Rock-fill dam material parameter uncertainty inversion method based on Bayesian inference

Abstract

The invention discloses a rock-fill dam material parameter uncertainty inversion method based on Bayesian inference, and the method specifically comprises the steps: building a rock-fill dam finite element model, and determining the prior distribution of to-be-inverted parameters; constructing an sPCE proxy model based on prior distribution of inversion parameters; a rock-fill dam displacement statistical model is established, and actually-measured displacement water pressure components are separated; constructing a rock-fill dam material likelihood function; carrying out uncertainty inversion on the rock-fill dam material parameters; and updating and inverting the uncertainty of the rock-fill dam material parameters. According to the method, a Bayesian inference method is utilized, and uncertainty distribution characteristics of different partition material parameters of a dam body are obtained through actual measurement displacement data, parameter prior distribution and a likelihood function of the dam. According to the method, the defect that parameter uncertainty cannot be considered in a traditional inversion method is overcome, and obtained parameter values are closer to engineering practice; compared with a traditional inversion method, parameter updating inversion can be carried out through monitoring data in different periods, and continuous tracking of parameter timeliness evolution is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of water conservancy engineering material parameter analysis, and in particular relates to a rockfill dam material parameter uncertainty inversion method based on Bayesian inference. Background Art

[0002] With the continuous development of water conservancy projects, the height of rockfill dams under construction has been continuously broken through, and dam safety has also received more and more attention. Structural analysis based on the actual material parameters of the dam body is an important way to understand the structural safety of the dam and evaluate the health of the dam operation. Inverse analysis, as a method based on numerical simulation analysis, obtains mechanical properties or initial stress conditions according to the changes in the properties of rock and soil under actual engineering loads, and has become one of the important means to determine the parameter values ​​of dam materials. At present, the traditional deterministic inversion method has been rapidly developed and widely used in the inversion analysis of geotechnical problems. It seeks the optimal parameter group that satisfies the objective function through the optimization algorithm to make the calculation results as close to the measured data as possible. However, in actual engineering, affected by factors such as geological exploration, geotechnical tests, design assumptions, construction technology, construction conditions, and material aging evolution, the actual mechanical parameters of rockfill materials have certain differences and random distribution characteristics from the design parameters. When using the traditional inversion method for analysis, the uncertainty of such parameters will be ignored, and the wrong cognition and assumptions about the parameters cannot be corrected through monitoring data, which often leads to certain errors in the results of dam structure analysis, and thus the actual operation status of the dam cannot be truly understood.

[0003] As an inferential statistical method, Bayesian inference can use existing information to modify the prior distribution of the original parameters and update it to a posterior distribution close to the actual project. Therefore, the use of Bayesian inference for parameter inversion analysis can effectively obtain material mechanical parameter distribution information close to the actual dam and provide a more accurate description of parameter uncertainty. However, the analysis results of this method are affected by many factors such as prior distribution, proxy model, sampling method, likelihood function, etc., and arbitrary determination will greatly reduce the accuracy of Bayesian analysis. Therefore, it is necessary to determine the above-mentioned influencing factors based on the actual engineering characteristics and establish an efficient and reasonable inversion method for material parameter uncertainty of rockfill dams based on Bayesian inference. Summary of the invention

[0004] The purpose of the present invention is to provide a rockfill dam material parameter uncertainty inversion method based on Bayesian inference, thereby realizing material parameter update inversion under different monitoring data.

[0005] The technical solution adopted by the present invention is a method for inverting uncertainty of rockfill dam material parameters based on Bayesian inference, which is specifically implemented in 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 the sPCE proxy model based on the prior distribution of the inversion parameters;

[0008] Step 3, establish a statistical model of rockfill dam displacement and separate the water pressure component of the measured displacement;

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

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

[0011] Step 6: Update and invert the uncertainty of rockfill dam material parameters.

[0012] The present invention is also characterized in that:

[0013] In step 1, specifically:

[0014] Step 1.1, based on the acquired rockfill dam engineering design data, including: rockfill dam plan layout drawing, rockfill dam cross-section design drawing, dam deformation monitoring design drawing, establish a finite element model of the rockfill dam;

[0015] Step 1.2: To describe the stress-strain relationship of each material unit in the finite element model of the rockfill dam, parameter inversion analysis is performed 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. Initial tangent modulus slope n, tangent bulk modulus intercept K b The three parameters are used as the research object for uncertainty inversion; n. K b The parameter prior distribution follows the normal distribution N(μ,σ 2 ).

[0016] In step 2, specifically:

[0017] Step 2.1: Based on the material parameters of the main rockfill area and the downstream rockfill area n. K b The prior distribution is used to sample using Latin hypercube to generate a sample set X = {X1, X2, ..., X m}, each element X in the sample i For parameters n. K b A random combination of sample values, i.e. Substitute the parameter samples into the finite element calculation to obtain the sample set of displacement response values ​​of the rockfill dam corresponding to the parameter samples Y = {Y1, Y2, ..., Y m}; Integrate each sample to form a "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 ]}, test set Z′={X′,Y′}={[X i ′,Y i ′]}={[X1,Y1],[X2,Y2],...,[X m / 4 ,Y m / 4 ]}; In the training set {X i} is the input variable, {Y i} is the output variable, the sPCE proxy model is established and fitting analysis is performed to obtain the trained sPCE proxy model;

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

[0020]

[0021] Where y is the output variable; a0, ,...are the coefficients of the polynomial to be solved; are mutually independent random variables that obey a normal distribution and are input variables in uncertainty analysis; x(·) is the basis function of PCE;

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

[0023]

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

[0025] The orthogonal matching pursuit method is used as the calculation strategy for the optimal item set of the adaptive complete PCE surrogate model to calculate the expansion coefficient of each item in the optimal order of the complete PCE initial surrogate model. Only the PCE basis function items 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), and then the training of the sPCE proxy model is completed to obtain the trained sPCE proxy model;

[0026] Step 2.3, take the test set {X i ′} is the input variable, and after being substituted into the sPCE proxy model, the calculated displacement value {y i ′}, the displacement value {y i ′} and the test set {Y i ′} Perform comparative analysis to verify the calculation error of the sPCE proxy model. If it does not meet the accuracy requirements, repeat step 2.2; if it meets the accuracy requirements, output the obtained sPCE proxy model.

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

[0028]

[0029]

[0030] In step 3, specifically:

[0031] The statistical model of rockfill dam displacement is:

[0032] δ=δ H +δ T +δ θ (4)

[0033] Where, δ is the displacement of the dam body; δ H is the water pressure component; δ T is the temperature component; δ θ For the time-effectiveness component.

[0034] The expressions of displacement components are selected with reference to earth-rock dam as follows:

[0035]

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

[0037] The monitoring data of three environmental variables, water depth H, temperature T, and observation time t, and the measured displacement data of the dam body were substituted into the statistical model, and the regression coefficients were obtained by the least squares method. Substituting into the water pressure component expression in equation (5), we can obtain the water pressure component value δ separated from the measured displacement: H .

[0038] In step 4, specifically:

[0039] Step 4.1: Based on 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 to [μ-3σ,μ+3σ], set the number of Markov chains p=4 and the number of samples in each chain q=20000. Use the DREAM method to sample the parameter group and generate the main rockfill area parameter samples. Parameter samples of downstream rockfill area

[0040] Substitute the parameter samples S and S′ into the sPCE proxy model in step 2 to simulate the 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 μ of the monitoring data wi =0, error distribution standard deviation σ wi =1mm; According to the parameter prior distribution form, select the corresponding likelihood function form:

[0042]

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

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

[0045] In step 5, specifically:

[0046] Establish a Bayesian inference model based on Bayesian theory:

[0047]

[0048] In the formula, θ is The parameters to be inverted in space; For Actual observation data in 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 parameter to be inverted; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function:

[0049]

[0050] Substitute the prior distribution of each parameter, water pressure component, and likelihood function obtained in steps 1 to 4 into equation (7) to calculate the posterior distribution N(μ′,σ′) of the material parameter to be inverted. 2 ) to determine the inverted values ​​of the parameters.

[0051] In step 6, specifically:

[0052] Based on the parameter inversion results obtained in step 5, the new measured displacement values ​​of the subsequent time series are selected for parameter update inversion; the posterior distribution of the parameters obtained from the previous measured displacement inversion is used as the prior distribution of the parameters in the next inversion, and the update inversion capability of Bayesian inference is used to repeat steps 3 to 5, and the water pressure component, prior distribution, and likelihood function separated from the new measured value are substituted into formula (6) for Bayesian inference update inversion to obtain the posterior distribution information of parameters in different periods corresponding to the measured data of different time series. To achieve continuous tracking and updating of rockfill dam material parameters.

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

[0054] (1) The present invention adopts the sparse chaotic polynomial expansion (sPCE) method to simulate the nonlinear relationship between the parameters to be inverted and the dam body deformation, thereby constructing a forward proxy model for the finite element analysis of the rockfill dam. Therefore, the dam body displacement value can be obtained through the parameters to be inverted without performing a large number of finite element analysis calculations, thereby ensuring a high inversion accuracy and greatly improving the inversion efficiency.

[0055] (2) The present invention 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 parameters, and the likelihood function. This method solves the shortcoming that the traditional inversion method cannot consider parameter uncertainty, and the obtained parameter values ​​are closer to the actual engineering; compared with the traditional inversion method, the parameter update inversion can be performed through monitoring data of different periods, and the continuous tracking of the time-effective evolution of parameters can be achieved.

[0056] (3) The method of the present invention selects highly sensitive parameters in the constitutive model as parameters to be inverted based on the actual material properties of the rockfill dam, and sets likelihood functions and error distribution parameters that conform to the actual engineering practice, so that the parameter inversion results are more accurate and the authenticity of the parameter inversion is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the uncertainty inversion method of rockfill dam material parameters based on Bayesian inference of the present invention;

[0058] Figure 2 It is a schematic diagram of the cross-sectional structure of a finite element model of a rockfill dam in the uncertainty inversion method of rockfill dam material parameters based on Bayesian inference of the present invention;

[0059] Figure 3 It is a schematic diagram of a three-dimensional finite element model of a rockfill dam in the uncertainty inversion method of rockfill dam material parameters based on Bayesian inference of the present invention;

[0060] Figure 4 It is a schematic diagram of the displacement monitoring position of the rockfill dam in the uncertainty inversion method of the material parameters of the rockfill dam based on Bayesian inference of the present invention;

[0061] Figure 5 A comparison diagram of calculation errors of different proxy models in an embodiment of the present invention;

[0062] Figure 6 The parameters of the main rockfill area and the downstream rockfill area at different times in the embodiment of the present invention are shown in FIG. Inversion result diagram;

[0063] Figure 7 is the parameter K in the main rockfill area and the downstream rockfill area at different times in the embodiment of the present invention. b Inversion result diagram;

[0064] Figure 8 The parameters of the main rockfill area and the downstream rockfill area at different times in the embodiment of the present invention are shown in FIG. n Inversion result diagram;

[0065] Fig. 9 This is a comparison diagram of the prediction effects of various models on the measured displacement during period 1 in the embodiment of the present invention;

[0066] Fig.10 This is a comparison chart of the prediction effects of each model on the measured displacement in period 2 in the embodiment of the present invention. DETAILED DESCRIPTION

[0067] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] The present invention provides a method for inverting uncertainty of rockfill dam material parameters based on Bayesian inference, specifically:

[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 proxy model based on the prior distribution of the inversion parameters;

[0072] Step 3, establish a statistical model of rockfill dam displacement and separate the water pressure component of the measured displacement;

[0073] Step 4, constructing the material likelihood function of the rockfill dam;

[0074] Step 5, inversion of uncertainty of rockfill dam material parameters;

[0075] Step 6: Update and invert the uncertainty of rockfill dam material parameters.

[0076] Example 2

[0077] The present invention provides a method for inverting uncertainty of rockfill dam material parameters based on Bayesian inference, which is specifically implemented according to the following steps:

[0078] Step 1: Establish a finite element model of the rockfill dam and determine the material constitutive model of the rockfill dam and the prior distribution of the parameters to be inverted; specifically:

[0079] Step 1.1, based on the acquired rockfill dam engineering design data, establish a finite element model of the rockfill dam;

[0080] (1) The engineering design data obtained include: rockfill dam plan layout, rockfill dam cross-section design, and dam deformation monitoring design. The rockfill dam plan layout and rockfill dam cross-section design are used to establish the finite element model of the rockfill dam; the dam deformation monitoring design is used to consider setting nodes at (or near) the monitoring point when dividing the model mesh.

[0081] (2) Based on the plan layout and cross-sectional design of the rockfill dam, the different cross-sections of the dam are connected in computer-aided design (CAD) software to generate a three-dimensional solid model, which is then imported into finite element analysis (FEA) software for finite element mesh generation. The internal structure of the dam is shown in Figure 1. Figure 2 As shown in the figure, in order to consider the layered compaction construction of the rockfill dam, the unit size is controlled at about 5% of the model size during mesh generation, so that layered loading can be performed during finite element analysis to simulate the layered compaction construction.

[0082] (3) According to the location of the rockfill dam displacement monitoring equipment, nodes are set at the corresponding locations (or nearby) in the model.

[0083] Considering the different material partitions of the dam body, such as the face plate, cushion layer, transition layer, primary rockfill, secondary rockfill, etc., the layered rolling construction of the rockfill dam, the arrangement of deformation monitoring points, etc., a finite element model of the rockfill dam is established. In order to meet the accuracy of deformation simulation, the model grid uses quadrilateral elements (two-dimensional model) or hexahedral elements (three-dimensional model), such as Figure 3As shown in the figure, according to the layout of the vertical displacement monitoring equipment of the rockfill dam, nodes are set at the corresponding positions in the model to facilitate displacement extraction analysis, such as Figure 4 As shown;

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

[0085] set up n. K b The parameter prior distribution follows the normal distribution N(μ,σ 2 ), whose mean μ is the design parameter value, and the coefficient of variation C υ is 0.1, standard deviation σ=μC υ The remaining parameters of the EB model are considered constants, and their sizes are all design parameter values.

[0086] Step 2, constructing the sPCE proxy model based on the prior distribution of the inversion parameters;

[0087] Step 2.1: Based on the material parameters of the main rockfill area and the downstream rockfill area n. K b The prior distribution is used to sample using Latin hypercube (LHS) to generate a sample set X = {X1, X2, ..., X m}, each element X in the sample i For parameters n. K b A random combination of sample values, i.e. Substitute the parameter samples into the finite element calculation to obtain the sample set of displacement response values ​​of the rockfill dam corresponding to the parameter samples Y = {Y1, Y2, ..., Y m}; Integrate each sample 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 a training set and a test set in a ratio of 3:1, i.e., the training set Z = {X, Y} = {[X i ,Y i]}={[X1,Y1],[X2,Y2],...,[X 3m / 4 ,Y 3m / 4 ]}, test set Z′={X′,Y′}={[X i ′,Y i ′]}={[X1,Y1],[X2,Y2],...,[X m / 4 ,Y m / 4 ]}. In the training set {X i} is the input variable, {Y i} is the output variable, the sPCE proxy model is established and fitting analysis is performed to obtain the trained sPCE proxy model;

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

[0090]

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

[0092] When solving the PCE polynomial coefficients, the sparsity of the PCE proxy model is used to select the PCE basis function terms that have a greater impact on the output variables, and the coefficients of the remaining PCE expansion terms with less impact are set to 0, so as to retain the main influence relationship between the input variables and the output variables, and reduce the coefficients of the expansion terms to be calculated to improve the analysis efficiency. Therefore, the solution of the PCE expansion term coefficients is expressed as:

[0093]

[0094] In the formula, is the coefficient to be determined; ||a||0 is the number of non-zero elements in the expansion coefficient vector to be determined; ξ (i) is the i-th sample of the input random variable vector ξ; Ψ(·) is Abbreviation of .

[0095] The orthogonal matching pursuit method is used as the calculation strategy for the optimal item set of the adaptive complete PCE surrogate model to calculate the expansion coefficients of each item in the optimal order of the complete PCE initial surrogate model. Only the PCE basis function items that have a greater impact on the output variables are retained, the basis functions are reconstructed to form the sPCE model, and the non-zero coefficients of the sPCE are obtained by formula (2), thereby completing the training of the sPCE proxy model and obtaining the trained sPCE proxy model.

[0096] Step 2.3, take the test set {X i ′} is the input variable, and after being substituted into the sPCE proxy model, the calculated displacement value {y i ′}, the displacement value {y i ′} and the test set {Y i ′} Perform comparative analysis to verify the calculation error of the sPCE proxy model. If it does not meet the accuracy requirements, repeat step 2.2; if it meets the accuracy requirements, output the obtained sPCE proxy model.

[0097] Among them, the error test indicators use root mean square error RMSE, root mean square relative error RMSPE, average error MAE, average relative error MAPE, and correlation coefficient R, and the calculation formulas are:

[0098]

[0099] Step 3, establish a statistical model of rockfill dam displacement and separate the water pressure component of the measured displacement;

[0100] A statistical model of rockfill dam displacement is established. Based on the environmental quantities of the actual project and the measured data of dam displacement, the least squares method is used to determine the regression coefficients of each displacement component in the model, and then the water pressure component in the measured dam displacement is separated.

[0101] The statistical model of rockfill dam displacement is:

[0102] δ=δ H +δ T +δ θ (4)

[0103] Where, δ is the displacement of the dam body; δ H is the water pressure component; δ T is the temperature component; δ θ For the time-effectiveness component.

[0104] The expressions of displacement components are selected with reference to earth-rock dam as follows:

[0105]

[0106] Where H is the upstream water depth; is the average upstream water depth of the previous i days; T iis the average temperature of the i-th day before the observation day; t is the time between the observation day and the start day (days); m1 is generally 3, and m2 and m3 are generally 9 or 10; θ is the time-dependent displacement factor, which is equal to t / 100; a, b, and c are regression coefficients.

[0107] The monitoring data of three environmental variables, water depth H, temperature T, and observation time t, and the measured displacement data of the dam body were substituted into the statistical model, and the regression coefficients were obtained by the least squares method. Substituting into the water pressure component expression in equation (5), we can obtain the water pressure component value δ separated from the measured displacement: H .

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

[0109] Step 4.1: Based on 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, the sampling range of each parameter value in different inversion stages is set to [μ-3σ, μ+3σ], the number of Markov chains (MC) p = 4 and the number of samples in each chain q = 20000. The DREAM method is used to sample the parameter group and generate the main rockfill area parameter samples. Parameter samples of downstream rockfill area

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

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

[0112]

[0113] In the formula, y i is the water pressure component separated from the measured value; h i (θ) is the displacement response value of the dam body calculated by finite element method; μ wi is the mean value of the measurement error of the monitoring project; σ wi It is the standard deviation of measurement error for monitoring items.

[0114] The water pressure component y separated from the measured value i =δ Hi 、Finite element calculation of dam displacement response value h i (θ), mean value of measurement error μ wi With standard deviation σ wiSubstitute into formula (6) to construct the likelihood function of rockfill dam material parameters.

[0115] Step 5, inversion of uncertainty of rockfill dam material parameters;

[0116] Establish a Bayesian inference model based on Bayesian theory:

[0117]

[0118] In the formula, θ is The parameters to be inverted in space; For Actual observation data in 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 parameter to be inverted; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function:

[0119]

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

[0121] Step 6: Update and invert the uncertainty of rockfill dam material parameters.

[0122] Based on the parameter inversion results obtained in step 5, the new measured displacement values ​​of the subsequent time series are selected for parameter update inversion. The posterior distribution of the parameters obtained from the previous measured displacement inversion is used as the prior distribution of the parameters in the next inversion. Using the update inversion capability of Bayesian inference, steps 3 to 5 are repeated, and the water pressure component, prior distribution, and likelihood function separated from the new measured value are substituted into the Bayesian inference model (Equation 6) for Bayesian inference update inversion, and the posterior distribution information N (μ) of the parameters in different periods corresponding to the measured data of different time series is obtained. i ′,σ i ' 2 ) to achieve continuous tracking and updating of rockfill dam material parameters.

[0123] Example 3

[0124] See also Figure 5, This figure is a comparison of the calculation errors of the sPCE proxy model, the ORELM proxy model, and the SVM proxy model. It can be seen from the figure that the overall error levels of the three proxy models are small. The sPCE model is better than the ORELM model in the indicators MAPE and R, while the analysis error of the SVM model is significantly greater than that of other models; Overall, the calculation accuracy of the sPCE model is slightly better than that of the ORELM model and significantly better than that of the SVM model. Therefore, the use of the sPCE method to establish a proxy model can more accurately simulate the finite element analysis process and ensure the correctness and efficiency of the inversion analysis.

[0125] Example 4

[0126] Figure 6-Figure 8 It is the parameter inversion result of the main rockfill area and the downstream rockfill area, and the change trend of the mean and standard deviation of the material parameters of each measuring point in different periods. It can be seen from the figure that the mean values ​​of the dam body material parameters obtained by inversion of the measured displacement of the dam body in different periods have certain changes. Among them, the material parameters of the main rockfill area n1, K b1 The average values ​​are basically around 50, 0.84, and 450. The material parameters of the downstream rockfill area n2, K b2 The mean values ​​are basically around 45, 0.85, and 440; under the influence of different water levels in the four monitoring periods, the mean values ​​of material parameters in each subarea have no obvious periodic changes. Among them, the mean values ​​of material parameters obtained by inversion under the corresponding upstream low water level (around 2001.5m) and high water level (around 2004.5m) during the period from February 2005 to June 2007, and from November 2008 to April 2010 have slightly changed with the growth of the monitoring time series, but the overall difference is not large, indicating that the change of reservoir water level has little effect on the mean values ​​of dam material parameters; comparing the inversion results between June 2007 and November 2008, it can be seen that due to the influence of the "5.12" Wenchuan earthquake, the mean values ​​of dam body rockfill material parameters have changed greatly compared with the former, among which parameter n1, K b2 Increased, n2, K b1 Different from the mean value change, the standard deviation of material parameters in each subarea has an obvious trend of change, that is, it gradually decreases with the increase of monitoring time series, and the coefficient of variation decreases from the initially set 0.1 to below 0.057; the standard deviation obtained from the first two inversions changes most significantly, while the standard deviation obtained from the subsequent inversion decreases compared with the former but the difference is not large.

[0127] The above content shows that a small change in the upstream reservoir water level during the dam operation period has little effect on the mean of the dam material parameters, but due to the secondary consolidation of the rockfill material, some parameters will have a slight trend change with the increase of the monitoring time series; the standard deviation of the material parameters gradually decreases with the increase of the monitoring time series, indicating that as the Bayesian update proceeds, the posterior distribution range of the parameters gradually narrows, and the uncertainty of the parameters gradually decreases and gradually stabilizes. Therefore, the traditional deterministic inversion method cannot analyze the uncertainty of the real parameters of the dam body and the continuous change trend, especially when experiencing load fluctuations such as earthquakes or high water level differences, the uncertainty inversion of the dam material parameters should be carried out in time to grasp the real mechanical properties and operating status of the dam.

[0128] Example 5

[0129] In order to verify the accuracy of the uncertainty inversion method of rockfill dam material parameters based on Bayesian inference, the posterior distribution mean of the inversion parameters was selected, and the hybrid model of rockfill dam displacement monitoring was established based on the vertical displacement monitoring data of the two measuring points VS1-05 and VS2-05 for verification. Since the material parameters of the dam changed to a certain extent after the "5.12" Wenchuan earthquake, this time point was selected as the endpoint to divide the monitoring sequence into two periods, and the models were built from December 2004 to April 2008 and from May 2008 to June 2010, respectively, and the monitoring data in each time period were fitted and predicted, and the prediction samples were the last 10 monitoring values ​​of the monitoring sequence.

[0130] The above hybrid model is based on the statistical model of equations (4) and (5), and uses finite element method to calculate the water pressure component, replacing δ in equation (5) H The statistical model expression of the rockfill dam displacement hybrid model is formed. The Bayesian inversion parameters of June 19, 2007 and April 19, 2010 were used for finite element calculation in period 1 and period 2, respectively, to obtain the water level-displacement fitting curve equations of the VS1-05 and VS2-05 measuring points under different water levels, which were used to replace the water pressure components in the statistical model. Subsequently, the regression coefficients were obtained through least squares fitting to determine the Bayesian inversion hybrid model of different periods. In order to compare with the traditional deterministic inversion results, the traditional deterministic parameter inversion analysis based on the ORELM proxy model was performed using the measured values ​​on December 3, 2004, so as to obtain the inversion parameter values ​​and establish the corresponding deterministic inversion hybrid model.

[0131] Example 6

[0132] Fig. 9 and Fig.10The comparison of the prediction effects of each model on the measured displacement at different periods shows that the "hybrid model" in the figure is the Bayesian inversion hybrid model, and the "hybrid model 2" is the deterministic inversion hybrid model. It can be seen from the figure that compared with the traditional deterministic parameter inversion, the rockfill dam hybrid model established by the Bayesian inference inversion method shows higher fitting and prediction accuracy for the dam displacement at different periods, indicating that the inversion method can more realistically reflect the actual material parameter changes of the dam body, and the water pressure component calculated by this method is closer to the actual water pressure component.

[0133] Bayesian inference has high analytical accuracy in the inversion of material parameters of rockfill dams, and can easily obtain material mechanical parameter values ​​close to the actual dam, providing accurate and reliable material parameter basis for engineering safety state analysis; in addition, based on the parameter sensitivity characteristics, it is reasonable and feasible to select material parameters with greater sensitivity and assume them to be in the form of normal distribution, and use the mean of the posterior distribution of the parameters to establish a mixed model for dam safety state analysis.

[0134] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

[0135] In addition, it should be understood that although this specification is described in accordance with the implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation modes that can be understood by those skilled in the art. The above content is only to illustrate the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. The uncertainty inversion method of rockfill dam material parameters based on Bayesian inference is characterized by: Follow the steps below to implement it: Step 1, establish a finite element model of the rockfill dam and determine the prior distribution of the parameters to be inverted; Step 2, constructing the sPCE proxy model based on the prior distribution of the inversion parameters; Step 3, establish a statistical model of rockfill dam displacement and separate the water pressure component of the measured displacement; Step 4, constructing the material likelihood function of the rockfill dam; Step 5, inversion of uncertainty of rockfill dam material parameters; Step 6: Update and invert the uncertainty of rockfill dam material parameters.

2. The material parameter uncertainty inversion method for rockfill dam based on Bayesian inference according to claim 1, characterized in that: In the step 1, specifically: Step 1.1, based on the acquired rockfill dam engineering design data, including: rockfill dam plan layout drawing, rockfill dam cross-section design drawing, dam deformation monitoring design drawing, establish a finite element model of the rockfill dam; Step 1.2: To describe the stress-strain relationship of each material unit in the finite element model of the rockfill dam, parameter inversion analysis is performed 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. Initial tangent modulus slope n, tangent bulk modulus intercept K b The three parameters are used as the research object for uncertainty inversion; n. K b The parameter prior distribution follows the normal distribution N(μ,σ 2 ).

3. The material parameter uncertainty inversion method for rockfill dam based on Bayesian inference according to claim 2, characterized in that: In the step 2, specifically: Step 2.1: Based on the material parameters of the main rockfill area and the downstream rockfill area n. K b The prior distribution is used to sample using Latin hypercube to generate a sample set X = {X1, X2, ..., X m }, each element Xi in the sample is a parameter n. K b A random combination of sample values, i.e. Substitute the parameter samples into the finite element calculation to obtain the sample set of displacement response values ​​of the rockfill dam corresponding to the parameter samples Y = {Y1, Y2, ..., Y m }; Integrate each sample to form a "parameter-displacement" sample set Z = {X, Y} = {[X1, Y1], [X2, Y2], ..., [X m ,Y m ]}; 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 ]}, test set Z′={X′,Y′}={[X i ′,Y i ′]}={[X1,Y1],[X2,Y2],...,[X m / 4 ,Y m / 4 ]}; In the training set {X i } is the input variable, {Y i } is the output variable, the sPCE proxy model is established and fitting analysis is performed to obtain the trained sPCE proxy model; According to the distribution form of the parameters to be inverted, Hermite orthogonal polynomials are selected as basis functions, and the constructed PCE proxy model is as follows: In the formula, y is the output variable; are the coefficients of the polynomial to be solved; are mutually independent random variables that obey a normal distribution and are input variables in uncertainty analysis; x(·) is the basis function of PCE; The solution of the PCE expansion coefficient is expressed as: In the formula, is the coefficient to be determined; ||a||0 is the number of non-zero elements in the expansion coefficient vector to be determined; ξ (i) is the i-th sample of the input random variable vector ξ; Ψ(·) is abbreviation of; The orthogonal matching pursuit method is used as the calculation strategy for the optimal item set of the adaptive complete PCE surrogate model to calculate the expansion coefficients of each item in the optimal order of the complete PCE initial surrogate model. Only the PCE basis function items 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), and then the training of the sPCE proxy model is completed to obtain the trained sPCE proxy model; Step 2.3, take the test set {X i ′} is the input variable, and after being substituted into the sPCE proxy model, the calculated displacement value {y i ′}, the displacement value {y i ′} and the test set {Y i ′} Perform comparative analysis to verify the calculation error of the sPCE proxy model. If it does not meet the accuracy requirements, repeat step 2.2; if it meets the accuracy requirements, output the obtained sPCE proxy model.

4. The method for inversion of uncertainty of rockfill dam material parameters based on Bayesian inference according to claim 3, characterized in that: In step 2.3, the error test indicators are root mean square error RMSE, root mean square relative error RMSPE, average error MAE, average relative error MAPE, and correlation coefficient R, and the calculation formulas are:

5. The method for inversion of uncertainty of rockfill dam material parameters based on Bayesian inference according to claim 3, characterized in that: In the step 3, specifically: The statistical model of rockfill dam displacement is: d=d H +d T +d θ (4) Where, δ is the displacement of the dam body; δ H is the water pressure component; δ T is the temperature component; δ θ It is the time-effectiveness component; The expressions of displacement components are selected with reference to earth-rock dam as follows: Where H is the upstream water depth; is the average upstream water depth of the previous i days; T i is the average temperature of the i-th day before the observation day; t is the time from the observation day to the start day; m1 is 3, m2 and m3 are 9 or 10; θ is the time-dependent displacement factor; a, b, c are regression coefficients; The monitoring data of three environmental variables, water depth H, temperature T, and observation time t, and the measured displacement data of the dam body were substituted into the statistical model, and the regression coefficients were obtained by the least squares method. Substituting into the water pressure component expression in equation (5), we can obtain the water pressure component value δ separated from the measured displacement: H .

6. The material parameter uncertainty inversion method for rockfill dam based on Bayesian inference according to claim 5, characterized in that: In the step 4, specifically: Step 4.1: Based on 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, the sampling range of the parameter values ​​in different inversion stages is set to [μ-3σ, μ+3σ], the number of Markov chains p=4 and the number of samples in each chain q=20000; the DREAM method is used to sample the parameter group and generate the main rockfill area parameter samples. Parameter samples of downstream rockfill area Substitute the parameter samples S and S′ into the sPCE proxy model in step 2 to simulate the finite element analysis and obtain the vertical displacement value h corresponding to the sample parameters. i (θ); Step 4.2: Set the mean error μ of the monitoring data wi =0, error distribution standard deviation σ wi =1mm; According to the parameter prior distribution form, select the corresponding likelihood function form: In the formula, y i is the water pressure component separated from the measured value; h i (θ) is the displacement response value of the dam body calculated by finite element method; μ wi is the mean value of the measurement error of the monitoring project; σ wi The standard deviation of measurement error for monitoring items; The water pressure component y separated from the measured value i =δ Hi 、Finite element calculation of dam displacement response value h i (θ), mean value of measurement error μ wi With standard deviation σ wi Substitute into formula (6) to construct the likelihood function of rockfill dam material parameters.

7. The method for inversion of uncertainty of rockfill dam material parameters based on Bayesian inference according to claim 6, characterized in that: In the step 5, specifically: Establish a Bayesian inference model based on Bayesian theory: In the formula, θ is The parameters to be inverted in space; For Actual observation data in 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 parameter to be inverted; is the normalization factor, which can be obtained by integrating the prior distribution and the likelihood function: Substitute the prior distribution of each parameter, water pressure component, and likelihood function obtained in steps 1 to 4 into equation (7) to calculate the posterior distribution N(μ′,σ′) of the material parameter to be inverted. 2 ) to determine the inverted values ​​of the parameters.

8. The method for inversion of uncertainty of rockfill dam material parameters based on Bayesian inference according to claim 7, characterized in that: In the step 6, specifically: Based on the parameter inversion results obtained in step 5, the new measured displacement values ​​of the subsequent time series are selected for parameter update inversion; the posterior distribution of the parameters obtained from the previous measured displacement inversion is used as the prior distribution of the parameters in the next inversion, and the update inversion capability of Bayesian inference is used to repeat steps 3 to 5, and the water pressure component, prior distribution, and likelihood function separated from the new measured value are substituted into formula (6) for Bayesian inference update inversion to obtain the posterior distribution information of parameters in different periods corresponding to the measured data of different time series. To achieve continuous tracking and updating of rockfill dam material parameters.

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