensional entity model is imported into the finite element analysis (FEA) software for finite element mesh division. The internal structure of the dam body is as shown in Figure 2 ; In order to consider the layered compaction construction of the rock-fill dam, the element size is controlled at about 5% of the model size during mesh division, so as to perform layered loading during finite element analysis to simulate the layered compaction construction.

[0082] (3) For the rock-fill dam displacement monitoring equipment layout position, nodes are set at (or near) the corresponding parts in the model.

[0083] Considering the different material zoning conditions inside the dam body, such as face plate, cushion layer, transition layer, main rock-fill, secondary rock-fill, and the layered compaction construction of the rock-fill dam, and the deformation monitoring point arrangement, a rock-fill dam finite element model is established. In order to meet the accuracy of deformation simulation, the model mesh adopts quadrilateral elements (two-dimensional model) or hexahedral elements (three-dimensional model), such as Figure 3The monitoring equipment for the vertical displacement of the rock-fill dam is shown; nodes are set at the corresponding parts in the model to facilitate displacement extraction analysis, such as Figure 4 ;

[0084] Step 1.2, in order to describe the stress-strain relationship of each material unit in the finite element model, the upstream panel, toe plate and other concrete structures are simulated by a linear elastic model, and the cushion layer, transition layer, main rock-fill area and other soil and rock structures are simulated by the commonly used Duncan-Chang EB model in engineering. Since the overall displacement of the dam body is mainly affected by the deformation of the main rock-fill area and the downstream rock-fill area, the parameter inversion analysis is performed on the main rock-fill area and the downstream rock-fill area, that is, the initial internal friction angle of the main rock-fill area and the downstream rock-fill area with greater vertical displacement sensitivity is selected as the research object. The initial tangent modulus slope n and the tangent bulk modulus intercept K b are three parameters for uncertainty inversion.

[0085] Let n、K b be the prior distribution of the parameters obeying the normal distribution N(μ,σ 2 ), the mean value μ is the design parameter value, the coefficient of variation C υ is 0.1, and the standard deviation σ = μC υ ; the rest of the EB model parameters are considered as constants, and their sizes are the design parameter values.

[0086] Step 2, based on the prior distribution of the inversion parameters, an sPCE surrogate model is constructed;

[0087] Step 2.1, based on the prior distribution of the material parameters n、K b of the main rock-fill area and the downstream rock-fill area, Latin hypercube sampling (LHS) is used to generate m sets of material parameter combinations sample set X = {X1, X2,..., X m}, each element X i in the sample is a random combination of parameter n、K b sample values, that is The parameter samples are substituted into the finite element calculation to obtain the displacement response value sample set Y = {Y1, Y2,..., Y m} corresponding to the parameter samples; the samples are integrated to form a "parameter-displacement" sample set Z = {X, Y} = {[X1, Y1], [X2, Y2],..., [X m , Y m ]};

[0088] Step 2.2, divide the "parameter-displacement" sample set Z into training set and test set in the ratio of 3:1, that is, the training set Z = {X, Y} = {[X i , Y i]}={[X1,Y1],[X2,Y2],...,[X 3m / 4 ,Y 3m / 4 ]}, the test set Z′={X′,Y′}={[X i ′,Y i ′]}={[X1,Y1],[X2,Y2],...,[X m / 4 ,Y m / 4 ]}. Using the training set {X i} represents the input variable, {Y i} is the output variable. An sPCE surrogate model is established and a fitting analysis is performed to obtain the trained sPCE surrogate model.

[0089] Based on the distribution of the parameters to be inverted, Hermite orthogonal polynomials are selected as basis functions, and the constructed PCE surrogate model is as follows:

[0090]

[0091] In the formula, y is the output variable, and its PCE expression is an infinite series; a0, ...represents the coefficients of the polynomial to be solved; The variables are independent random variables that follow a normal distribution, and serve as input variables in uncertainty analysis; x(·) is the basis function of PCE. To meet the requirements of computational efficiency and accuracy (convergence), a 2nd to 3rd order polynomial expansion is generally used for fitting analysis, and the relative error can be controlled within 1%.

[0092] When solving for the PCE polynomial coefficients, the sparsity of the PCE surrogate model is utilized to select the PCE basis function terms that have a significant impact on the output variables, while setting the coefficients of the remaining PCE expansion terms with less influence to 0. This preserves the main influence relationship between the input and output variables and reduces the number of coefficients to be calculated, thereby improving analytical efficiency. Therefore, the solution for the PCE expansion coefficients is expressed as:

[0093]

[0094] In the formula, ξ represents the coefficients to be determined; ||a||0 represents the number of non-zero elements in the expanded coefficient vector; (i) Let ξ be the i-th sampled input random variable vector; Ψ(·) is The abbreviation of .

[0095] Orthogonal matching pursuit is adopted as the calculation strategy for the optimal itemset of the adaptive full PCE surrogate model. The expansion coefficients of each number of items in the optimal order of the initial full PCE surrogate model are calculated. Only the PCE basis function terms that have a significant impact on the output variables are retained. The basis functions are reconstructed to form the sPCE model. The coefficients of the non-zero terms of sPCE are obtained by equation (2). Then, the training of the sPCE surrogate model is completed, and the trained sPCE surrogate model is obtained.

[0096] Step 2.3, using the test set {X} i ′} is the input variable, and after substituting it into the sPCE surrogate model, the calculated displacement value {y} is obtained. i ′} will calculate the displacement value {y i ′} and {Y} in the test set i A comparative analysis is performed to verify the calculation error of the sPCE proxy model. If it does not meet the accuracy requirements, step 2.2 is repeated; if it meets the accuracy requirements, the obtained sPCE proxy model is output.

[0097] The error test indicators include root mean square error (RMSE), root mean square relative error (RMSPE), mean error (MAE), mean relative error (MAPE), and correlation coefficient (R). The calculation formulas are as follows:

[0098]

[0099] Step 3: Establish a statistical model of rockfill dam displacement and separate the measured displacement water pressure components;

[0100] A statistical model of rockfill dam displacement was established. Based on the environmental quantities and measured displacement data of the actual project, the regression coefficients of each displacement component in the model were determined by the least squares method, and then the water pressure component in the measured displacement of the dam body was separated.

[0101] The statistical model for rockfill dam displacement is as follows:

[0102] δ=δ H +δ T +δ θ (4)

[0103] In the formula, δ represents the dam displacement; δ H δ is the water pressure component; T For temperature components; δ θ For time-sensitive components.

[0104] The expressions for each displacement component are selected with reference to those for earth-rock dams:

[0105]

[0106] In the formula, H is the upstream water depth; T represents the average upstream water depth over the previous i days; iwhere i is the day of the observation; t is the time (days) from the starting day to the observation day; m1 is generally taken as 3, and m2 and m3 are generally taken as 9 or 10; θ is a time-dependent displacement factor, equal to t / 100; a, b, and c are regression coefficients.

[0107] The three environmental variables, water depth H, air temperature T, and observation time t, and the measured displacement data of the dam body are substituted into the statistical model, and the least squares method is used to fit to obtain the regression coefficients; the obtained regression coefficients a and H, are substituted into the water pressure component expression in equation (5) to obtain the water pressure component value δ H separated from the measured displacement.

[0108] Step 4, construct the rockfill dam material likelihood function; specifically:

[0109] Step 4.1, according to the initial prior distribution of the parameters of the main rockfill area and the downstream rockfill area of the dam body in step 1.2, set the sampling range of the parameter values in different inversion stages as [μ-3σ, μ+3σ], set the number of Markov chains (MC) p=4 and the sample number q=20000 of each chain. The DREAM method is used to sample the parameter groups, and the main rockfill area parameter samples and the downstream rockfill area parameter samples

[0110] Substitute the parameter samples S and S' into the sPCE surrogate model in step 2 to simulate finite element analysis, and obtain the vertical displacement values h i (θ) corresponding to the sample parameters.

[0111] Step 4.2, set the mean error μ wi =0 and the error distribution standard deviation σ wi =1 mm. According to the prior distribution form of the parameters, select the corresponding likelihood function form:

[0112]

[0113] where y i is the water pressure component separated from the measured value; h i (θ) is the finite element calculated dam displacement response value; μ wi is the mean measurement error of the monitoring item; and σ wi is the measurement error standard deviation of the monitoring item.

[0114] Substitute the water pressure component y i =δ Hi separated from the measured value, the finite element calculated dam displacement response value h i (θ), the mean measurement error μ wi , and the standard deviation σ wiSubstitute equation (6) to construct the rock-fill dam material parameter likelihood function.

[0115] Step 5, rock-fill dam material parameter uncertainty inversion;

[0116] According to the Bayesian theory, the Bayesian inference model is established:

[0117]

[0118] In the formula, θ is the to-be-inverted parameter belonging to the space; is the actual observation data in the space Here is the water pressure component separated from the measured value; p(θ) is the prior distribution; is the likelihood function; is the posterior distribution of the to-be-inverted parameter; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function:

[0119]

[0120] Substitute the prior distribution, water pressure component, and likelihood function obtained in steps 1-4 into equation (7) to calculate the posterior distribution N(μ′,σ′ 2 of the to-be-inverted material parameter, so as to determine the inversion value of the parameter.

[0121] Step 6, rock-fill dam material parameter uncertainty updating inversion.

[0122] Based on the parameter inversion result obtained in step 5, select the new measured displacement value of the subsequent time sequence for parameter updating inversion. Take the parameter posterior distribution obtained by the previous measured displacement inversion as the prior distribution of the parameter in the next inversion, use the updating inversion ability of Bayesian inference, repeat steps 3-5, substitute the water pressure component separated from the new measured value, the prior distribution, the likelihood function into the Bayesian inference model (equation 6) for Bayesian inference updating inversion, and obtain the posterior distribution information N(μ i ′,σ i ′ 2 ) of the parameter corresponding to the measured data of different time sequences, so as to realize the continuous tracking and updating of the rock-fill dam material parameter.

[0123] Example 3

[0124] Referring to Figure 5, which is a comparison chart of the calculation errors of the sPCE surrogate model and the ORELM surrogate model and the SVM surrogate model. As can be seen from the chart, the overall error levels of the three surrogate models are relatively small, the sPCE model is superior to the ORELM model in terms of the indicators MAPE and R, and the analysis error of the SVM model is obviously larger than those of the other models; in general, the calculation accuracy of the sPCE model is slightly superior to that of the ORELM model and significantly superior to that of the SVM model. Therefore, the sPCE method can be used to establish a surrogate model to accurately simulate the finite element analysis process and ensure the correctness and efficiency of the inversion analysis.

[0125] Example 4

[0126] Figure 6-8 are the parameter inversion results of the main rockfill area and the downstream rockfill area, and the mean values and standard deviation variation trends of the material parameters of each measuring point in different periods. As can be seen from the chart, the mean values of the material parameters of the dam body in different periods obtained by inversion of the measured displacement of the dam body have certain changes. Among them, the material parameters of the main rockfill area n1, K b1 are basically around 50, 0.84 and 450, and the material parameters of the downstream rockfill area n2, K b2 are basically around 45, 0.85 and 440; under the influence of different water levels in the four monitoring periods, the mean values of the material parameters of each partition have no obvious periodic changes, among which the mean values of the material parameters obtained by inversion under the upstream low water level (around 2001.5 m) and the high water level (around 2004.5 m) during the period from February 2005 to June 2007 and the period from November 2008 to April 2010 have slight changes with the growth of the monitoring time sequence, but the overall difference is not large, indicating that the change of the reservoir water level has little effect on the mean values of the material parameters of the dam body; by comparing the inversion results during June 2007 and November 2008, it can be seen that due to the influence of the “5.12” Wenchuan earthquake, the mean values of the material parameters of the dam body have relatively large changes compared with the former, among which the parameters n1, K b2 have increased, n2, K b1 have decreased. Unlike the mean value changes, the standard deviations of the material parameters of each partition have obvious variation trends, i.e., they gradually decrease with the growth of the monitoring time sequence, and the coefficient of variation decreases from the initially set 0.1 to below 0.057; the changes of the standard deviations obtained from the first two inversions are the most obvious, and the standard deviations obtained from the subsequent inversions are slightly smaller than the former but have little difference.

[0127] From the above, it is shown that the small change of upstream reservoir water level in dam operation period has little effect on the mean value of dam material parameters, but due to the secondary consolidation of rockfill material, some parameters will have a slight trend change with the growth of monitoring time. The standard deviation of material parameters gradually decreases with the growth of monitoring time, indicating that the range of parameter posterior distribution gradually narrows, the uncertainty of parameters gradually reduces and tends to be stable. Therefore, the traditional deterministic inversion method cannot analyze the uncertainty and continuous change trend of real parameters of the dam, especially when the dam experiences load fluctuations such as earthquakes or high water level differences, the uncertainty inversion of dam material parameters should be carried out in time to master the real mechanical properties and operation state of the dam.

[0128] Example 5

[0129] In order to verify the accuracy of the rockfill dam material parameter uncertainty inversion method based on Bayesian inference, the mean value of the posterior distribution of the inversion parameters is selected, and based on the vertical displacement monitoring data of VS1-05 and VS2-05 two measuring points, a mixed model of rockfill dam displacement monitoring is established for verification. Since the material parameters of the dam changed after the "5.12" Wenchuan earthquake, the monitoring sequence is divided into two periods with this time point as the endpoint, and the modeling is carried out respectively from December 2004 to April 2008 and from May 2008 to June 2010, and the fitting and prediction of the monitoring data in the respective time periods are carried out, wherein the prediction samples are the last 10 monitoring values of the monitoring sequence.

[0130] The above mixed model is based on the statistical model of formula (4) and formula (5), and the water pressure component is calculated by finite element method, which replaces the statistical model expression of δ H in formula (5), to form a mixed model of rockfill dam displacement. The Bayesian inversion parameters of June 19, 2007 and April 19, 2010 are used for finite element calculation in period one and period two respectively, to obtain the water level-displacement fitting curve equation of VS1-05 and VS2-05 measuring points under different water levels, which replaces the water pressure component in the statistical model. Then the least square fitting is carried out to obtain the regression coefficients to determine the Bayesian inversion mixed model in different periods. In order to compare with the traditional deterministic inversion result, the traditional deterministic parameter inversion analysis based on ORELM proxy model is carried out by using the measurement value on December 3, 2004, to obtain the inversion parameter value and establish the corresponding deterministic inversion mixed model.

[0131] Example 6

[0132] Figure 9 and Figure 10For the prediction effect comparison of measured displacement of each model in different periods, the "mixed model" in the figure is the Bayesian inversion mixed model, and the "mixed model 2" is the deterministic inversion mixed model. As can be seen from the figure, compared with the traditional deterministic parameter inversion, the mixed model of the rockfill dam established by using the Bayesian inference inversion method shows higher fitting and prediction accuracy for the displacement of the dam body in different periods, indicating that the inversion method can more truly reflect the actual material parameter change of the dam body, and the calculated water pressure component is closer to the actual water pressure component.

[0133] The Bayesian inference has high analysis accuracy in the material parameter inversion of the rockfill dam, can conveniently obtain the material mechanics parameter value close to the actual dam, and provides accurate and reliable material parameter basis for engineering safety state analysis; in addition, based on the parameter sensitivity characteristics in the analysis, the material parameters with larger sensitivity are selected and assumed to be in normal distribution form, and the mixed model is established by using the mean value of the parameter posterior distribution to analyze the safety state of the dam, which is reasonable and feasible.

[0134] The above shows and describes the basic principles and main features of the present application and the advantages of the present application. For those skilled in the art, it is obvious that the present application is not limited to the details of the above exemplary embodiments, and the present application can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application. Any reference signs in the claims should not be considered as limiting the claims involved.

[0135] In addition, it should be understood that although the present specification is described in terms of embodiments, each embodiment does not contain only one independent technical solution, and the description manner of the specification is only for clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be properly combined to form other embodiments that can be understood by those skilled in the art. The above is only for illustrating the technical idea of the present application, and cannot limit the protection scope of the present application, and any modification made according to the technical idea of the present application on the basis of the technical solution falls within the protection scope of the claims of the present application.

Claims

1. A method for rockfill dam material parameter uncertainty inversion based on Bayesian inference, characterized in that, The following steps are implemented in detail: Step 1, establish a finite element model of the rock-fill dam, and determine the prior distribution of the parameters to be inverted; specifically: Step 1.1, based on the obtained rock-fill dam engineering design data, including: rock-fill dam layout, rock-fill dam section design, dam deformation monitoring design, establish a finite element model of the rock-fill dam; Step 1.2, in order to describe the stress-strain relationship of each material unit in the finite element model of the rockfill dam, the parameter inversion analysis is carried out on the main rockfill area and the downstream rockfill area, that is, the initial internal friction angle with greater vertical displacement sensitivity in the main rockfill area and the downstream rockfill area is selected φ 0, initial tangent modulus slope n , tangent bulk modulus intercept K b Three parameters are the research objects for uncertainty inversion; it is assumed that φ 0, n , K b The prior distribution of the parameters obeys normal distribution ; Step 2, construct a sPCE surrogate model based on the prior distribution of the inverted parameters; specifically: Step 2.1, based on the material parameters of the main rockfill zone and the downstream rockfill zone respectively φ 0、 n 、 K b The prior distribution of the parameters is sampled using Latin hypercube, generating a sample set of combinations of material parameters m Each element in the sample set is X i a parameter φ 0、 n 、 K b a random combination of sample values, i.e. The parameter samples are substituted into the finite element calculation to obtain a sample set of displacement response values of the rockfill dam corresponding to the parameter samples The samples are integrated to form a "parameter-displacement" sample set ;​ Step 2.2, extract the "parameter-displacement" sample set. Z It is divided into a training set and a test set, i.e., the training set test set ; with training focus For input variables, As the output variable, an sPCE surrogate model is established and a fitting analysis is performed to obtain the trained sPCE surrogate model. According to the distribution form of the parameters to be inverted, Hermite orthogonal polynomials are selected as the basis functions, and the PCE surrogate model is constructed as follows: （1） wherein y is an output variable; is a polynomial coefficient to be solved; is a random variable independent of each other and subject to normal distribution, which is an input variable in uncertainty analysis; is a basis function of PCE; The solution of PCE expansion term coefficient is expressed as: （2） wherein are to-be-solved coefficients; a ||0is the number of non-zero elements in the to-be-determined expansion coefficient vector; is an input random variable vector ξ is the i-th sampling sample of i is the i-th sampling sample of is a short form of … The orthogonal matching pursuit method is used as a calculation strategy of an optimal term set of an adaptive complete PCE proxy model, and the expansion coefficients of the number of terms in the optimal order of the initial proxy model of the complete PCE are calculated The PCE base function items with greater influences on the output variables are reserved, the base function is reconstructed to form an sPCE model, the non-zero term coefficients of the sPCE are obtained through formula (2), the training of the sPCE proxy model is completed, and the trained sPCE proxy model is obtained. Step 2.3, using the test set The calculated displacement values ​​are obtained by substituting the input variables into the sPCE surrogate model. The displacement value will be calculated. With the test set Perform a comparative analysis to verify the calculation error of the sPCE surrogate model. If it does not meet the accuracy requirements, repeat step 2.2; if it meets the accuracy requirements, output the obtained sPCE surrogate model. Step 3, establish a displacement statistical model of the rock-fill dam, and separate the measured displacement water pressure component; Step 4, construct a rock-fill dam material likelihood function; Step 5, rock-fill dam material parameter uncertainty inversion; Step 6, rock-fill dam material parameter uncertainty update inversion.

2. The Bayesian inference-based rockfill dam material parameter uncertainty inversion method of claim 1, wherein, In step 2.3, the error test index adopts root mean square error RMSE, root mean square relative error RMSPE, mean error MAE, mean relative error MAPE, and correlation coefficient R, and the calculation formulas are respectively: （3）。 3. The Bayesian inference-based rockfill dam material parameter uncertainty inversion method of claim 1, wherein, In step 3, specifically: The displacement statistical model of the rock-fill dam is: （4） wherein is the dam displacement; is the water pressure component; is the temperature component; is the aging component; Each displacement component expression is selected as: （5） wherein H is the upstream water depth; is the average upstream water depth for the previous i day; is the average air temperature for the previous i day; t is the time from the start date to the observation date; is 3, is 9 or 10; is the time-lag factor; a , b , c is the regression coefficient; water depth H , air temperature T , observation time t The three environmental quantity monitoring data and the dam measured displacement data are substituted into the statistical model, and the least square method is used to fit to obtain each regression coefficient; the obtained regression coefficient a and H、 are substituted into the water pressure component expression in formula (5) to obtain the water pressure component value separated from the measured displacement .

4. The Bayesian inference-based rockfill dam material parameter uncertainty inversion method of claim 3, wherein, In step 4, specifically: Step 4.1, according to the initial prior distribution of each parameter of the main rockfill zone and the downstream rockfill zone in step 1.2, the sampling range of each parameter value in different inversion stages is set as μ -3 σ , μ +3 σ ], the number of Markov chains is set as p =4 and the sample number of each chain is set as q =20000; the DREAM method is used to sample the parameter groups, and the main rockfill zone parameter samples and the downstream rockfill zone parameter samples are generated; The parameter sample is substituted into the sPCE agent model of step 2 to simulate finite element analysis, to obtain the vertical displacement value corresponding to the sample parameter S With The parameter sample is substituted into the sPCE agent model of step 2 to simulate finite element analysis, to obtain the vertical displacement value corresponding to the sample parameter ; Step 4.2, set monitoring data error mean = 0, error distribution standard deviation = 1 mm; according to the parameter prior distribution form, select the corresponding likelihood function form: （6） In the formula, is the water pressure component separated from the measured value; is the finite element calculated dam displacement response value; is the mean measurement error of the monitoring project; is the standard deviation of the measurement error of the monitoring project; The water pressure component separated from the measured value , finite element calculation of dam displacement response value , mean of measurement error and standard deviation Substitute equation (6) to construct the rockfill dam material parameter likelihood function.

5. The Bayesian inference-based rockfill dam material parameter uncertainty inversion method of claim 4, wherein, In step 5, specifically: According to the Bayesian theory, a Bayesian inference model is established: （7） wherein is the parameter to be inverted belonging to the space; is the actual observation data in the space , here the water pressure component separated from the measured values; is the prior distribution; is the likelihood function; is the posterior distribution of the parameter to be inverted; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function: （8） The obtained parameter prior distribution, water pressure component and likelihood function in steps 1-4 are substituted into formula (7) to calculate the posterior distribution of the material parameter to be inverted to determine the inversion value of the parameter.

6. The Bayesian inference-based rockfill dam material parameter uncertainty inversion method of claim 5, wherein, In step 6, specifically: Based on the parameter inversion result obtained in step 5, new measured displacement values of subsequent time series are selected for parameter updating inversion; the posterior distribution of the parameters obtained by the previous measured displacement inversion is used as the prior distribution of the parameters in the next inversion, the updating inversion ability of Bayesian inference is used, steps 3-5 are repeated, the water pressure component separated from the new measured value, the prior distribution and the likelihood function are substituted into formula (6) for Bayesian inference updating inversion, and the posterior distribution information of the parameters corresponding to different time series of measured data in different periods is obtained The continuous tracking and updating of the material parameters of the rock-fill dam are realized.

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