Rock-soil mass parameter probability inversion analysis method based on constrained Bayesian update

Abstract

The invention relates to the technical field of slope engineering parameter inversion, in particular to a rock-soil mass parameter probability inversion analysis method based on constrained Bayesian updating, which comprises the following steps: determining prior distribution of slope rock-soil mass parameters, and constructing a slope monitoring data likelihood function; constructing a target constraint likelihood function according to the target constraint condition; combining prior distribution, a slope monitoring data likelihood function and a target constraint likelihood function by using a Bayesian theory to determine posterior distribution of rock-soil body parameters, thereby determining equivalent samples of the rock-soil body parameters by using a target sampling algorithm, and updating reliable indexes of a target slope by using the equivalent samples, thereby improving the reliability of the target slope. And obtaining the updated slope reliability index. Therefore, the problems that the traditional Bayesian inference in the related technology is mainly used for inverting the geotechnical material parameters by fusing the monitoring data, and when the types and the number of the monitoring data are limited, the traditional Bayesian inference is often uncertain, the inversion stability is poor, and the uncertainty of the geotechnical material parameters cannot be effectively reduced are solved.

Description

Technical Field

[0001] The present application relates to the technical field of slope engineering parameter inversion, and in particular to a rock and soil parameter probability inversion analysis method based on constrained Bayesian updating. Background Art

[0002] Due to the complexity and time-consuming nature of in-situ and laboratory experiments, measured data on geotechnical parameters at a specific site are often scarce. Furthermore, due to the significant variability of geotechnical materials, the geotechnical parameter values estimated from these small amounts of measured data may not represent their true values, leading to significant errors in slope stability assessments using numerical simulations.

[0003] On the other hand, with the development of monitoring technology, certain monitoring data, such as ground deformation and anchor stress, can be collected during slope engineering practice. This monitoring data records the true response of the slope system. In response to this, parameter inversion methods based on Bayesian reasoning are gradually emerging. These monitoring data complement the lack of measured geotechnical parameter data, reducing the uncertainty of these parameters and thus improving the accuracy of slope stability assessments.

[0004] However, traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data. When the types and quantity of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem. The inversion stability is poor and it cannot effectively reduce the uncertainty of geotechnical parameters, resulting in excessive variability in the calculated safety factor, which needs to be solved urgently. Summary of the Invention

[0005] This application is based on the following problems and understandings made by the inventors:

[0006] In slope engineering, safety factors are often used to evaluate slope stability. Conventional deterministic analysis treats geotechnical parameters as fixed values and calculates a single safety factor. However, sometimes the calculated safety factor exceeds 1, yet the slope still fails. This gradually led to the recognition of the shortcomings of deterministic analysis, which led to the emergence of probabilistic analysis. In probabilistic analysis, geotechnical parameters are treated as random variables, and a probability distribution of the slope safety factor is calculated. Reliability indices are often used to evaluate slope stability. However, calculating an accurate slope reliability index requires an accurate probability distribution of the geotechnical parameters, including the distribution type and distribution parameters. However, due to the complexity and time-consuming nature of in-situ and laboratory experiments, measured data on geotechnical parameters at specific sites are often scarce. Obviously, due to the significant variability of geotechnical materials, geotechnical parameter values estimated from a small amount of measured data cannot represent their true values, resulting in significant errors in the calculation of slope safety factors using numerical simulations.

[0007] Fortunately, with the development and diversification of monitoring technology and the birth of automated monitoring instruments, in addition to limited measured data, slope engineering practice also has various monitoring data, such as ground deformation and anchor stress. These monitoring data record the real response of the slope system. Using monitoring data to make up for the shortcomings of measured data and promote the reasonable selection of geotechnical parameters is a research with practical significance. In this regard, people have explored a variety of parameter inversion methods, such as maximum likelihood method, neural network, ensemble Kalman filter and Bayesian update. Bayesian update has at least the following two advantages: (1) integrating prior information and monitoring data into the posterior distribution to provide a reliable probability distribution of geotechnical parameters for reliability analysis; (2) not only can the uncertainty of geotechnical parameters be explicitly modeled, but also the uncertainty of geotechnical parameters can be reduced by using monitoring data. Based on the above two reasons, Bayesian update has been widely used in parameter probability inversion of various geotechnical engineering problems.

[0008] However, the complexity and particularity of geotechnical engineering mean that the application of traditional Bayesian updating still has some shortcomings. Bayesian updating mainly infers the posterior probability distribution of geotechnical parameters by integrating monitoring data. Although monitoring technology has made significant progress in recent years, the types and quantities of monitoring data are still generally limited in most geotechnical engineering practices. This makes Bayesian reasoning less effective in reducing the uncertainty of geotechnical parameters, resulting in excessive variability in the calculated safety factors. To solve this problem, the general strategy is to incorporate more monitoring data into the inversion process, but data collection is usually time-consuming and labor-intensive, and needs to be improved urgently.

[0009] The present application provides a probabilistic inversion analysis method for geotechnical parameters based on constrained Bayesian updating to solve the problem in related technologies that traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data. When the types and quantities of monitoring data are limited, traditional Bayesian reasoning has poor stability and cannot effectively reduce the uncertainty of geotechnical parameters, resulting in large variability in the calculated safety factor.

[0010] The first aspect of the present application provides a probabilistic inversion analysis method for rock and soil parameters based on constrained Bayesian updating, comprising the following steps: determining the prior distribution of the rock and soil parameters based on the prior information of the rock and soil parameters of the target slope, and constructing a monitoring data likelihood function based on the slope monitoring data of the target slope; determining the target constraints of the rock and soil parameters based on the target physical characteristics of the rock and soil parameters, and constructing a target constraint likelihood function based on the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints; constructing the posterior distribution of the rock and soil parameters using Bayesian theory based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function, and based on the posterior distribution, determining the equivalent samples of the rock and soil parameters using a target sampling algorithm, and updating the reliability index of the target slope using the equivalent samples to obtain the updated slope reliability index.

[0011] Optionally, in one embodiment of the present application, constructing the monitoring data likelihood function based on the slope monitoring data of the target slope includes: obtaining the slope monitoring data of the rock and soil parameters, and determining the observation error of the slope monitoring data; and constructing the monitoring data likelihood function based on the slope monitoring data and the observation error.

[0012] Optionally, in one embodiment of the present application, the use of the equivalent sample to update the reliability index of the target slope to obtain the updated slope reliability index includes: calculating the target slope safety factor based on the equivalent sample of the geotechnical parameters, and calculating the slope failure probability of the geotechnical parameters using the target slope safety factor; based on the slope failure probability, updating the reliability index of the target slope to obtain the updated slope reliability index.

[0013] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality constraint likelihood function and an inequality constraint likelihood function;

[0014] The equality constraint likelihood function is represented as follows:

[0015]

[0016] Among them, g(θ)=0 is the constraint condition, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ) respectively;

[0017] Among them, if there is a correlation between the two variables θ1 and θ2, and the linear regression equation is: θ2 = aθ1 + b, then we can construct the constraint: g(θ) = θ2 - aθ1 - b = 0. According to the least squares method, we can get:

[0018]

[0019] Among them, ρ (θ1,θ2) is the correlation coefficient between variables θ1 and θ2;

[0020] Then the mean μ of g(θ) is g(θ) and standard deviation σ g(θ) They are characterized as:

[0021]

[0022] The inequality constraint likelihood function is characterized as:

[0023]

[0024] Where a1 is a normalization constant.

[0025] Optionally, in one embodiment of the present application, the posterior distribution is characterized as:

[0026] P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ)

[0027] Where P(θ) is the prior distribution, P(Y|θ) is the monitoring data likelihood function, P(g(θ)|θ) is the constrained likelihood function, and a2 is the normalization constant.

[0028] Optionally, in one embodiment of the present application, the updated slope reliability index is expressed as:

[0029] β=Φ -1 (1-P f )

[0030] Among them, β is the updated slope reliability index, Φ is the standard normal cumulative distribution function, P f is the probability of slope failure. The second embodiment of the present application provides a rock and soil parameter probability inversion analysis device based on constrained Bayesian updating, including: a determination module for determining the prior distribution of the rock and soil parameters according to the prior information of the rock and soil parameters of the target slope, and constructing a monitoring data likelihood function according to the slope monitoring data of the target slope; a construction module for determining the target constraint conditions of the rock and soil parameters based on the target physical characteristics of the rock and soil parameters, so as to construct a target constraint likelihood function according to the target constraint conditions, wherein the target constraint conditions are divided into equality constraints and inequality constraints; an inversion analysis module for constructing the posterior distribution of the rock and soil parameters using Bayesian theory based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function, and based on the posterior distribution, determining the equivalent samples of the rock and soil parameters using a target sampling algorithm, and updating the reliability index of the target slope using the equivalent samples to obtain the updated slope reliability index.

[0031] Optionally, in one embodiment of the present application, the determination module includes: an acquisition unit for acquiring slope monitoring data of the rock and soil parameters and determining the observation error of the slope monitoring data; and a construction unit for constructing the monitoring data likelihood function based on the slope monitoring data and the observation error.

[0032] Optionally, in one embodiment of the present application, the inversion analysis module includes: a determination unit for calculating the target slope safety factor based on the equivalent sample of the rock and soil parameters, and using the target slope safety factor to calculate the slope failure probability of the rock and soil parameters; an updating unit for updating the reliability index of the target slope based on the slope failure probability to obtain the updated slope reliability index.

[0033] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality constraint likelihood function and an inequality constraint likelihood function;

[0034] The equality constraint likelihood function is represented as follows:

[0035]

[0036] Among them, g(θ)=0 is the constraint condition, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ) respectively;

[0037] Among them, if there is a correlation between the two variables θ1 and θ2, and the linear regression equation is: θ2 = aθ1 + b, then we can construct the constraint: g(θ) = θ2 - aθ1 - b = 0. According to the least squares method, we can get:

[0038]

[0039] Among them, ρ (θ1,θ2) is the correlation coefficient between variables θ1 and θ2;

[0040] Then the mean μ of g(θ) is g(θ) and standard deviation σ g(θ) They are characterized as:

[0041]

[0042] The inequality constraint likelihood function is characterized as:

[0043]

[0044] Where a1 is a normalization constant.

[0045] Optionally, in one embodiment of the present application, the posterior distribution is characterized as:

[0046] P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ)

[0047] Where P(θ) is the prior distribution, P(Y|θ) is the monitoring data likelihood function, P(g(θ)|θ) is the constrained likelihood function, and a2 is the normalization constant.

[0048] Optionally, in one embodiment of the present application, the updated slope reliability index is expressed as:

[0049] β=Φ -1 (1-P f )

[0050] Among them, β is the updated slope reliability index, Φ is the standard normal cumulative distribution function, P f is the slope failure probability.

[0051] The third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement a probabilistic inversion analysis method for rock and soil parameters based on constrained Bayesian updating as described in the above embodiment.

[0052] The fourth aspect of the present application provides a computer-readable storage medium, which stores a computer program. When the program is executed by a processor, it implements the above-mentioned rock and soil parameter probabilistic inversion analysis method based on constrained Bayesian updating.

[0053] The fifth aspect of the present application provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned rock and soil parameter probabilistic inversion analysis method based on constrained Bayesian updating.

[0054] The embodiment of the present application can use Bayesian theory to combine the prior distribution, the likelihood function of slope monitoring data, and the target constraint likelihood function to determine the posterior distribution of the rock and soil parameters, thereby using the target sampling algorithm to determine the equivalent samples of the rock and soil parameters, and using the equivalent samples to update the reliability index of the target slope, effectively reducing the uncertainty of the rock and soil parameters and improving the reliability index of the slope. This solves the problem in the related art that traditional Bayesian reasoning mainly inverts rock and soil material parameters by fusing monitoring data. When the types and amount of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem, the inversion analysis is poorly stable, and it cannot effectively reduce the uncertainty of rock and soil parameters.

[0055] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0057] Figure 1 A flowchart of a method for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating according to an embodiment of the present application;

[0058] Figure 2 This is a logic diagram of a probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating according to a specific embodiment of the present application;

[0059] Figure 3 A schematic diagram of a classic infinite slope model according to a specific embodiment of the present application;

[0060] Figure 4 This is a sample diagram of measured data of shear strength parameters of a specific embodiment of the present application;

[0061] Figure 5 This is a constrained likelihood function diagram of geotechnical parameters according to a specific embodiment of the present application.

[0062] Figure 6 A priori and posterior probability function diagram of geotechnical parameters according to a specific embodiment of the present application;

[0063] Figure 7 A priori and posterior probability distribution diagram of the safety factor of a specific embodiment of the present application;

[0064] Figure 8 A diagram showing the relationship between the reliability index and the slope gradient of a specific embodiment of the present application;

[0065] Figure 9 Schematic diagram of the structure of a rock and soil parameter probability inversion analysis device based on constrained Bayesian updating according to an embodiment of the present application;

[0066] Figure 10 A schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0067] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0068] The following describes a method for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating according to an embodiment of the present application with reference to the accompanying drawings. In view of the fact that traditional Bayesian reasoning in the related technologies mentioned in the background technology center mainly inverts rock and soil material parameters by fusing monitoring data, when the types and quantities of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem, with poor inversion stability and inability to effectively reduce the uncertainty of rock and soil parameters, the present application provides a method for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating, in which the Bayesian theory can be used to combine the prior distribution, the likelihood function of slope monitoring data and the target constraint likelihood function to determine the posterior distribution of the rock and soil parameters, thereby using the target sampling algorithm to determine the equivalent samples of the rock and soil parameters, and using the equivalent samples to update the reliability index of the target slope, effectively reducing the uncertainty of the rock and soil parameters, thereby improving the reliability index of the slope. This solves the problem in related technologies that traditional Bayesian reasoning mainly inverts geotechnical material parameters by fusing monitoring data. When the types and quantities of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem with poor inversion stability and inability to effectively reduce the uncertainty of geotechnical parameters.

[0069] Specifically, Figure 1 A schematic flow chart of a method for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating provided in an embodiment of the present application.

[0070] like Figure 1 As shown, the rock and soil parameter probability inversion analysis method based on constrained Bayesian updating includes the following steps:

[0071] In step S101 , the prior distribution of the rock and soil parameters of the target slope is determined based on the prior information of the rock and soil parameters of the target slope, and a monitoring data likelihood function is constructed based on the slope monitoring data of the target slope.

[0072] In the embodiment of the present application, the target slope is the slope currently being monitored.

[0073] It can be understood that the embodiments of the present application can obtain prior information of slope rock and soil parameters. For example, first, the prior information of rock and soil parameters is collected based on in-situ experiments, laboratory tests, field surveys, engineering experience, published reports and research, and then the prior distribution P(θ) of the rock and soil parameters is determined based on the prior information, including the distribution type and distribution parameters. In addition, slope monitoring data Y can be collected according to a specific project monitoring plan to construct a monitoring data likelihood function P(Y|θ) to improve the accuracy of slope behavior prediction.

[0074] Among them, the prior distribution P(θ) is generally divided into informative prior distribution and non-informative prior distribution. The non-informative prior distribution is generally a uniform distribution within the possible range of parameters, and the informative prior distribution generally assumes that the rock and soil parameters obey the normal or log-normal distribution.

[0075] Optionally, in one embodiment of the present application, a monitoring data likelihood function is constructed based on the slope monitoring data of the target slope, including: obtaining slope monitoring data of rock and soil parameters, and determining the observation error of the slope monitoring data; and constructing a monitoring data likelihood function based on the slope monitoring data and the observation error.

[0076] For example, an embodiment of the present application can collect monitoring data Y according to a specific project monitoring plan, such as various slope response data such as ground deformation, pile top displacement and anchoring force. Then, the measurement error ε can be given according to the accuracy of the monitoring instrument and the level of monitoring technology. Finally, a monitoring data likelihood function P(Y|θ) is constructed based on the monitoring data Y and the measurement error ε. Specifically, it is assumed that the observation error ε obeys a normal distribution with a mean of 0 and a standard deviation of σ, where σ is determined according to the size of the observation error. If the monitoring data value is Y and the coefficient of variation COV = 0.1, then σ = 0.1×Y.

[0077] In step S102, target constraints of the geotechnical parameters are determined based on the target physical characteristics of the geotechnical parameters, so as to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints.

[0078] In the embodiment of the present application, the target physical characteristics may be theoretical formulas of the physical and mechanical properties of rock and soil parameters, empirical parameter relationships, and upper and lower limits of rock and soil parameters.

[0079] It can be understood that the embodiments of the present application can collect the possible constraints of various key material parameters under specific working conditions based on the physical characteristics of the rock and soil parameters, such as the theoretical formulas of the physical and mechanical properties of the rock and soil parameters, the relationship between empirical parameters, and the upper and lower limits of the rock and soil parameters, etc., and then construct the constrained likelihood function P(g(θ)|θ) based on the collected constraints g(θ), based on which the accuracy of the slope response update can be effectively improved.

[0080] In the embodiment of the present application, the target constraint conditions can be divided into equality constraints g(θ)=0 and inequality constraints g(θ)≤0 and g(θ)≥0; the target constraint likelihood function includes an equality constraint likelihood function and an inequality constraint likelihood function;

[0081] Among them, the equality constraint likelihood function is represented as:

[0082]

[0083] Among them, g(θ)=0 is the constraint condition, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ), respectively. It can be seen that under this constraint, g(θ)=0 is not required to be strictly true. This is called soft execution of the constraint. g(θ) controls the strictness of the constraint, σ g(θ) The smaller the constraint, the stricter it is;

[0084] In actual slope engineering, there is often a correlation between two variables. This correlation between parameters is also a typical constraint condition. When there is a correlation between the two variables θ1 and θ2, and the linear regression equation is: θ2 = aθ1 + b, then the constraint can be constructed: g(θ) = θ2 - aθ1 - b = 0. According to the least squares method, we can get:

[0085]

[0086] Among them, ρ (θ1,θ2) is the correlation coefficient between variables θ1 and θ2;

[0087] Then the mean μ of g(θ) is g(θ) and standard deviation σ g(θ) They are characterized as:

[0088]

[0089] The inequality constrained likelihood function is characterized as:

[0090]

[0091] Wherein, a1 is a normalization constant. Here, g(θ)≤0 is taken as an example. When g(θ)≥0, it is sufficient to change "max" in the formula to "min". Detailed description is omitted here.

[0092] In step S103, based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function, the Bayesian theory is used to construct the posterior distribution of the rock and soil parameters, and based on the posterior distribution, the target sampling algorithm is used to determine the equivalent samples of the rock and soil parameters, and the equivalent samples are used to update the reliability index of the target slope to obtain the updated slope reliability index.

[0093] It can be understood that the embodiment of the present application can use the Bayesian theory to construct the prior distribution P(θ) of the rock and soil parameters, the monitoring data likelihood function P(Y|θ) and the constraint likelihood function P(g(θ)|θ) to obtain the posterior distribution P(θ|Y,g(θ)) of the rock and soil parameters. Based on the posterior distribution, the DREAM algorithm is used to determine the equivalent samples of the rock and soil parameters, and the equivalent samples are used to update the slope reliability index to obtain the updated slope reliability index, thereby effectively reducing the uncertainty of the parameters, reducing the variability of the safety factor, and improving the reliability index of the slope.

[0094] Wherein, the posterior distribution is characterized as:

[0095] P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ)

[0096] where P(θ) is the prior distribution, P(Y|θ) is the monitored data likelihood function, and P(g(θ)|θ) is the constrained likelihood function. a2 is a normalization constant that ensures that P(θ|Y,g(θ)) integrates to 1 over the possible range of parameters.

[0097] In the actual implementation process, when using the DREAM algorithm to determine the equivalent samples of geotechnical parameters, the embodiment of the present application can first determine the required number of equivalent samples N; then, use the improved Markov chain Monte Carlo simulation method (such as the DREAM algorithm) to generate 2N equivalent samples, and take the last 50% of the samples as the equivalent samples Θ = [θ1, ..., θ k ,...,θ N ] T Finally, the PDF (Posterior Probability Density Function) of the rock and soil parameters is determined based on N equivalent samples, where the determination of N needs to meet the requirements of Markov chain stability and high precision and low variability of slope reliability update.

[0098] Optionally, in one embodiment of the present application, the reliability index of the target slope is updated using an equivalent sample to obtain an updated slope reliability index, including: calculating the target slope safety factor based on the equivalent sample of the geotechnical parameters, and calculating the slope failure probability of the geotechnical parameters using the target slope safety factor; based on the slope failure probability, updating the reliability index of the target slope to obtain an updated slope reliability index.

[0099] In some embodiments, the present application first converts the equivalent sample θ of the rock and soil parameters into k (k=1,…,N) is used as input to calculate N slope safety factors, and then the slope failure probability P is calculated using the following formula: f ,Right now:

[0100]

[0101] Where I[·] is the indicator function, when FS(θ k )<1, I[·]=1, otherwise I[·]=0; N is the number of equivalent samples; θ k It is an equivalent sample of rock and soil parameters.

[0102] Finally, based on the slope failure probability, the updated slope reliability index β is calculated using the following formula:

[0103] β=Φ -1 (1-P f )

[0104] Among them, β is the updated slope reliability index, Φ is the standard normal cumulative distribution function, P f is the slope failure probability.

[0105] Therefore, this application solves the problem that traditional Bayesian updating only uses monitoring data, and when monitoring data is scarce, the effect of reducing parameter uncertainty through parameter probability inversion is not significant, which leads to large uncertainty in the safety factor of the slope and low reliability index.

[0106] In addition to using monitoring data, the constrained Bayesian updating method proposed in this application also integrates some known constraints into traditional Bayesian updating, such as theoretical formulas for the physical and mechanical properties of geotechnical parameters, empirical parameter relationships, and upper and lower limits of geotechnical material parameters. Equality and inequality constraints are also proposed, and equality and inequality constraint likelihood functions are derived. Compared with traditional Bayesian updating, constrained Bayesian updating can more effectively reduce parameter uncertainty, thereby reducing the uncertainty of the slope safety factor and improving the reliability index of the slope.

[0107] For example, if Figure 2 As shown, the working principle of the embodiment of the present application is described in detail below with a specific embodiment.

[0108] Take an infinite slope as an example, Figure 3 As shown in the figure, the calculation of the slope safety factor involves five parameters, namely bulk density γ, slope angle α, sliding body thickness H, shear strength parameter c and Here, α and H are considered as deterministic constants, where α = 30° and H = 5m. Considered as a random variable, One of the groups c and The measured data of is used to determine its prior distribution, see Figure 4 Then c obeys the mean μ c=22.10kPa and coefficient of variation COV c =0.379 lognormal distribution. Obey the mean and coefficient of variation Since there is no measured data of heavy γ, it is assumed here that γ obeys the mean μ γ =17kN and coefficient of variation COV γ =0.10. This determines that Figure 2 The prior distribution P(θ) of the geotechnical parameters in .

[0109] Next, since there is no actual monitoring data available, it is assumed that the slope is in a stable state and the slope safety factor FS obeys μ FS =1.2 and COV FS =0.10, and thus construct Figure 2 The likelihood function P(Y|θ) of the monitoring data in .

[0110] Secondly, in most existing studies, the correlation of geotechnical parameters is not considered for the sake of simplicity. Figure 4 It can be seen that the measured data of the shear strength parameters have an obvious negative correlation, with a correlation coefficient of ρ = -0.65, and the linear regression equation is This correlation between parameters can be regarded as a constraint condition, from which the constraint expression of the variable g(θ) is constructed:

[0111]

[0112] Among them, c and is the shear strength parameter, where c is the cohesion, is the friction angle.

[0113] According to c and The measured data of g(θ) is calculated to have a mean of 0 and a standard deviation of 2.04, so it is assumed that g(θ) obeys μ g(θ) =0 and σ g(θ) = 2.04, and thus the constrained likelihood function P(g(θ)|θ) is constructed. Figure 5 , Figure 5 is a soft equality constraint on g(θ).

[0114] Thirdly, the Bayesian theory is used to combine the prior distribution P(θ) of rock and soil parameters, the likelihood function P(Y|θ) of monitoring data, and the constraint likelihood function P(g(θ)|θ) to obtain the posterior distribution P(θ|Y,g(θ)) of θ. The specific expression of the posterior distribution is:

[0115] P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ)

[0116] where a2 is a normalization constant that ensures that P(θ|Y,g(θ)) integrates to 1 over the possible range of parameters.

[0117] Next, we first determine the number of equivalent samples N required. The DREAM algorithm is an improved Markov chain Monte Carlo simulation algorithm. The determination of N needs to meet two requirements: the stability of the Markov chain and the high accuracy and low variability of the failure probability. Here, N = 10 5 Then, the DREAM algorithm is used to generate 2N equivalent samples, and the last 50% of the samples are taken as equivalent samples. Finally, the posterior probability density function (PDF) of the geotechnical parameters is determined based on N equivalent samples, see Figure 6 It can be seen that the coefficient of variation COV of bulk density γ remains basically unchanged before and after updating. This is because the influence of γ on the slope safety factor is significantly smaller than that of shear strength parameters c and Shear strength parameters c and The coefficient of variation of the rock and soil parameters obtained by constrained Bayesian updating is significantly reduced after updating. Moreover, the coefficient of variation of the rock and soil parameters obtained by constrained Bayesian updating is smaller than that obtained by traditional Bayesian updating, among which the friction angle The prior COV, COV after traditional Bayesian updating, and COV after constrained Bayesian updating are 0.10, 0.095, and 0.071, respectively. This shows that constrained Bayesian updating is more effective in reducing parameter uncertainty than traditional Bayesian updating.

[0118] It should be noted that the embodiment of the present application only takes correlation constraints as an example. When there are more constraints, constrained Bayesian updating will have greater advantages in reducing the uncertainty of rock and soil parameters.

[0119] Finally, the embodiment of the present application first converts the rock and soil parameter equivalent sample θ k (k=1,…,N) as input, and N=10 5 The safety factor of the infinite slope is calculated using the following formula:

[0120]

[0121] Where γ is the bulk density, c and is the shear strength parameter, α is the slope angle, and H is the thickness of the sliding body.

[0122] Based on N=10 5 The safety factor of the slope is obtained by the probability density function of the safety factor, see Figure 7 ,Depend on Figure 7It can be seen that the prior COV of the safety factor, the COV after traditional Bayesian updating, and the COV after constrained Bayesian updating are 0.184, 0.087, and 0.071, respectively. Although traditional Bayesian updating has achieved good results in reducing the uncertainty of the safety factor, constrained Bayesian updating can fully utilize the constraints to further reduce the COV of the safety factor. Then the slope failure probability P is calculated using the following formula f ,Right now:

[0123]

[0124] Where I[·] is the indicator function, when FS(θ k )<1, I[·]=1, otherwise I[·]=0.

[0125] Finally, based on the failure probability, the updated slope reliability index β is calculated using the following formula:

[0126] β=Φ -1 (1-P f ).

[0127] In the examples of this application, the slope prior β, β after traditional Bayesian updating, and β after constrained Bayesian updating are 2.05, 2.54, and 3.24, respectively. Clearly, a smaller COV corresponds to a larger slope reliability index. The reliability index obtained by constrained Bayesian updating is significantly greater than that obtained by traditional Bayesian updating, which is crucial in slope reliability design. Designing based on the reliability index obtained by traditional Bayesian updating will lead to more conservative slope design and increase economic costs.

[0128] like Figure 8 The figure shows the relationship between the reliability index and slope angle. It can be seen that as the slope angle increases, the slope reliability index gradually decreases. However, the slope reliability index after constrained Bayesian updating is greater than the reliability index after traditional Bayesian updating. Moreover, this gap becomes more pronounced as the slope reliability index increases. In other words, when the slope has a low probability of failure, ignoring the constraints will further underestimate the slope reliability index.

[0129] It can be seen that constrained Bayesian updating can make full use of some known constraints, such as the theoretical formulas of the physical and mechanical properties of rock and soil parameters, the relationship between empirical parameters, and the upper and lower limits of rock and soil material parameters, so that this method can more effectively reduce the uncertainty of rock and soil parameters, thereby reducing the variability of the slope safety factor and improving the reliability index of the slope.

[0130] According to the embodiment of the present application, a method for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating is proposed. The Bayesian theory can be used to combine the prior distribution, the likelihood function of slope monitoring data, and the target constraint likelihood function to determine the posterior distribution of the rock and soil parameters. The target sampling algorithm is then used to determine the equivalent samples of the rock and soil parameters, and the equivalent samples are used to update the reliability index of the target slope, effectively reducing the uncertainty of the rock and soil parameters and improving the reliability index of the slope. This solves the problem in the related art that traditional Bayesian reasoning mainly inverts rock and soil material parameters by fusing monitoring data. When the types and quantity of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem, with poor inversion stability and inability to effectively reduce the uncertainty of rock and soil parameters.

[0131] Next, a device for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating proposed in accordance with an embodiment of the present application will be described with reference to the accompanying drawings.

[0132] Figure 9 It is a block diagram of a device for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating according to an embodiment of the present application.

[0133] like Figure 9 As shown, the rock and soil parameter probability inversion analysis device 10 based on constrained Bayesian updating includes: a determination module 100, a construction module 200 and an inversion analysis module 300.

[0134] Specifically, the determination module 100 is used to determine the prior distribution of the rock and soil parameters of the target slope according to the prior information of the rock and soil parameters of the target slope, and to construct a monitoring data likelihood function according to the slope monitoring data of the target slope.

[0135] The construction module 200 is used to determine the target constraints of the rock and soil parameters based on the target physical characteristics of the rock and soil parameters, so as to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints.

[0136] The inversion analysis module 300 is used to construct the posterior distribution of the rock and soil parameters based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function using Bayesian theory, and based on the posterior distribution, use the target sampling algorithm to determine the equivalent samples of the rock and soil parameters, and use the equivalent samples to update the reliability index of the target slope to obtain an updated slope reliability index.

[0137] Optionally, in one embodiment of the present application, the determination module 100 includes: an acquisition unit and a construction unit.

[0138] The acquisition unit is used to acquire slope monitoring data of rock and soil parameters and determine the observation error of the slope monitoring data.

[0139] The construction unit is used to construct a monitoring data likelihood function based on the slope monitoring data and observation errors.

[0140] Optionally, in one embodiment of the present application, the inversion analysis module 300 includes: a determination unit and an update unit.

[0141] The determination unit is used to calculate the target slope safety factor based on the equivalent sample of the rock and soil parameters, and to calculate the slope failure probability of the rock and soil parameters using the target slope safety factor.

[0142] The updating unit is used to update the reliability index of the target slope based on the slope failure probability to obtain an updated slope reliability index.

[0143] Optionally, in one embodiment of the present application, the target constraint likelihood function includes an equality constraint likelihood function and an inequality constraint likelihood function;

[0144] Among them, the equality constraint likelihood function is represented as:

[0145]

[0146] Among them, g(θ)=0 is the constraint condition, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ) respectively;

[0147] Among them, if there is a correlation between the two variables θ1 and θ2, and the linear regression equation is: θ2 = aθ1 + b, then we can construct the constraint: g(θ) = θ2 - aθ1 - b = 0. According to the least squares method, we can get:

[0148]

[0149] Among them, ρ (θ1,θ2) is the correlation coefficient between variables θ1 and θ2;

[0150] Then the mean μ of g(θ) is g(θ) and standard deviation σ g(θ) They are characterized as:

[0151]

[0152] The inequality constrained likelihood function is characterized as:

[0153]

[0154] Where a1 is a normalization constant.

[0155] Optionally, in one embodiment of the present application, the posterior distribution is characterized as:

[0156] P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ)

[0157] where P(θ) is the prior distribution, P(Y|θ) is the monitored data likelihood function, P(g(θ)|θ) is the constrained likelihood function, and a2 is a normalization constant.

[0158] Optionally, in one embodiment of the present application, the updated slope reliability index is expressed as:

[0159] β=Φ -1 (1-P f )

[0160] Among them, β is the updated slope reliability index, Φ is the standard normal cumulative distribution function, P f It should be noted that the above explanation of the embodiment of a rock and soil parameter probability inversion analysis method based on constrained Bayesian updating is also applicable to the rock and soil parameter probability inversion analysis device based on constrained Bayesian updating in this embodiment, and will not be repeated here.

[0161] According to the embodiment of the present application, a device for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating can use Bayesian theory to combine the prior distribution, the likelihood function of slope monitoring data, and the target constraint likelihood function to determine the posterior distribution of the rock and soil parameters, thereby using the target sampling algorithm to determine the equivalent samples of the rock and soil parameters, and using the equivalent samples to update the reliability index of the target slope, effectively reducing the uncertainty of the rock and soil parameters and improving the reliability index of the slope. This solves the problem in the related art that traditional Bayesian reasoning mainly inverts rock and soil material parameters by fusing monitoring data. When the types and amount of monitoring data are limited, traditional Bayesian reasoning is often an ill-posed problem, with poor inversion stability and inability to effectively reduce the uncertainty of rock and soil parameters.

[0162] Figure 10 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0163] A memory 1001 , a processor 1002 , and a computer program stored in the memory 1001 and executable on the processor 1002 .

[0164] When the processor 1002 executes the program, a rock and soil parameter probability inversion analysis method based on constrained Bayesian updating provided in the above embodiment is implemented.

[0165] Furthermore, the electronic device further includes:

[0166] The communication interface 1003 is used for communication between the memory 1001 and the processor 1002 .

[0167] The memory 1001 is used to store computer programs that can be run on the processor 1002 .

[0168] The memory 1001 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0169] If the memory 1001, the processor 1002, and the communication interface 1003 are implemented independently, the communication interface 1003, the memory 1001, and the processor 1002 can be connected to each other via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 10 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0170] Optionally, in a specific implementation, if the memory 1001, the processor 1002 and the communication interface 1003 are integrated on a chip, the memory 1001, the processor 1002 and the communication interface 1003 can communicate with each other through an internal interface.

[0171] The processor 1002 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0172] This embodiment further provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the above-mentioned probabilistic inversion analysis method for rock and soil parameters based on constrained Bayesian updating is implemented.

[0173] This embodiment further provides a computer program product, including a computer program. When the computer program is executed, it is used to implement the above-mentioned rock and soil parameter probability inversion analysis method based on constrained Bayesian updating.

[0174] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0175] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "N" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0176] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing a custom logical function or process step, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed in a different order than shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application pertain.

[0177] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or N wires (electronic devices), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program can be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing it in other suitable ways as necessary, and then storing it in a computer memory.

[0178] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, it can be implemented using any one or a combination of the following technologies known in the art: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0179] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0180] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0181] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A probabilistic inversion analysis method for rock and soil parameters based on constrained Bayesian updating, characterized by: The following steps are involved: Determining a priori distribution of the rock and soil parameters of the target slope based on prior information of the rock and soil parameters, and constructing a monitoring data likelihood function based on the slope monitoring data of the target slope; Determining target constraints of the rock and soil parameters based on target physical characteristics of the rock and soil parameters, and constructing a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints; Based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function, the posterior distribution of the rock and soil parameters is constructed using Bayesian theory, and based on the posterior distribution, the equivalent samples of the rock and soil parameters are determined using a target sampling algorithm, and the reliability index of the target slope is updated using the equivalent samples to obtain the updated slope reliability index.

2. The method according to claim 1, characterized in that The constructing of a monitoring data likelihood function based on the slope monitoring data of the target slope includes: Acquiring slope monitoring data of the target slope and determining an observation error of the slope monitoring data; The monitoring data likelihood function is constructed based on the slope monitoring data and the observation error.

3. The method according to claim 1, characterized in that The updating of the target slope reliability index by using the equivalent sample to obtain the updated slope reliability index includes: Calculating a target slope safety factor based on an equivalent sample of the rock and soil mass parameters, and calculating a slope failure probability of the rock and soil mass parameters using the target slope safety factor; Based on the slope failure probability, the reliability index of the target slope is updated to obtain the updated slope reliability index.

4. The method according to claim 1, wherein The target constraint likelihood function includes an equality constraint likelihood function and an inequality constraint likelihood function; The equality constraint likelihood function is represented as follows: Among them, g(θ)=0 is the constraint condition, μ g(θ) and σ g(θ) are the mean and standard deviation of g(θ) respectively; Among them, if there is a correlation between the two variables θ1 and θ2, and the linear regression equation is: θ2 = aθ1 + b, then we can construct the constraint: g(θ) = θ2 - aθ1 - b = 0. According to the least squares method, we can get: Among them, ρ (θ1,θ2) is the correlation coefficient between variables θ1 and θ2; Then the mean μ of g(θ) is g(θ) and standard deviation σ g(θ) They are characterized as: The inequality constraint likelihood function is characterized as: Where a1 is a normalization constant.

5. The method according to claim 1, wherein The posterior distribution is characterized as: P(θ|Y,g(θ))=a2P(Y|θ)P(g(θ)|θ)P(θ) Where P(θ) is the prior distribution, P(Y|θ) is the monitoring data likelihood function, P(g(θ)|θ) is the constrained likelihood function, and a2 is the normalization constant.

6. The method according to claim 1, characterized in that The updated slope reliability index is expressed as: β=Φ -1 (1-P f ) Among them, β is the updated slope reliability index, Φ is the standard normal cumulative distribution function, P f is the slope failure probability.

7. A device for probabilistic inversion analysis of rock and soil parameters based on constrained Bayesian updating, characterized in that: include: a determination module, configured to determine a priori distribution of the rock and soil parameters of the target slope based on prior information of the rock and soil parameters, and to construct a monitoring data likelihood function based on the slope monitoring data of the target slope; a construction module, configured to determine target constraints of the rock and soil parameters based on target physical characteristics of the rock and soil parameters, so as to construct a target constraint likelihood function according to the target constraints, wherein the target constraints are divided into equality constraints and inequality constraints; The inversion analysis module constructs the posterior distribution of the rock and soil parameters based on the prior distribution, the monitoring data likelihood function and the target constraint likelihood function using Bayesian theory, and based on the posterior distribution, determines the equivalent samples of the rock and soil parameters using a target sampling algorithm, and uses the equivalent samples to update the reliability index of the target slope to obtain the updated slope reliability index.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a probabilistic inversion analysis method for rock and soil parameters based on constrained Bayesian updating as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement a rock and soil parameter probability inversion analysis method based on constrained Bayesian updating as described in any one of claims 1 to 6.

10. A computer program product comprising a computer program, characterized in that The computer program is executed by a processor to implement a rock and soil parameter probabilistic inversion analysis method based on constrained Bayesian updating as described in any one of claims 1 to 6.

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