1. A parameter inversion method of geotechnical engineering stochastic process is characterized by comprising the following steps:

s1: establishing a functional relation g (X) between input parameters and output parameters in geotechnical engineering, and describing an inversion problem as follows:

if the probability distribution B (mu '. sigma.') of the output parameter Y is known, solving the statistical parameters mu '. mu.and sigma'. sigma.of the input parameter X to make g (X). about.B (mu '. sigma.');

wherein both mu and sigma are statistical parameters; denotes theoretical values;

specifically, μ and μ 'are theoretical values of position parameters of the probability distribution of X and Y, respectively, and σ' are theoretical values of scale parameters of the probability distribution of X and Y, respectively;

s2: performing repeated random sampling on the input parameter X for multiple times according to the probability distribution B (mu ', sigma') of the output parameter Y, calculating sample values of multiple groups of output parameters Y according to the random sampling result, and estimating initial statistical parameters of the sample values;

s3: and starting iteration on the statistical parameters, and obtaining the probability distribution of the input parameter X according to the statistical parameters obtained after iteration convergence so as to obtain the inversion result of the input parameters in geotechnical engineering.

2. The parametric inversion method for the stochastic process of geotechnical engineering according to claim 1, wherein the step S3 specifically comprises:

s31: starting iteration on the statistical parameters, taking linear regression of the statistical parameters as an objective function, and obtaining the objective function of

λ′^(t)＝β^(t)λ^(t)+α^(t)

Wherein, λ is any statistical parameter of μ and σ; lambda [ alpha ]^(t)The statistical parameter, λ ', of the parameter X is input for the t-th iteration'^(t)Is a statistical parameter, alpha, of the output parameter Y at the t-th iteration^(t)And beta^(t)Is the regression coefficient of the t iteration, t is a positive integer, and t is more than or equal to 0;

s32 let λ 'after iteration convergence'^(t)Lambda', the statistical parameter lambda of the t-th iteration at convergence is solved^(t)＝(λ′*-α′^(t))/β′^(t)；

Wherein λ' is a theoretical value of a statistical parameter of the output parameter Y;

s33: and obtaining the probability distribution of the input parameter X according to the obtained statistical parameters, and further obtaining the inversion result of the rock-soil physical model.

3. The parametric inversion method for stochastic process of geotechnical engineering according to claim 2, wherein in S31:

when t is 0, then β⁽⁰⁾＝1，α⁽⁰⁾＝0；

When t is 1, then β⁽¹⁾＝λ′⁽⁰⁾/λ⁽⁰⁾，α⁽¹⁾＝0，λ′⁽⁰⁾As an initial statistical parameter of the output parameter Y, λ⁽⁰⁾Initial statistical parameters of the input parameters X;

when t is more than or equal to 2, the punishment needs to be carried out on alpha (t) and beta (t), and the objective function becomes

λ′^(t)＝β′^(t)λ^(t)+α′^(t)

Wherein, alpha'^(t)And beta'^(t)Penalized for the t-th iterationRegression coefficients, the degree of penalty decreases as the number of iterations increases.

4. The parametric inversion method for the geotechnical engineering random process according to claim 3, wherein when t is greater than or equal to 2, the regression coefficient at the t-th iteration is specifically:

wherein t is iteration times, and t is more than or equal to 2; alpha (t) and beta (t) are original regression coefficients obtained by linear regression of the statistical parameters, alpha '(t) and beta' (t) are regression coefficients after punishment,andstatistical parameter lambda 'of the previous t-1 iterations respectively'^(t)And λ^(t)Average value of (i), i.e.i is a positive integer.

5. The parametric inversion method for the stochastic process of geotechnical engineering according to claim 2, wherein the iterative convergence condition is as follows:

(2λ^(t)-λ^(t-1)-λ^(t-2))/2λ^(t)≤ω

wherein, ω is convergence tolerance, and if the above conditions are satisfied, the t-th iteration step is considered to be converged, and statistical parameters are output.

6. The parametric inversion method for geotechnical engineering stochastic processes according to claim 1, wherein the function g (X) is any parameter transfer process in geotechnical engineering, and can be expressed without explicit mathematics.

7. The parametric inversion method for the geotechnical engineering stochastic process according to claim 2, wherein the iteration time t is 20-40 times.

8. A parametric inversion system for a stochastic process of geotechnical engineering, comprising:

a processor and a memory for storing executable instructions;

wherein the processor is configured to execute the executable instructions to perform the parametric inversion method of the geotechnical engineering stochastic process of any one of claims 1 to 7.

9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out a method for parametric inversion of a stochastic process of geotechnical engineering according to any one of claims 1 to 7.

Background

Due to the complexity of the rock-soil mass and the uncertainty of indoor and outdoor tests, there are many practical difficulties in selecting physical mechanical parameters, and accurate material parameters are of great importance in analyzing the physical mechanical behavior of the rock-soil mass. In engineering, a large number of geotechnical tests are commonly used to obtain parameters such as internal friction angle, cohesive force and the like. However, for the soil body with complex structure, the parameters are obtained by the soil engineering test, which takes long time and has higher difficulty. Moreover, the spatial variability of some soil body strength parameters is large, the obtained test result is discrete, and accurate calculation parameters are difficult to obtain. In this case, obtaining the rock-soil body strength parameters by adopting a parametric inversion method has been widely used.

Inverse problem refers to the determination of model parameters characterizing the problem from the result and some principles, models. In engineering applications, the inversion problem widely appears in the fields of geophysical, biological, medical, building and the like. The inverse problem exists relative to the forward problem, and the general working procedure is as follows: model output data-forward model-estimate model input parameters, so the forward computational model is the basis for the inverse problem. The current inversion methods include linear inversion, nonlinear inversion, optimized inversion, iterative inversion, etc., where iterative inversion is a more common method.

The multi-solution problem of the inversion process is various, wherein the independent variable is the inverse problem of the random vector, and the related research is few at present, because the number of the independent variable is larger than that of the dependent variable, and the independent variable and the dependent variable are random. If a plurality of independent variables obey the same distribution and the number of statistical parameters of the independent variables is consistent with that of the statistical parameters obtained by observing dependent variables, a unique solution is theoretically provided, but forward calculations with the statistical parameters as variables are estimated values and are not one-to-one determined values, so that a plurality of problems occur in iterative inversion. Therefore, research on the inverse problem of the statistical parameters is required.

Patent application number cn201910316629.x discloses a rock-soil parameter random field inversion method, which comprises the following steps: analyzing conventional statistical characteristics, space correlation structures and space correlation functions of rock and soil parameters; determining a calculation range of the rock-soil parameter spatial correlation and a grid size of a numerical model, and constructing a spatial correlation matrix; and generating an initial random field by using a pseudorandom program, and sequentially and circularly operating each grid according to a basic inversion equation to generate a parameter random field. The method of the invention.

Disclosure of Invention

In view of the above, the invention provides a parameter inversion method and system for a geotechnical engineering stochastic process, which can quickly and efficiently process the inversion problem of complex stochastic variables in geotechnical engineering and can be applied to the probability distribution inversion problem of complex physical models without explicit mathematical expression.

In order to achieve the purpose, the invention adopts the technical scheme that:

according to a first aspect of the present invention, there is provided a parametric inversion method of a stochastic process of geotechnical engineering, the method comprising the steps of:

s1: establishing a functional relation g (X) between input parameters and output parameters in geotechnical engineering, and describing an inversion problem as follows:

if the probability distribution B (mu '. sigma.') of the output parameter Y is known, solving the statistical parameters mu '. mu.and sigma'. sigma.of the input parameter X to make g (X). about.B (mu '. sigma.');

wherein both mu and sigma are statistical parameters; denotes theoretical values;

specifically, μ and μ 'are theoretical values of position parameters of the probability distribution of X and Y, respectively, and σ' are theoretical values of scale parameters of the probability distribution of X and Y, respectively;

s2: performing repeated random sampling on the input parameter X for multiple times according to the probability distribution B (mu ', sigma') of the output parameter Y, calculating sample values of multiple groups of output parameters Y according to the random sampling result, and estimating initial statistical parameters of the sample values;

s3: and starting iteration on the statistical parameters, and obtaining the probability distribution of the input parameter X according to the statistical parameters obtained after iteration convergence so as to obtain the inversion result of the input parameters in geotechnical engineering.

Further, the S3 specifically includes:

s31: starting iteration on the statistical parameters, taking linear regression of the statistical parameters as an objective function, and obtaining the objective function of

λ′^(t)＝β^(t)λ^(t)+α^(t)

Wherein, λ is any statistical parameter of μ and σ; lambda [ alpha ]^(t)The statistical parameter, λ ', of the parameter X is input for the t-th iteration'^(t)Is a statistical parameter, alpha, of the output parameter Y at the t-th iteration^(t)And beta^(t)Is the regression coefficient of the t iteration, t is a positive integer, and t is more than or equal to 0;

s32 let λ 'after iteration convergence'^(t)Lambda', the statistical parameter lambda of the t-th iteration at convergence is solved^(t)＝(λ′*-α′^(t))/β′^(t)；

Wherein λ' is a theoretical value of a statistical parameter of the output parameter Y;

s33: and obtaining the probability distribution of the input parameter X according to the obtained statistical parameters, and further obtaining the inversion result of the rock-soil physical model.

Further, in S31:

when t is 0, then β⁽⁰⁾＝1，α⁽⁰⁾＝0；

When t is 1, then β⁽¹⁾＝λ′⁽⁰⁾/λ⁽⁰⁾，α⁽¹⁾＝0，λ′⁽⁰⁾As an initial statistical parameter of the output parameter Y, λ⁽⁰⁾Initial statistical parameters of the input parameters X;

when t is more than or equal to 2, the punishment needs to be carried out on alpha (t) and beta (t), and the objective function becomes

λ′^(t)＝β′^(t)λ^(t)+α′^(t)

Wherein, alpha'^(t)And beta'^(t)For the regression coefficient after the penalty of the t iteration, the penalty degree is reduced along with the increase of the iteration number.

Further, when t is greater than or equal to 2, the regression coefficient at the time of the tth iteration is specifically:

wherein t is iteration times, and t is more than or equal to 2; alpha (t) and beta (t) are original regression coefficients obtained by linear regression of the statistical parameters, alpha '(t) and beta' (t) are regression coefficients after punishment,andstatistical parameter lambda 'of the previous t-1 iterations respectively'^(t)And λ^(t)Average value of (i), i.e.i is a positive integer.

Further, the iteration convergence condition is as follows:

(2λ^(t)-λ^(t-1)-λ^(t-2))/2λ^(t)≤ω

wherein, ω is convergence tolerance, and if the above conditions are satisfied, the t-th iteration step is considered to be converged, and statistical parameters are output.

Further, the function g (x) is any parameter transfer process in geotechnical engineering, and can have no explicit mathematical expression.

Furthermore, the iteration time t is 20-40 times.

According to a second aspect of the present invention, there is provided a parametric inversion system for a stochastic process of geotechnical engineering, comprising:

a processor and a memory for storing executable instructions;

wherein the processor is configured to execute the executable instructions to perform the parametric inversion method of the geotechnical engineering stochastic process described above.

According to a third aspect of the present invention, there is provided a computer readable storage medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the above-mentioned method for parametric inversion of a geotechnical engineering stochastic process.

Compared with the prior art, the parameter inversion method and system for the geotechnical engineering random process have the following advantages:

(1) the invention combines the statistical analysis and the inversion problem, can quickly and efficiently process the inversion problem of complex random variables in geotechnical engineering, and is also suitable for the probability distribution inversion problem of a complex physical model without explicit mathematical expression;

(2) the problem of difficult convergence caused by errors of statistical parameter estimation is solved by linear regression analysis and slope punishment, and the algorithm can be ensured to be stable in convergence and accurate and reliable in result;

(3) the method has universality in the geotechnical field, is not limited to a certain data type, and can economically and accurately obtain various geotechnical parameters of the whole engineering area.

Drawings

The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is an inversion of the mean value of the normal distribution random vector in geotechnical engineering described in example 1 of the present invention:

FIG. 3 is an inversion of the maximum value of the normally distributed random vector in geotechnical engineering according to embodiment 2 of the present invention.

Detailed Description

Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the invention, as detailed in the appended claims.

The terms first, second and the like in the description and in the claims of the present invention are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

A plurality, including two or more.

And/or, it should be understood that, as used herein, the term "and/or" is merely one type of association that describes an associated object, meaning that three types of relationships may exist. For example, a and/or B, may represent: a exists alone, A and B exist simultaneously, and B exists alone.

A parameter inversion method for a geotechnical engineering random process comprises the following specific technical scheme:

a. assuming that the input and output parameters of a physical mathematical model are random variables and there is a functional relationship g (x) Y, the inverse problem to be solved is described as: if the probability distribution of the variable Y is known as B (mu)₂*,σ₂X), solving the statistical parameter μ of the variable X₁Sum σ₁Let g (X) to B (μ)₂*,σ₂X), the solution is as follows.

b. Performing repeated random sampling on the variable X for multiple times, calculating sample values of multiple groups of random variables Y through g (X) and Y, and estimating statistical parameters of the sample values;

c. the linear regression equation for the input and output statistical parameters λ, λ 'at the t-th iteration can be expressed as λ' ═ β, as the iteration progresses, the closer the regression line is to the tangent of the objective function at the theoretical solution, approximating the target function with a linear regression of the data produced by all iterations^(t)λ+α^(t)Wherein the statistical parameter λ represents any one of μ and σ.

d. In order to avoid the tangential direction abnormality caused by the error of the estimated value of the initial statistical parameter of the iteration, the slope of the regression line needs to be punished, and the coefficient of the regression line in the t iteration step becomes:

wherein alpha'^(t)And beta'^(t)When the penalty is given, t is 2, …, t₀。

e. Let λ ═ λ ·, then solve to get t th iteration step, the statistical parameter λ^(t)＝(λ*-α′^(t))/β′^(t)；

f. Due to the uncertainty of the dependent variable estimate, the convergence criterion is defined by the argument:

(2λ^(t)-λ^(t-1)-λ^(t-2))/2λ^(t)≤ω

if the above conditions are satisfied, the convergence is considered in the t-th iteration step, and if the conditions are not satisfied, the process returns to the step b.

Preferably, the function g (X) in step a may be a complex physical mathematical process without explicit mathematical expression, where X ═ { X ═₁,X₂,...,X_nIs a random vector, random argument X₁,X₂,...,X_nAre all obeyed to A distribution A (mu)₁,σ₁) The random dependent variable Y obeys the B distribution B (mu)₂,σ₂) Where X and Y may be different types of distributions and μ and σ are the location parameter and scale parameter, respectively, of the statistical distribution.

Preferably, in step c, without performing regression analysis when t is 0 and 1, the coefficients are directly specified: when t is 0, beta⁽⁰⁾＝1，α⁽⁰⁾0; when t is 1, beta⁽⁰⁾＝λ′⁽⁰⁾/λ⁽⁰⁾，α⁽⁰⁾＝0，λ′⁽⁰⁾Is the estimated value of the statistical parameter output in the initial (0 th) iteration;

preferably, the slope penalty of step d is to move the slope towards β early in the iteration⁽¹⁾Punishment is carried out, the degree of the iteration punishment is reduced along with the increase of the iteration times, and the stability and the accuracy of the iterative calculation are ensured.

Preferably, the more the repeated calculation times of each iteration in the step b are, the more accurate the parameter estimation is, but the larger the calculation amount is, the more the parameter estimation is suggested to be between 20 and 40, and the convergence can be ensured and the convergence speed can be ensured.

The inversion analysis of geotechnical engineering parameters (such as elastic modulus, Poisson's ratio and the like) is a process of inversion analysis of material parameters of rock masses according to displacement values or stress values and the like of a few known measuring points, and is a basis for design and numerical calculation of hydroelectric engineering. The determination of rock mass mechanics parameters is a key problem in the calculation of geotechnical engineering numerical values. Because the parameters of the rock mass are often difficult to determine, the results of numerical calculation are greatly influenced, the measurement of the rock mass parameters in a laboratory has the problem of scale effect, and in consideration of economic cost, the number of field samples is often not large, so that the real rock mass parameters of the whole engineering area cannot be obtained.

Next, the present invention will be described in detail with reference to a distribution type.

Example 1: inversion of average value of normal distribution random vector in geotechnical engineering

Is provided with a random vector X ═ X₁,X₂,...,X₁₀In which the variable X is random₁,X₂,...,X₁₀Are all subject to a normal distribution N (mu)₁,σ₁ ²) If the input and output parameters of a physical mathematical model are random variables and there is a functional relationship Y ═ mean (x), the random variables Y also obey the normal distribution B (μ ═ n ×)₂,σ₂ ²)。

The inverse problem to be solved is described as: if the probability distribution of the variable Y is known to be N (100, 2)²) Solving the statistical parameter mu of the independent variable X₁Sum σ₁Let mean (X) to N (100, 2)²). Theoretical solution of mu₁*＝100，The standard deviation sigma of the variable X is compared according to the scheme shown in FIG. 1₁The solution to perform the iterative inversion is as follows:

let the initial distribution of the random vector X be consistent with the distribution of the known random variable Y, i.e. obey a normal distribution N (100, 2)²) Then, 30 times of repeated random sampling is performed, and a plurality of sets of sample values of the random variable Y are calculated by mean (x) ═ Y and the average value and standard deviation thereof are calculated.

Then, a first iteration is carried out, the slope beta of which⁽⁰⁾＝σ₂ ⁽⁰⁾/σ₁ ⁽⁰⁾＝0.569/2＝0.284，α⁽⁰⁾When 0, then σ₁ ⁽¹⁾＝σ₂*/β⁽⁰⁾2/0.284-7.03. Then substituted into a functionThe relationship is iterated through the calculation and the statistical parameters of the variable Y are estimated, the iteration process being shown in figure 2 a.

When the iteration step is more than 2, the linear regression of the data generated by all the iteration steps is used for approximately replacing the objective function, the closer the regression line is to the tangent line of the objective function at the theoretical solution as the iteration progresses, and the input and output statistical parameters sigma are output at the t-th iteration₁、σ₂Can be expressed as sigma₂＝β^(t)σ₁+α^(t)。

In order to avoid the tangential direction abnormity caused by the error of the estimated value of the statistical parameter in the initial iteration stage, the slope of the regression line needs to be punished, and the slope is towards beta in the initial iteration stage⁽¹⁾Punishment, the slope of the regression line at the t-th iteration step becomes: | β' ((iii) B)^t)|＝((t-2)|β^(t)|+|β(¹) I.)/(t-1), the new intercept is calculated by the center point coordinates of the historical iteration data as:

let sigma₂＝σ₂Then, when t-th iteration step is obtained by solving, the statistical parameter sigma₁ ^(t)＝(σ₂*-α′^(t))/β′^(t)Then calculating whether convergence is achieved, if (2 sigma) is satisfied₁ ^(t)-σ₁ ^(t-1)-σ₁ ^(t-2))/2σ₁ ^(t)If the value is less than or equal to 0.1, the convergence in the t iteration step can be considered, and if the value is not more than 0.1, the steps are repeated.

The final calculated convergence value solution is 6.26, the relative error with the theoretical solution 6.32 is 0.9%, and the convergence curve and penalty curve are shown in fig. 2 b.

Example 2: inversion of maximum value of normally distributed random vector in geotechnical engineering

Is provided with a random vector X ═ X₁,X₂,...,X₁₀In which the variable X is random₁,X₂,...,X₁₀Are all subject to a normal distribution N (mu)₁,σ₁ ²) Setting input and output parameters of a physical mathematical modelAll are random variables and have a functional relationship Y ═ max (x), the random variable Y follows a gummy-type maximum distribution G (μ ═ max (x))₂,σ₂) In which μ₂And σ₂And a position parameter and a scale parameter, which are maximum value distributions, respectively.

The inverse problem to be solved is described as: if the probability distribution of the variable Y is known as G (100,10), the statistical parameter mu of the independent variable X is solved₁Sum σ₁Let max (X) to G (100, 10). The problem is not solved theoretically, and the standard deviation sigma of the variable X is corrected according to the flow shown in FIG. 1₁The solution to perform the iterative inversion is as follows:

let the initial distribution of the random vector X be consistent with the statistical parameters of the known random variable Y, i.e. obey a normal distribution N (100,10)²) Then, 30 times of repeated random sampling is carried out, sample values of a plurality of groups of random variables Y are calculated through max (x) ═ Y, the variance var (Y) of the sample values is calculated, and the scale parameter of the extreme value distribution is further calculated as follows:

then, the first iteration is carried out, and the slope beta is set⁽⁰⁾＝σ₂ ⁽⁰⁾/σ₁ ⁽⁰⁾＝5.44/10＝0.544，α⁽⁰⁾When 0, then σ₁ ⁽¹⁾＝σ₂*/β⁽⁰⁾10/0.544-18.39. Then substituting the function relation into the function relation to perform repeated sampling calculation and estimate the statistical parameter sigma of the variable Y₂The iterative process is shown in figure 3 a.

When the iteration step is larger than 2, the regression analysis is firstly carried out, and then the slope is punished to obtain a new regression line equation which is as follows: sigma₂＝β′^(t)σ₁+α′^(t)。

Let sigma₂＝σ₂Then, when t-th iteration step is obtained by solving, the statistical parameter sigma₁ ^(t)＝(σ₂*-α′^(t))/β′^(t)Then calculating whether convergence is achieved, if (2 sigma) is satisfied₁ ^(t)-σ₁ ^(t-1)-σ₁ ^(t-2))/2σ₁ ^(t)If the value is less than or equal to 0.1, the convergence in the t iteration step can be considered, and if the value is not more than 0.1, the steps are repeated.

The final calculated convergence value solution is 18.31, and the iterative convergence curve and penalty curve are shown in fig. 3 b.

The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.

While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.