A non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm

Abstract

The present invention provides a non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm, which belongs to the technical field of tunnel engineering. On the basis of the existing non-probabilistic reliability analysis method, the present invention introduces a machine learning algorithm, and through the combination of a neural network proxy model and a Bayesian regularization algorithm, the implicit expression of the tunnel surrounding rock state function is explicitly expressed, and the credibility of the neural network proxy model is defined, which can quantitatively describe the effectiveness of the neural network proxy model, and can effectively solve the problem in the prior art that the tunnel surrounding rock state function is an implicit function and non-probabilistic reliability analysis cannot be performed.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering, and in particular relates to a non-probabilistic reliability analysis method for surrounding rock of a deep tunnel based on a machine learning algorithm. Background Art

[0002] Due to the great burial depth of deep tunnels and their complex geological environment, the actual engineering characteristics make it very difficult to obtain samples of the statistical characteristics of the uncertainty parameters of the surrounding rock of deep tunnels, which mainly manifests itself in the form of small samples. This makes the traditional probabilistic reliability method based on large sample statistical data often have large deviations in its analysis results when facing small sample situations, and even misjudgments occur. Therefore, it is necessary to introduce non-probabilistic reliability methods from a non-probabilistic perspective to conduct research; on the other hand, with the continuous increase of burial depth, the mechanical action mechanism of the surrounding rock of deep tunnels becomes more complex, resulting in the inability to directly give an explicit functional function describing the state of the tunnel surrounding rock in the non-probabilistic reliability analysis, that is, the state function required for its reliability calculation is usually in the form of a highly complex implicit function, and the current related methods based on non-probabilistic reliability are still difficult to deal with such complex implicit state function problems without explicit analytical expressions.

[0003] Therefore, it is necessary to provide a non-probabilistic reliability analysis method for deep tunnel surrounding rock based on machine learning algorithm to solve the above problems. Summary of the invention

[0004] The present invention provides a non-probabilistic reliability analysis method for surrounding rock of deep tunnel based on machine learning algorithm. On the basis of the existing non-probabilistic reliability analysis method, the present invention introduces machine learning algorithm, combines neural network proxy model with Bayesian regularization fitting algorithm to analyze and solve the actual engineering problems of deep tunnel, that is, the implicit stable state function is explicitly represented by neural network proxy model, and the Bayesian regularization fitting algorithm is used in the explicit process to ensure that the model has high validity, and then the interval non-probabilistic method is used to calculate the non-probabilistic reliability index, and the stability reliability of the tunnel surrounding rock is determined according to the index; on this basis, sensitivity analysis is carried out around the fitting effect of the neural network proxy model, the interval expansion of the uncertainty parameter and the change of the maximum displacement of the tunnel surrounding rock, so as to solve at least one technical problem involved in the background technology.

[0005] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0006] A non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm includes the following steps:

[0007] Step S1, establishing a mechanical analysis model of the tunnel surrounding rock based on a finite element numerical simulation method;

[0008] Step S2, constructing an implicit expression of the tunnel surrounding rock state function and a set vector of the variable space according to the influencing factors of the tunnel surrounding rock stability and pressure;

[0009] Step S3, using a random number function to generate a number of random numbers for each interval variable in the variable space, selecting a random number for each interval variable in the variable space to form a group of samples, and obtaining the true response value of the maximum displacement of the tunnel surrounding rock under the group of samples based on finite element numerical simulation;

[0010] Step S4, constructing a data set with multiple groups of samples and the true response values ​​of the maximum displacement of the tunnel surrounding rock under the samples, inputting the data set into the neural network proxy model for iterative training, fitting to obtain an explicit representation of the tunnel surrounding rock state function, and introducing a Bayesian regularization fitting algorithm to ensure the effectiveness of the model during the fitting process;

[0011] Step S5, according to the fitted state function, an interval non-probability method is used to solve the non-probability reliability index of the tunnel surrounding rock, and the stability reliability of the tunnel surrounding rock is determined based on the non-probability reliability index.

[0012] As a preferred improvement, during the construction of the finite element numerical model, the model constraints are set as the left and right boundaries are fixed in normal, the lower boundary is completely fixed, and the upper boundary is free. A pair of horizontal uniformly distributed loads of equal size and opposite direction are added to the left and right boundaries to represent the horizontal ground stress, and a vertical uniformly distributed load is added to the upper boundary to represent the vertical ground stress, where the horizontal ground stress σ h and vertical geostress σ v The value of is expressed as:

[0013] σ h =0.01766H+1.0583;

[0014] σ v =0.02532H+0.8177;

[0015] Where H is the tunnel depth.

[0016] As a preferred improvement, the model used for tunnel surrounding rock reliability analysis is the Hoek-Brown model, and the state function Ψ of the tunnel surrounding rock is expressed as:

[0017] Ψ=g(χ)=u max -u;

[0018] Where χ is the set vector of the variable space, χ={γ,E,v,σ ci ,m i ,GSI,D,ψ,σ ψ}, γ is the rock mass bulk density; E is the rock mass elastic modulus; v is the rock mass Poisson's ratio; σ ciis the uniaxial compressive strength; m i is the constant of intact rock material; GSI is the geological strength parameter; D is the disturbance factor of the rock mass caused by the technical measures in construction; ψ, σ ψ is the dilatancy parameter; u max is the maximum allowable displacement of the tunnel surrounding rock, and the value is determined according to the specifications for tunnels with the same rock mass and the same section; u is the true response value of the maximum displacement of the tunnel surrounding rock, u = f(χ).

[0019] As a preferred improvement, the non-probabilistic reliability index η′ is expressed as:

[0020]

[0021] In the formula, Ψ′ ub ,Ψ′ lb Respectively represent the upper and lower bounds of the fitting state function Ψ′; u′ ub , u′ lb They represent the upper and lower bounds of the maximum displacement prediction value u′ of the tunnel surrounding rock, respectively; MSE max is the maximum value of the mean square error of the fitting state function Ψ′.

[0022] As a preferred improvement, the stability of the tunnel surrounding rock is determined according to the relationship between η′ and 1. The determination process is as follows:

[0023] If η′<1, it indicates that the tunnel surrounding rock is unreliable and needs to be reinforced or rebuilt;

[0024] If η′=1, it indicates that the tunnel surrounding rock is in a critical state and early warning needs to be strengthened;

[0025] If η′>1, it indicates that the tunnel surrounding rock structure is reliable.

[0026] As a preferred improvement, the credibility ξ of the neural network proxy model is defined to quantify the effectiveness of the neural network proxy model. The credibility ξ is defined as follows:

[0027]

[0028] In the formula, ξ is a real number between (-∞,1]; |Ψ′ c | is the absolute value of the mean of the fitting state function Ψ′.

[0029] As a preferred improvement, in the neural network proxy model, the number of hidden neurons is confirmed by the following steps:

[0030] (1) Estimate the number of hidden neurons based on the size of the variable space;

[0031] (2) Analyze the influence of sample size on the effectiveness of neural network proxy model fitting and determine the optimal sample size based on the results;

[0032] (3) Reversely verify the rationality of the number of hidden neurons based on the optimal number of samples.

[0033] As a preferred improvement, the method further comprises the following steps:

[0034] Step S6, for the fitting results of the neural network proxy model, further sensitivity analysis is carried out through the influence of the number of hidden neurons of the samples and the neural network proxy model on the fitting effect, the influence of the interval expansion of the uncertainty parameter on the neural network proxy model, and the influence of the change of the maximum allowable displacement of the tunnel surrounding rock on the non-probabilistic reliability index, so as to reduce the number of samples as much as possible while ensuring the effectiveness of the neural network proxy model.

[0035] The beneficial effects of the present invention are:

[0036] (1) Based on the interval non-probabilistic reliability analysis method, interval variables are used to characterize the uncertainty of the surrounding rock parameters of deep tunnels, which overcomes the problem that the traditional probabilistic reliability method is no longer applicable due to the difficulty in obtaining the statistical characteristics of the uncertainty parameters;

[0037] (2) In view of the highly complex implicit characteristics of the functional function describing the stability state of the surrounding rock of deep tunnels, a machine learning algorithm is introduced to explicitly represent the implicit state function through a neural network proxy model, which effectively solves the problem that the interval non-probabilistic reliability analysis method is difficult to handle such complex implicit state functions without explicit analytical expressions;

[0038] (3) The Bayesian regularization algorithm is used in the neural network fitting process, which has strong generalization ability and can effectively reduce the mean square error of the fitting function and improve the effectiveness of the neural network proxy model, so that the calculated non-probabilistic reliability index is closer to reality;

[0039] (4) The credibility of the neural network proxy model is defined, the effectiveness of the neural network proxy model is quantitatively described, and a reference table is given based on numerical simulation and engineering practice to judge the effectiveness of the neural network proxy model and guide subsequent work. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flow chart showing a non-probabilistic reliability analysis method for surrounding rock of a deep tunnel based on a machine learning algorithm provided by the present invention;

[0041] Figure 2 The Hoek-Brown strength curve discriminant diagram of surrounding rock failure provided by the present invention;

[0042] Figure 3 is an actual cross-sectional view of the tunnel in Example 1;

[0043] Figure 4 This is a schematic diagram of a finite element numerical model of a tunnel in Example 1;

[0044] Figure 5 Schematic diagram of total displacement of tunnel surrounding rock in finite element numerical simulation results in Example 1;

[0045] Figure 6 is an error histogram of training and test data in a neural network fitting model training in Example 1;

[0046] Figure 7 In Example 1, a single hidden layer with 6 nodes is used and the maximum number of training rounds is specified to be 1000. The maximum mean square error (MSE) corresponding to the number of samples n1 is max Calculation results and change trend chart;

[0047] Figure 8 The calculation results and change trend diagram of the non-probabilistic reliability index η′ corresponding to the sample number n1 of the model trained by using a single hidden layer with 6 nodes and specifying a maximum training round of 1000 rounds in Example 1;

[0048] Fig. 9 The calculation results and change trend diagram of the neural network proxy model credibility ξ corresponding to the sample number n1 of the model trained by a single hidden layer with 6 nodes and a maximum training round of 1000 rounds in Example 1;

[0049] Fig.10 In Example 1, 60 sets of data are fixed for training and testing, and the maximum number of training rounds is specified as 1000. The maximum mean square error MSE corresponding to the number of hidden neurons n2 is max Calculation results and change trend chart;

[0050] Fig.11 In Example 1, 60 sets of data are fixed for training and testing, and the maximum training round is specified as 1000 rounds. The calculation results and change trend diagram of the non-probabilistic reliability index η′ corresponding to the number of hidden neurons n2 are shown;

[0051] Fig.12 In Example 1, 60 sets of data are fixed for training and testing, and the maximum training round is specified to be 1000 rounds. The calculation results and change trend diagram of the credibility ξ of the neural network proxy model corresponding to the number of hidden neurons n2;

[0052] Fig.13 is the maximum displacement u allowed by the tunnel surrounding rock in Example 1 maxThe calculation results and change trend diagram of the corresponding non-probabilistic reliability index η′ when taking different values;

[0053] Fig.14 is the maximum displacement u allowed by the tunnel surrounding rock in Example 1 max The corresponding neural network proxy model credibility ξ calculation results and change trend diagram when taking different values;

[0054] Fig.15 is the maximum displacement u allowed by the tunnel surrounding rock in Example 1 max When the mean is fixed and the fluctuation range is different, u,max , the corresponding non-probabilistic reliability index η′ calculation results and change trend diagram. DETAILED DESCRIPTION

[0055] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] Please refer to Figure 1-Figure 15 The present invention provides a non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on a machine learning algorithm, comprising the following steps:

[0057] Step S1, based on the finite element numerical simulation method, a mechanical analysis model of the tunnel surrounding rock is established.

[0058] The finite element numerical analysis software selected in the process of establishing the mechanical analysis model is PLAXIS2D. The model constraints are set as the left and right boundaries are fixed in normal, the lower boundary is completely fixed, and the upper boundary is free. A pair of horizontal uniformly distributed loads of equal size and opposite direction are added to the left and right boundaries to represent the horizontal ground stress, and a vertical uniformly distributed load is added to the upper boundary to represent the vertical ground stress, where the horizontal ground stress σ h and vertical geostress σ v The value of is expressed as:

[0059] σ h =0.01766H+1.0583;

[0060] σ v =0.02532H+0.8177;

[0061] Where H is the tunnel depth.

[0062] Step S2, constructing an implicit expression of the tunnel surrounding rock state function and a set vector of the variable space according to the influencing factors of the tunnel surrounding rock stability and pressure.

[0063] The model used for tunnel surrounding rock reliability analysis is the Hoek-Brown model. The Hoek-Brown strength curve for tunnel surrounding rock failure is as follows: Figure 2 The state function Ψ of the tunnel surrounding rock is expressed as:

[0064] Ψ=g(χ)=u max -u;

[0065] Where χ is the set vector of the variable space, χ={γ,E,v,σ ci ,m i ,GSI,D,ψ,σ ψ}, where γ is the rock mass bulk density; E is the rock mass elastic modulus; υ is the rock mass Poisson's ratio; σ ci is the uniaxial compressive strength; m i is the constant of intact rock material; GSI is the geological strength parameter; D is the disturbance factor of the rock mass caused by the technical measures in construction; ψ, σ ψ is the dilatancy parameter; u max is the maximum allowable displacement of the tunnel surrounding rock. For tunnels with the same rock mass and the same section, the value is generally determined according to the specifications; u is the true response value of the maximum displacement of the tunnel surrounding rock, which can be written in the form of u=f(χ).

[0066] Step S3, using a random number function to generate a number of random numbers for each interval variable in the variable space, selecting a random number for each interval variable in the variable space to form a group of samples, and obtaining the true response value of the maximum displacement of the tunnel surrounding rock under the group of samples based on finite element numerical simulation.

[0067] The finite element simulation process can adopt conventional techniques in this field. Specifically: with the help of the "Material Set" function in the PLAXIS2D software, input the data of each group of samples, and then run the "Calculate" command. After the calculation is completed, find the maximum value of |u| in the "Table" tab. This value is the true response value u of the maximum displacement of the tunnel surrounding rock under this group of samples.

[0068] Step S4, constructing a data set with multiple groups of samples and the true response values ​​of the maximum displacement of the tunnel surrounding rock under the samples, inputting the data set into the neural network proxy model for iterative training, and fitting to obtain an explicit representation of the tunnel surrounding rock state function. During the fitting process, the Bayesian regularization fitting algorithm is introduced to ensure the effectiveness of the model.

[0069] The neural network proxy model can adopt a conventional model in the art, and its training process also adopts conventional technology in the art, which will not be described in detail in this embodiment.

[0070] In the neural network proxy model, the number of hidden neurons is determined by the following steps:

[0071] (1) Preliminarily estimate the number of hidden neurons based on the size of the variable space (the number of parameters in the variable space) (generally, the number of hidden neurons is taken as the number of parameters or the number of parameters + 1);

[0072] (2) Analyze the influence of sample size on the effectiveness of model fitting and determine the optimal sample size based on the results;

[0073] (3) Based on the optimal number of samples, the rationality of the number of hidden neurons is verified to obtain the optimal number of hidden neurons.

[0074] The fitted state function expression is:

[0075] Ψ′=g′(χ)=u max -f′(χ);

[0076] Where Ψ′ represents the fitting state function of the tunnel surrounding rock and Ψ′ is the explicit function.

[0077] The Bayesian regularization fitting algorithm can be implemented using conventional techniques in the art, and this embodiment will not be described in detail. The credibility ξ of the neural network proxy model is defined to quantify the effectiveness of the neural network proxy model. The credibility ξ is defined as follows:

[0078]

[0079] In the formula, ξ is a real number between (-∞,1]; |Ψ′ c | is the absolute value of the mean of the fitting state function Ψ′.

[0080] The credibility ξ takes into account the impact of the mean square error and the value of the fitting state function Ψ′ on the effectiveness of the neural network proxy model, and can be effectively used to determine the effectiveness of the neural network proxy model.

[0081] The rules for determining the effectiveness of the neural network proxy model are shown in Table 1:

[0082] Table 1. Judgment rules for the effectiveness of the neural network proxy model

[0083]

[0084] Taking into account the error, a “high” rating for model effectiveness is sufficient to prove its credibility.

[0085] Step S5, according to the fitted state function, an interval non-probability method is used to solve the non-probability reliability index of the tunnel surrounding rock, and the stability reliability of the tunnel surrounding rock is determined based on the non-probability reliability index.

[0086] The non-probabilistic reliability index η′ is expressed as:

[0087]

[0088] In the formula, ψ′ ub ,ψ′ lb They represent the upper and lower bounds of the fitting state function Ψ′, respectively; u′ ub , u′ lb They represent the upper and lower bounds of the maximum displacement prediction value u′ of the tunnel surrounding rock, u′=f′(χ), u′ ub , u′ lb It can be solved using the fmincon function in MATLAB. Its boundary conditions correspond to the value range of the variable space X. MSE max is the maximum value of the mean square error of the fitting state function Ψ′.

[0089] After obtaining the η′ value, the stability of the tunnel surrounding rock is determined based on the relationship between η′ and 1. The specific determination process is as follows:

[0090] If η′<1, it indicates that the tunnel surrounding rock is unreliable and needs to be reinforced or rebuilt;

[0091] If η′=1, it indicates that the tunnel surrounding rock is in a critical state and early warning needs to be strengthened;

[0092] If η′>1, it indicates that the tunnel surrounding rock structure is reliable.

[0093] Step S6, for the fitting results of the neural network proxy model, further sensitivity analysis is carried out through the influence of the number of hidden neurons of the samples and the neural network proxy model on the fitting effect, the influence of the interval expansion of the uncertainty parameter on the neural network proxy model, and the influence of the change of the maximum allowable displacement of the tunnel surrounding rock on the non-probabilistic reliability index, and the number of samples is reduced as much as possible while ensuring the effectiveness of the neural network proxy model.

[0094] Sensitivity analysis specifically includes:

[0095] (1) When analyzing the fitting effect of the neural network proxy model, the influence of another influencing factor on the fitting effect is explored by fixing one of the influencing factors, such as the number of samples or hidden neurons;

[0096] (2) When analyzing the impact of uncertainty parameter interval expansion on the neural network proxy model, we use the fmincon function in the MATLAB environment to find the coordinate points where Ψ′ takes the maximum and minimum values ​​before the interval expansion, χ1 = {E1,σ ci1 ,m i1 ,GSI1} and χ2={E2,σ ci2 ,m i2 ,GSI2}, and fix the values ​​of other parameters, and only consider the change of one parameter in the corresponding expansion interval;

[0097] (3) When analyzing the influence of the maximum allowable displacement of the tunnel surrounding rock on the non-probabilistic reliability index, it is necessary to analyze the maximum displacement of the tunnel surrounding rock from two aspects: different single values ​​and different interval variables. In view of the influence of the maximum allowable displacement of the tunnel surrounding rock from different interval variables, the maximum allowable displacement of the tunnel surrounding rock can be used as a fluctuating variable with a fixed mean value, thereby simplifying the model.

[0098] Example 1

[0099] In this embodiment, the analysis object is a single-hole double-track railway tunnel with a total length of 17.9km, of which the K7+578-K10+672.5 section is 3094.5m long and buried 500m below the ground. The highest altitude is 117.87m and the lowest altitude is 110.50m. The tunnel section is a straight-wall arch tunnel. According to geological surveys, the surrounding rock of the tunnel is mainly slightly weathered medium-coarse-grained granite, with joints ranging from relatively developed to undeveloped, and the rock mass ranging from relatively complete to complete, and the rock quality is relatively hard; a small part is slightly weathered and broken granite, and the rock mass is seriously affected by the geological structure, with extremely developed joints and fissures. The actual cross-section of the tunnel is shown in the figure below. Figure 3 shown.

[0100] According to the engineering profile of the tunnel, the tunnel section, ground stress and grid model are constructed, such as Figure 4 In the process of model construction, only the stability of the rock mass after blasting excavation is considered, and the parameters introduced by the support are not considered, so there is no need to add support structure.

[0101] The tunnel surrounding rock is hard, the rock mass is relatively complete, and the overall quality is good; there are joints and cracks of poor quality from time to time, and the surrounding rock mass quality can be set to level III or IV. The maximum allowable displacement of the tunnel surrounding rock (measured in vault) is the average value corresponding to level III and IV surrounding rock according to relevant engineering specifications. The maximum allowable displacement of level III surrounding rock is 32mm, and the maximum allowable displacement of level IV surrounding rock is 75mm. The maximum allowable displacement of the tunnel surrounding rock is u max =(32+75) / 2mm=53.5mm.

[0102] According to the construction data and project overview, the rock mass γ=25.7kN / m 3 , the rock mass Poisson's ratio υ = 0.2, the drilling and blasting method has a certain disturbance to the rock mass, and its disturbance factor D = 0.5. The remaining rock mass mechanical parameters are taken as uncertainty parameters and are taken according to Table 2:

[0103] Table 2 Uncertainty parameter value range

[0104] parameter Value range Rock mass elastic modulus E [20,30] / GPa <![CDATA[Unconfined compressive strength σ ci > [50,65] / MPa <![CDATA[Complete rock material constant m i > [5.011,9.197] Geological Strength Parameter GSI [30,45]

[0105] In this example, the effect of shear dilatancy on the surrounding rock is not considered, and the default values ​​of ψ,σ ψ is 0. This simplifies the interval variable space into a set vector of 4 variables, namely:

[0106] χ={E,σ ci ,m i ,GSI};

[0107] Before using random numbers to obtain the true response value of the sample, the approximate range of the displacement can be determined by calculating the response value at the boundary of the variable space. The true response value at its boundary will also become an important reference for the neural network proxy model and its effectiveness. The upper and lower bounds of the variable space are calculated below, and the results are shown in Table 3:

[0108] Table 3 End point response values ​​calculated by finite element numerical simulation

[0109]

[0110] It can be estimated from Table 3 that the displacement fluctuation range is roughly around 10-50 mm. Now, 60 sets of data are generated using the random number function of the Excel software platform and the true response value of the maximum displacement of the tunnel surrounding rock is calculated using PLAXIS. A data set is constructed with 60 sets of samples and the true response value of the maximum displacement of the tunnel surrounding rock under the samples. The data set is input into the neural network proxy model for iterative training, and the explicit representation of the tunnel surrounding rock state function is obtained by fitting. During the fitting process, the Bayesian regularization fitting algorithm is introduced to ensure the effectiveness of the model. The first 50 groups are used for training and testing, and the last 10 groups are used to additionally verify the effectiveness of the model.

[0111] To ensure sufficient effectiveness, the number of hidden neurons in the neural network proxy model is set to 6 according to the number of parameters. After 315 trainings, the training round with the best performance is the 221th round, and its mean square error and regression coefficient are shown in Table 4:

[0112] Table 4 Mean square error (MSE) and regression coefficient (R) corresponding to the best performance (round 221)

[0113] Number of observations Mean Square Error (MSE) Regression coefficient R Training Data 42 0.0020 1.0000 Test Data 8 0.0713 0.9984

[0114] Now we add 10 more groups of observations to verify the effectiveness of the neural network proxy model. The results are shown in Table 5:

[0115] Table 5 Verification results of additional verification data

[0116]

[0117]

[0118] According to the training data and test data, there is a very high correlation between the variables, and the mean square error is about 0.07mm 2 , the standard deviation is about 0.265 mm, which proves that the neural network proxy model has a good fitting effect, but its error cannot be ignored.

[0119] The fitting function can be derived and its interval maximum value can be found through the fmincon function in the MATLAB environment. The non-probabilistic reliability index of the tunnel surrounding rock is obtained by using the explicit function obtained by fitting and the interval non-probabilistic method, and the stability reliability of the tunnel surrounding rock is determined based on this.

[0120] Use the fmincon function in the MATLAB environment to find the maximum displacement u′ ub =51.6508mm and minimum value u′ lb =10.6209mm. Therefore, the predicted value interval of the real response value of the maximum displacement of the tunnel surrounding rock can be determined as u′=[10.6209,51.6508](mm). The interval range of Ψ′ can be calculated from the interval range of u′:

[0121] Ψ′=u max -u′=53.5-[10.6209,51.6508]=[1.8492,42.8791](mm)

[0122] According to the previous article, the MSE of this model max =0.0713mm 2 、u max =53.5mm, substitute it into the calculation formula of non-probability reliability index and solve it to get the fitted non-probability reliability index:

[0123]

[0124] Therefore, the structure is stable and reliable. In fact, due to the timely adoption of reasonable support measures, the tunnel has never suffered any disaster caused by surrounding rock failure since its completion, which further confirms the effectiveness and rationality of this method.

[0125] Continue with sensitivity analysis:

[0126] First, consider the effect of sample size on the fitting effect of the neural network proxy model. Now take the sample size n1 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 for training respectively. The neural network proxy model adopts a single hidden layer 6-node model, specifies the maximum training round as 1000 rounds, and plots the maximum mean square error of training, test and additional validation data, the reliability index and credibility corresponding to different sample sizes, and the changing trends of the three, as shown in the figure below: Figures 7 to 9 As shown. Figures 7 to 9It can be seen that as the number of samples increases, the maximum mean square error MSE of the neural network proxy model max The non-probabilistic reliability index η′ gradually increases, and the credibility ξ of the model also gradually increases. When the number of samples exceeds 60 groups, the data and change trends of the three gradually stabilize. Among them, the credibility ξ finally stabilizes at around 0.98-0.99, which proves that the fitting effect is good, but the impact of errors needs to be considered. Therefore, for this project, only 60 groups of data are needed to fit a more satisfactory result.

[0127] Secondly, consider the influence of the number of hidden neurons on the fitting effect of the neural network proxy model. Now take the number of hidden neurons n2 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 for training, fix the number of samples used for training and testing to 60 groups, specify the maximum training rounds to 1000 rounds, and plot the maximum mean square error of training, testing and additional validation data, the reliability index and credibility corresponding to different numbers of hidden neurons, and the changing trends of the three, as shown in the figure below: Figures 10 to 12 As shown by Figures 10 to 12 It can be seen that after determining the amount of sample data, the non-probabilistic reliability index η′ has no obvious correlation with the number of hidden neurons. As the number of hidden neurons increases, the maximum mean square error MSE of the neural network proxy model max decreases rapidly, and the credibility of the model ξ also increases. When the number of hidden neurons exceeds 5, MSE max tends to be stable, while ξ even shows a downward trend. At the same time, it is noted during training that an increase in the number of hidden neurons usually means more training times, and the maximum number of training times set in this example is only 1000, which leads to insufficient training times when the number of hidden neurons is too large, resulting in an increase in the mean square error and a decrease in the credibility of the neural network proxy model. More training times often means longer time and storage space consumption. In view of this, it is more reasonable to take 5-6 hidden neurons.

[0128] Then, the influence of the expansion of the uncertainty parameter interval on the neural network proxy model is considered. Assume that the actual measured rock elastic modulus E is expanded from [20GPa, 30GPa] to [19GPa, 31GPa], while the value ranges of other parameters remain unchanged. With the help of the fmincon function in the MATLAB environment, the coordinate points χ1={E1,σ ci1 ,m i1 ,GSI1} and χ2={E2,σ ci2 ,m i2,GSI2}. Here we only need to verify the impact of the interval expansion of E on Ψ′, so we can fix the values ​​of other parameters and only consider the change of this parameter in the expansion interval. Now we fix σ ci =65MPa,m i =9.197, GSI = 45 and σ ci =50MPa,m i =5.011, GSI=30, and 5 values ​​are uniformly taken in the upward and downward expansion intervals of the elastic modulus E, and the true response value and the model prediction value of the displacement are calculated respectively, and the mean square error is calculated. The results are shown in Tables 6 and 7:

[0129] Table 6 Comparison of expansion interval u and u′ on E (fixed σ ci =65MPa,m i =9.197,GSI=45)

[0130] Elastic modulus E / GPa True response value u / mm Model predicted value u' / mm Deviation 30.2 10.533 10.507 -0.026 30.4 10.464 10.394 -0.070 30.6 10.395 10.281 -0.114 30.8 10.326 10.170 -0.156 31 10.261 10.060 -0.201 Mean square error 0.0166

[0131] Table 7 Comparison of expansion interval u and u′ under E (fixed σ ci =50MPa,m i =5.011,GSI=30)

[0132] Elastic modulus E / GPa True response value u / mm Model predicted value u' / mm Deviation 19 54.374 54.361 -0.013 19.2 53.807 53.822 0.015 19.4 53.253 53.282 0.029 19.6 52.709 52.739 0.030 19.8 52.177 52.195 0.018 Mean square error 0.0005

[0133] It can be seen from Tables 6 and 7 that the mean square errors of the upper expansion interval and the lower expansion interval of the elastic modulus E correspond to 0.0166 and 0.0005 (mm 2 ), and through the fmincon function, we find that the value range of Ψ′ in the expanded interval is [-0.8610, 43.4396] (mm), and thus calculate its mean value Ψ′ c =21.2893mm. According to the definition of model credibility and the mean square error of E in the upper and lower expansion intervals, the credibility of the model in the upper and lower expansion intervals ξ is calculated respectively. ux =0.9939 and ξ lx =0.9990. According to Table 1, the effectiveness of the neural network proxy model in the expansion interval is at a high (or extremely high) level, the fitting effect is good, and there is no need to consider the problem of refitting. The new non-probabilistic reliability index η′=0.9276<1 is calculated, indicating that the structure is no longer reliable. It is worth noting that for the maximum mean square error MSE max If the mean square error of the upper expansion interval and the lower expansion interval of a variable is greater than this value, the MSE should be max The correction is the maximum value of the mean square error of its upper expansion interval and lower expansion interval.

[0134] Secondly, the influence of different single values ​​of the maximum displacement allowed by the tunnel surrounding rock on the non-probabilistic reliability index is analyzed.max Considered as a constant, the displacement prediction function u′=f′(χ) and its variable space χ remain unchanged, and the maximum mean square error (MSE) of the neural network proxy model is max and deviation u' ub -u′ lb unchanged. However, since Ψ′ means Ψ' c Will follow you max The model credibility ξ will inevitably change with the change of , so the changes in the credibility and effectiveness of the neural network proxy model must be considered. Here, we take u max =30, 36.3, 40.6, 44.9, 49.2, 53.5, 57.8, 62.1, 66.4, 70.7, 75 mm, and plot the values ​​and changing trends of the corresponding non-probabilistic reliability index η′ and the credibility ξ of the neural network proxy model, as shown in Figure 13-14 As shown. Fig.13 and Fig.14 It can be seen that as the allowable displacement increases from 32mm to 75mm, the reliability index η' increases linearly from 0.0405 to 2.0578, and the credibility of the neural network proxy model ξ increases from 0.6910 to 0.9939, and gradually approaches 1. And as the mean value Ψ' c (or the maximum displacement u of the tunnel surrounding rock max ) decreases, the credibility of the neural network proxy model also decreases, especially when Ψ' c When it approaches 0, the credibility ξ decreases rapidly. This shows that when the mean of the fitting function Ψ′ c When it is too low, the credibility of the neural network proxy model will often be very low. At this time, the tunnel must be reinforced or rebuilt so that the non-probabilistic reliability index η′ and the credibility of the neural network proxy model ξ are both within the allowable range.

[0135] Finally, the influence of different interval variables of the maximum displacement allowed by the tunnel surrounding rock on the non-probabilistic reliability index is analyzed. max As a fluctuating variable with a fixed mean, its fluctuation range can be expressed as follows:

[0136]

[0137] Where λ u,max for u max The fluctuation range, u max The mean and deviation of .

[0138] Since the neural network fitting is directly performed on u in this embodiment, the fitting interval range and mean square error of the variable can be directly obtained. Based on this and the above calculation results, the new variable space χ' and the value range can be determined as shown in the following table:

[0139] Table 8 Parameters and ranges in the new variable space (unit: mm)

[0140] Variable space parameters Value range Mean Deviation Fluctuation Range <![CDATA[Allow displacement u max > [32,75] 53.5 21.5 0～0.40 Actual displacement u′ [10.6209,51.6508] 31.1359 20.5150 -

[0141] According to the above variable space, Ψ′=g′(u max ,u′)=u max -u′. Since the value range of the variable space is determined, the mean value of the fitting function Ψ′ c =22.3641mm is a constant value, and the credibility of the neural network proxy model ξ = 0.9881 is also uniquely determined, so there is no need to consider u max The influence of the value of on the effectiveness of the neural network proxy model. Now take the fluctuation amplitude λ u,max =0, 0.04, 0.08, 0.12, 0.16, 0.2, 0.24, 0.28, 0.32, 0.36, 0.4, and use the interval theory to calculate the corresponding non-probabilistic reliability. The calculation results and change trends are shown in the figure. Fig.15 As shown. It can be seen that when u max When the fluctuation amplitude increases from 0 to 0.4, the reliability index η' decreases from 1.0492 to 0.5236, with a decrease amplitude of Δη'=0.5256, and the decreasing speed gradually decreases with the increase of the fluctuation amplitude. Therefore, the fluctuation of the allowable displacement has a significant impact on the reliability index.

[0142] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm, characterized in that: The steps include: Step S1, establishing a mechanical analysis model of the tunnel surrounding rock based on a finite element numerical simulation method; Step S2, constructing an implicit expression of the tunnel surrounding rock state function and a set vector of the variable space according to the influencing factors of the tunnel surrounding rock stability and pressure; Step S3, using a random number function to generate a number of random numbers for each interval variable in the variable space, selecting a random number for each interval variable in the variable space to form a group of samples, and obtaining the true response value of the maximum displacement of the tunnel surrounding rock under the group of samples based on finite element numerical simulation; Step S4, constructing a data set with multiple groups of samples and the true response values ​​of the maximum displacement of the tunnel surrounding rock under the samples, inputting the data set into the neural network proxy model for iterative training, fitting to obtain an explicit representation of the tunnel surrounding rock state function, and introducing a Bayesian regularization fitting algorithm to ensure the effectiveness of the model during the fitting process; Step S5, according to the fitted state function, an interval non-probability method is used to solve the non-probability reliability index of the tunnel surrounding rock, and the stability reliability of the tunnel surrounding rock is determined based on the non-probability reliability index; The model used for reliability analysis of tunnel surrounding rock is the Hoek-Brown model, and the state function Ψ of tunnel surrounding rock is expressed as: Ψ=g(χ)=u max -u; Where χ is the set vector of the variable space, χ={γ,E,υ,σ ci ,m i ,GSI,D,ψ,σ ψ }, γ is the rock mass bulk density; E is the rock mass elastic modulus; υ is the rock mass Poisson's ratio; σ ci is the uniaxial compressive strength; m i is the constant of intact rock material; GSI is the geological strength parameter; D is the disturbance factor of the rock mass caused by the technical measures in construction; ψ, σ ψ is the dilatancy parameter; u max is the maximum allowable displacement of the tunnel surrounding rock, and the value is determined according to the specifications for tunnels with the same rock mass and the same section; u is the true response value of the maximum displacement of the tunnel surrounding rock, u = f(χ).

2. The non-probabilistic reliability analysis method for surrounding rock of deep tunnel based on machine learning algorithm according to claim 1 is characterized in that: In the process of constructing the finite element numerical model, the model constraints are set as the left and right boundaries are fixed in normal, the lower boundary is completely fixed, and the upper boundary is free. A pair of horizontal uniformly distributed loads of equal size and opposite direction are added to the left and right boundaries to represent the horizontal ground stress, and a vertical uniformly distributed load is added to the upper boundary to represent the vertical ground stress, where the horizontal ground stress σ h and vertical geostress σ v The value of is expressed as: s h =0.01766H+1.0583; s v =0.02532H+0.8177; Where H is the tunnel depth.

3. The non-probabilistic reliability analysis method for surrounding rock of deep tunnel based on machine learning algorithm according to claim 1 is characterized in that: The non-probabilistic reliability index η′ is expressed as: In the formula, Ψ′ ub ,Ψ′ lb Respectively represent the upper and lower bounds of the fitting state function Ψ′; u′ ub , u′ lb They represent the upper and lower bounds of the maximum displacement prediction value u′ of the tunnel surrounding rock, respectively; MSE max is the maximum value of the mean square error of the fitting state function Ψ′.

4. The non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm according to claim 3 is characterized in that: The stability of the tunnel surrounding rock is determined according to the relationship between η′ and 1. The specific determination process is as follows: If η′<1, it indicates that the tunnel surrounding rock is unreliable and needs to be reinforced or rebuilt; If η′=1, it indicates that the tunnel surrounding rock is in a critical state and early warning needs to be strengthened; If η′>1, it indicates that the tunnel surrounding rock structure is reliable.

5. The non-probabilistic reliability analysis method for surrounding rock of deep tunnel based on machine learning algorithm according to claim 3 is characterized in that: The credibility ξ of the neural network proxy model is defined to quantify the effectiveness of the neural network proxy model. The credibility ξ is defined as follows: In the formula, ξ is a real number between (-∞,1]; |Ψ′ c | is the absolute value of the mean of the fitting state function Ψ′.

6. The non-probabilistic reliability analysis method for surrounding rock of deep tunnel based on machine learning algorithm according to claim 1 is characterized in that: In the neural network proxy model, the number of hidden neurons is determined by the following steps: (1) Estimate the number of hidden neurons based on the size of the variable space; (2) Analyze the influence of sample size on the effectiveness of neural network proxy model fitting and determine the optimal sample size based on the results; (3) Reversely verify the rationality of the number of hidden neurons based on the optimal number of samples.

7. The non-probabilistic reliability analysis method for surrounding rock of deep tunnels based on machine learning algorithm according to claim 6 is characterized in that: The following steps are also included: Step S6, for the fitting results of the neural network proxy model, further sensitivity analysis is carried out through the influence of the number of hidden neurons of the samples and the neural network proxy model on the fitting effect, the influence of the interval expansion of the uncertainty parameter on the neural network proxy model, and the influence of the change of the maximum allowable displacement of the tunnel surrounding rock on the non-probabilistic reliability index, so as to reduce the number of samples as much as possible while ensuring the effectiveness of the neural network proxy model.

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