Deep foundation pit displacement prediction method combining finite element and data driving

Abstract

The invention belongs to the field of intelligent construction, and discloses a deep foundation pit displacement prediction method combining finite element and data driving, which comprises the following steps: calculating a theoretical elastic modulus according to an investigation report, and constructing a sample space by adopting a Latin hypercube sampling method and an orthogonal experiment design method; a proper constitutive model is selected, and corresponding lateral displacement is calculated through finite elements; dimensionality reduction processing is carried out on the data set based on global sensitivity analysis of variance so as to accelerate convergence during subsequent inversion; training an SKRR-LSBOOST model through an ensemble learning method to replace a traditional model; combining an improved Hemma optimization algorithm with a substitution model, and applying the combined model to parameter inversion; and performing forward analysis based on the finite element model defined by the inversion parameters to predict the deformation of the deep foundation pit in the next excavation stage. According to the method, the advantages of numerical simulation and data driving are fully exerted, the calculation cost is reduced according to the rock and soil parameters, higher prediction precision is achieved, and the accuracy of foundation pit deformation prediction is improved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent construction, and in particular to a deep foundation pit displacement prediction method combining finite element and data drive. Background Art

[0002] With the continuous advancement of urbanization, foundation pit projects are developing in multiple directions such as large depth and large area. The influencing factors are complex and changeable, and the requirements for related technologies such as monitoring and control are gradually increasing. In order to ensure the safety and stability of the foundation pit construction stage and provide an important reference basis for the subsequent construction tasks, the analysis and prediction of the lateral displacement in the foundation pit is very important. However, the influencing factors of lateral displacement are relatively complex, and the resulting multi-parameter inversion is difficult to solve; on the other hand, the static penetration points on site are also very limited, and there is a problem of insufficient acquisition of geotechnical parameters. These problems bring great difficulties and challenges to the lateral displacement of the foundation pit.

[0003] Traditional methods for simulating and predicting deformation include empirical formulas of traditional geotechnical mechanics, numerical simulations such as the finite element method (FEM), and data-driven machine learning models. Although each has its own advantages, these methods also have their own shortcomings: (1) Traditional principle formula calculations cannot take into account the dynamic effects of construction; (2) Numerical simulations such as the finite element method are very expensive to calculate, and the accuracy of the input parameters is high and difficult to obtain; (3) The data quality of the data driven machine learning model is dependent on the lack of certain physical interpretability. When the geotechnical parameters are not yet clear or the field conditions deviate from the training data, its effectiveness will be limited.

[0004] Therefore, there is an urgent need for a deep foundation pit displacement prediction method that combines finite element and data-driven methods. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a new framework combining an improved finite element method with a data-driven model to accurately identify geotechnical parameters and improve the accuracy of foundation pit displacement prediction: a nonlinear model between geotechnical parameters and calculated deformation is constructed through finite elements, and a synthetic data set is built. The dimension of the synthetic data set is reduced through global sensitivity analysis to improve the convergence speed of inversion, an ensemble learning method is used to enhance the generalization ability, the improved Hippo optimization algorithm is combined with the alternative model obtained by ensemble learning to perform parameter inversion, and the inverted elastic modulus is brought into the finite element forward modeling to predict the displacement of the next stage.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A deep foundation pit displacement prediction method combining finite element and data-driven, comprising the following steps:

[0008] S1 Data preparation: Parameters are obtained based on the on-site geotechnical investigation report and soil physical information obtained from the field investigation, the theoretical value of the elastic modulus is calculated, and the sample space is determined and optimized using orthogonal experimental design and Latin hypercube sampling;

[0009] S2 numerical simulation: construct a Mohr-Coulomb constitutive model, input the theoretical value of the elastic modulus obtained in step S1 into the finite element model and output the horizontal displacement;

[0010] S3 global sensitivity analysis: Perform variance-based global sensitivity analysis based on the horizontal displacement output in step S2, remove measurement points with low sensitivity, and achieve dimensionality reduction of the synthetic data set;

[0011] S4 ensemble learning alternative model: Based on the data set of the global sensitivity analysis in step S3, the weight of each sample is adjusted using the AdaBoost ensemble optimization algorithm, and multiple machine learning algorithms are trained and integrated to form an alternative model;

[0012] S5 Improved Hippo Algorithm: Based on the substitute model obtained in step S4, the Hippo Algorithm is improved by using Sin mapping, reverse learning and Cauchy mutation and applied to parameter inversion, and the elastic modulus is output through the objective function;

[0013] S6 Finite element analysis prediction: The result obtained by multi-parameter inversion in step S5 is input into the finite element model for forward analysis. The output lateral displacement is the predicted value for the next stage, so as to realize the prediction of deep foundation pit displacement.

[0014] Preferably, the parameters in step S1 include soil mass, deadweight, layer thickness, porosity and porosity ratio, permeability, and groundwater level.

[0015] Preferably, the soil body includes, in order of depth, miscellaneous fill, plain fill, silt, clay, silty clay, silt, silt-sand interlayers, and sand.

[0016] Preferably, in step S1, the elastic modulus calculation formula corresponding to the soil information is calculated as follows:

[0017]

[0018] Where v is Poisson's ratio, E S is the compression modulus.

[0019] Preferably, in step S1, the size of the data sampling space is determined by adopting an upper threshold and a lower threshold which are 0.5 times and 2 times the elastic modulus respectively, and a Latin hypercube sampling method and an orthogonal experimental design method are used to generate sample data from the specified sampling space, and the sample data is evenly and comprehensively distributed.

[0020] Preferably, the object soil for constructing the Mohr-Coulomb constitutive model in step S2 includes all soil types, and the input value of the finite element model in step S2 is the theoretical elastic modulus E={E 1 ,E 2 ,E 3 ,…,E n}, where n is the number of soil layers inverted; the output value is the lateral displacement of the foundation pit: y = {y 1 ,y 2 ,y 3 ,…,y m}, where m is the number of measuring points for detecting horizontal displacement.

[0021] Preferably, in step S3, the specific measurement indicators for the variance-based global sensitivity analysis include: first-order sensitivity index S i Total effect index S Ti , the calculation formula is as follows:

[0022]

[0023] In the formula, Y and X are related by the model Y = f(X), and the i-th variable X i The sensitivity of is given by Var, where Var and E are operators representing variance and expectation, respectively, and X ～i Indicates the division by X i The set of all input variables except i Measured the contribution to uncertainty, S Ti Provides the total variance of Y.

[0024] Preferably, in step S4, the object of the AdaBoost integrated optimization algorithm includes two single machine learning algorithms, SKRR and LSBOOST, each with its own advantages, and a more suitable proxy model SKRR-LSBOOST is formed by combining the two.

[0025] Preferably, in the integrated optimization algorithm of step S4, each time the iteration is updated, the basic model H is selected. q , according to the current distribution of sample weights, its error e q The calculation formula is:

[0026]

[0027] Among them, x i represents the training set, represents the true result of the training set, I represents the error calculation function, and w qi is the weight of the qth training sample of the i-th basic model;

[0028] The weight coefficient λ of the basic model in the ensembleq for:

[0029]

[0030] Among them, e q represents the calculated error;

[0031] During ensemble learning, the updated weight distribution D in the training sample set q+1 for:

[0032]

[0033] Among them, w qi represents the weight of the qth training sample of the i-th basic model; λ q Represents the basic model weight coefficient calculated by the above formula;

[0034] For the above ensemble learning, each basic model is combined with its weight coefficient, and the sign function is used to obtain the final comprehensive prediction value H final , the calculation formula is:

[0035]

[0036] Among them, Q represents the total amount of the basic model, H q Indicates the selected base model.

[0037] For the replacement model formed by the above ensemble learning, the basis for quantifying the accuracy of the model is two important indicators in regression prediction: the coefficient of determination R 2 The calculation formula for the sum of absolute differences (SAD) is:

[0038]

[0039] In the formula, R 2 The range of y is [0,1]. The value closer to 1 means that the model prediction value is closer to the actual value. i is the result of model parameter inversion, is the average value of the inversion results.

[0040] Preferably, in step S5, the basic hippopotamus optimization algorithm includes population initialization, position update phase, defense strategy phase and predator avoidance phase.

[0041] Preferably, the basic Hippo algorithm comprises the following specific steps:

[0042] S5.1 Population initialization: Initialize the hippo population through Sin mapping. The initial value cannot be set to 0 to avoid zero points and fixed points. The mapping equation is as follows:

[0043]

[0044] Among them, x i+1 It represents the position of the first candidate solution in the population after Sin chaotic mapping, and C represents the size of the population.

[0045] S5.2 Position update phase: Introduce a dynamic adaptive weighting factor ω to accelerate convergence and improve search accuracy. The calculation formula is as follows:

[0046]

[0047] Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations;

[0048] The position of a female hippopotamus or an immature hippopotamus is updated using the following calculation formula:

[0049]

[0050] Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; variables lb and ub represent the lower and upper limits of the decision variable, respectively, and r is a random number from 0 to 1.

[0051] The male hippopotamus position is updated, and the calculation formula is as follows:

[0052]

[0053] Where E is the position of the female hippopotamus or immature hippopotamus, h 1 It consists of random numbers and random vectors, and its calculation formula is as follows:

[0054]

[0055] Among them, I represents 1 or 2, and Q represents 0 or 1.

[0056] The position of the male leader hippopotamus is updated, and the calculation formula is as follows:

[0057]

[0058] Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; r is a random number from 0 to 1;

[0059] The optimal solution for this stage is calculated as follows:

[0060]

[0061] in, The location of the male leader hippopotamus. is the position of the male hippopotamus, and Fit is the appropriate evaluation function.

[0062] S5.3 Defense strategy stage: The Hippo algorithm is unchanged in this stage. After the update, the new candidate solution is compared with the current candidate solution, and the optimal solution is selected for iteration. The calculation formula is as follows:

[0063]

[0064] in, is the new candidate solution in the defense strategy phase, X i is the current candidate solution.

[0065] S5.4 Predator avoidance stage: Introduce a dynamic selection strategy to update the target position, based on the selection probability P s The calculation formula is as follows:

[0066]

[0067] Among them, t and t max Represent the current number of iterations and the maximum number of iterations respectively.

[0068] Introducing the reverse learning strategy into the Hippo algorithm, the algorithm space is expanded, the corresponding inverse solution is obtained by reversing the current solution, and a better solution is selected by comparison. 1 It represents the information exchange control parameter, and its calculation formula is as follows:

[0069]

[0070] Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations;

[0071] Cauchy mutation is introduced in the Hippo algorithm, and the random variables obeying the Cauchy distribution are calculated according to the following formula.

[0072] η=tan[(ξ-0.5)π]

[0073] Here, ξ represents a random number in the interval [0,1].

[0074] According to the selection probability, the reverse learning strategy and the Cauchy mutation strategy are used alternately to dynamically adjust the target position. s Select Cauchy mutation; otherwise use the reverse learning strategy. The candidate solution generated in the predator avoidance phase is calculated as follows:

[0075]

[0076] Among them, r represents a random number in the interval [0,1], η represents a random variable with Cauchy mutation, and b 1 Indicates information exchange control parameters.

[0077] After the Hippo algorithm completes the update of this stage, it compares the candidate solution generated in this stage with the final solution (current candidate solution) of the defense strategy stage, and determines the optimal solution of this iteration. The calculation formula is as follows:

[0078]

[0079] in, represents the candidate solution generated in the predator avoidance phase, X i is the current candidate solution.

[0080] The improved Hippo algorithm is applied to parameter inversion, and its inversion objective function is:

[0081]

[0082] F(X best )=minF(X i )

[0083] In the formula, the lateral displacement value measured at the nth monitoring point is The corresponding model calculated value is H n , w n is the weight of the monitoring point, X best is the optimal solution X generated by all iterations i The minimum value in .

[0084] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0085] (1) A new framework combining finite element analysis and data-driven method is proposed to achieve more accurate prediction while reducing costs, providing a new solution for predicting foundation pit deformation.

[0086] (2) Global sensitivity analysis is used to focus on monitoring points with higher sensitivity, simplify the synthetic data set to improve the efficiency of inversion, and reduce the complexity of multi-input and multi-output nonlinear mapping.

[0087] (3) The AdaBoost ensemble algorithm is used to intelligently adjust the sample weights to form a more suitable alternative model (SKRR-LSBOOST) to replace the machine learning model, improve the model's ability to capture nonlinear relationships, enhance generalization capabilities, and significantly improve the prediction accuracy of the prediction model, thus solving the limitations of using only traditional machine learning models.

[0088] (4) The Hippo algorithm is improved by using sin mapping, reverse learning and Cauchy mutation to enhance the global search capability and avoid it from falling into the local optimal solution. The improved Hippo algorithm is applied as an optimization algorithm to multi-parameter inversion to solve the problem that traditional optimization methods are difficult to apply to multi-parameter inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 This is a flow chart of the deep foundation pit displacement prediction method combining finite element and data-driven;

[0090] Figure 2 It is a framework diagram combining finite element and data-driven models.

[0091] Figure 3 It is a combined framework diagram of IHO-SKRR-LSBOOST formed by the proxy model and the improved Hippo optimization algorithm. DETAILED DESCRIPTION

[0092] In order to more clearly understand the purpose, advantages and features of the present invention, the present invention is further described and analyzed in detail below in combination with the accompanying drawings and embodiments. Please note that the specific implementation operations described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the embodiments of the present invention described in detail later can be combined with each other as long as they do not conflict with each other.

[0093] See also Figure 1 This embodiment adopts a deep foundation pit displacement prediction method that combines finite element and data-driven, including: data preparation, numerical simulation, global sensitivity analysis, integrated learning replacement model, improved Hippo algorithm, finite element analysis prediction. The specific implementation steps are as follows:

[0094] S1 Data preparation: Parameters were obtained based on the on-site geotechnical investigation report and soil physical information obtained from the field investigation, the theoretical value of the elastic modulus was calculated, and the sample space was determined and optimized using orthogonal experimental design and Latin hypercube sampling (LHS);

[0095] The contents of the geotechnical investigation report include soil mass, deadweight, layer thickness, porosity and porosity ratio, permeability, and groundwater level. The soil mass includes, in order of depth, miscellaneous fill, plain fill, silt, clay, silty clay, silt, interbedded silt and sand, and sand.

[0096] Based on the empirical formula of geotechnical mechanics, the elastic modulus calculation formula corresponding to the soil information is as follows:

[0097]

[0098] Where v is Poisson's ratio, E S is the compression modulus, both of which are determined through indoor or field tests.

[0099] Furthermore, the size of the data sampling space is determined by adopting an upper threshold and a lower threshold that are 0.5 times and 2 times the elastic modulus, respectively.

[0100] The Latin hypercube sampling method (LHS) and orthogonal experimental design (OED) method were used to generate 32 groups of sample data (16 groups for each method) from the specified sampling space. The sampling data were evenly distributed and comprehensive.

[0101] S2 numerical simulation: construct a Mohr-Coulomb constitutive model, input the theoretical value of the elastic modulus obtained in step S1 into the finite element model and output the horizontal displacement;

[0102] The object soil for constructing the Mohr-Coulomb constitutive model in step S2 includes all soil types, and the finite element analysis includes: using geotechnical engineering analysis software PLAXIS 3D for numerical simulation, selecting the Mohr-Coulomb (MC) constitutive model to represent the nonlinear behavior of the soil, and constructing a finite element model of appropriate size.

[0103] The input value of the finite element model is the theoretical elastic modulus E = {E 1 ,E 2 ,E 3 ,…,E n}, where n is the number of soil layers inverted; the output value is the lateral displacement of the foundation pit: y = {y 1 ,y 2 ,y 3 ,…,y m}, where m is the number of measuring points for detecting horizontal displacement.

[0104] That is, certain monitoring points are arranged in the supporting piles, and the input elastic modulus E={E 1 ,E 2 ,E 3 ,……,E n}, numerical simulation is performed to obtain the lateral displacement of the foundation pit y = {y 1 ,y 2 ,y 3 ,…,y m}.

[0105] S3 global sensitivity analysis: Perform variance-based global sensitivity analysis based on the horizontal displacement output in step S2, remove measurement points with low sensitivity, and achieve dimensionality reduction of the synthetic data set;

[0106] The variance-based global sensitivity analysis is characterized by being able to accurately analyze the sensitivity of nonlinear input values, expressing the output variance as a finite sum of increasing order terms, indicating the contribution of each individual parameter and its interaction with other parameters to the overall variance; its specific measurement indicators include: first-order sensitivity index S i Total effect index S Ti .

[0107] Perform a global sensitivity analysis on the lateral displacement output from step S2:

[0108]

[0109] In the formula, Y and X are related by the model Y = f(X), and the i-th variable X i The sensitivity of is given by Var, where Var and E are operators representing variance and expectation, respectively, and X ～i Indicates the division by X i The set of all input variables except i Measured the contribution to uncertainty, S Ti This provides the total variance of Y.

[0110] The main effect index (S) and total effect size (S) of the lateral displacement were calculated for each data set. T ), and arrange them in descending order, calculate the cumulative sum of S and ST respectively, and consider that the monitoring points with cumulative sum exceeding 95% can be used for model training; this method can realize the dimension reduction of data set and accelerate the convergence speed of subsequent algorithms.

[0111] S4 ensemble learning alternative model: Based on the data set of the global sensitivity analysis in step S3, the weight of each sample is adjusted using the AdaBoost ensemble optimization algorithm, and multiple machine learning algorithms are trained and integrated to form an alternative model;

[0112] The data set used by the S4 ensemble learning optimization algorithm is the synthetic data set reduced in dimension based on global sensitivity analysis in step S3. The object of the AdaBoost ensemble optimization algorithm includes two single machine learning algorithms, SKRR and LSBOOST, each with its own advantages, and combines the two to form a more suitable proxy model SKRR-LSBOOST.

[0113] See also Figure 2 , set the initial sample weight w i =1 / N, N represents the total number of training samples, and the sample weights are continuously updated iteratively. Each time the iteration is updated, the selected basic model H q , according to the current distribution of sample weights, its error e q The calculation formula is:

[0114]

[0115] Among them, x i represents the training set, represents the true result of the training set, I represents the error calculation function, and w qi is the weight of the qth training sample of the i-th basic model;

[0116] And use this to calculate the weight coefficient λ of the basic model q for:

[0117]

[0118] Among them, e q Represents the calculated error.

[0119] During ensemble learning, the updated weight distribution D in the training sample set q+1 for:

[0120]

[0121] Among them, w qi represents the weight of the qth training sample of the ith basic model, λ q Represents the basic model weight coefficient calculated by the above formula.

[0122] Finally, different weight coefficients λ q The basic model H q (x) to obtain the comprehensive prediction value H final , forming an alternative model with better overall performance.

[0123]

[0124] Among them, Q represents the total amount of the basic model, H q Indicates the selected base model.

[0125] For the replacement model formed by the above ensemble learning, the basis for quantifying the accuracy of the model is two important indicators in regression prediction: the coefficient of determination R 2 The calculation formula for the sum of absolute differences (SAD) is:

[0126]

[0127] In the formula, R 2 The range of y is [0,1]. The value closer to 1 means that the model prediction value is closer to the actual value. i is the result of model parameter inversion, is the average value of the inversion results.

[0128] In this embodiment, the AdaBoost optimization algorithm selects two machine learning algorithms, SKRR (structured kernel ridge regression) that can efficiently handle nonlinear relationships and LSBOOST (least squares regression) that can adjust model parameters according to prediction results, to form an efficient alternative model through integration.

[0129] In this embodiment, compared with other single machine learning algorithms, the loss of the proxy model SKRR-LSBOOST decreases rapidly and converges to a smaller value, and the training time is also shorter, which is consistent with the expected and target efficacy of the invention.

[0130] S5 improved Hippo algorithm: based on the replacement model obtained in step S4, the Hippo algorithm is improved by using Sin mapping, reverse learning and Cauchy mutation and applied to parameter inversion, and the elastic modulus is output through the objective function; the basic Hippo algorithm includes population initialization, position update stage, defense strategy stage and predator avoidance stage.

[0131] Population initialization is to randomly generate initial solutions according to the upper and lower thresholds of decision variables.

[0132]

[0133] In the position update phase, the position of the dominant hippo in the hippo population is updated individually according to the current optimal solution. represents the potential high-quality optimal solution in the optimization process; the positions of the remaining hippos are updated as Compare the current solution with the candidate solutions and take the best solution to enter the next stage.

[0134] In the defense strategy phase, the algorithm determines the position of the predator. Calculating the distance between predators and hippo populations Depending on the distance, the hippo population adopts two different defense strategies and the position is updated to The candidate solution The iterative update is completed by comparing with the current solution.

[0135] Predator avoidance phase, when the hippopotamus cannot resist the predator, the algorithm updates the information that the hippopotamus is in a safe location The candidate solution The iterative update is completed by comparing with the current solution.

[0136] The improved Hippo algorithm is characterized by providing corresponding improvement schemes to address the problems of the existing random initialization of the Hippo algorithm missing potential solutions and falling into local optimal solutions in some cases, thereby ensuring the global optimization capability of the Hippo algorithm so as to be applicable to complex multi-parameter inversion problems.

[0137] See also Figure 3 , the improved Hippo algorithm steps are broken down as follows:

[0138] S5.1 Population initialization: According to the ergodicity and randomness of chaotic mapping, in the initialization stage of the Hippo algorithm, the Hippo population is initialized by Sin mapping. The initial value cannot be set to 0 to avoid zero points and fixed points, improve the initial quality of the Hippo population and the efficiency of algorithm optimization: that is, the upper and lower limits of the search space up and lp are initialized by chaotic mapping, and the vector X is randomly generated. 0 , each component of the vector is in the interval [0,1]. Generate N vectors using Sin mapping.

[0139]

[0140] Among them, X i+1 It represents the position of the i-th candidate solution in the population after Sin chaotic mapping, and C represents the size of the population.

[0141] S5.2 Position update phase: Introduce a dynamic adaptive weighting factor ω, based on the current number of iterations t and the maximum number of iterations t max The relationship between the weights is adaptively adjusted to accelerate convergence while improving search accuracy, taking into account both global and local search capabilities. The calculation formula is as follows:

[0142]

[0143] Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations;

[0144] The position of a female hippopotamus or an immature hippopotamus is updated using the following calculation formula:

[0145]

[0146] Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; variables lb and ub represent the lower and upper limits of the decision variable, respectively, and r is a random number from 0 to 1.

[0147] The male hippopotamus position is updated, and the calculation formula is as follows:

[0148]

[0149] Where E is the position of the female hippopotamus or immature hippopotamus, h 1 It consists of random numbers and random vectors, and its calculation formula is as follows:

[0150]

[0151] Among them, I represents 1 or 2, and Q represents 0 or 1.

[0152] The position of the male leader hippopotamus is updated, and the calculation formula is as follows:

[0153]

[0154] Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; r is a random number from 0 to 1.

[0155] The optimal solution for this stage is calculated as follows:

[0156]

[0157] in, The location of the male leader hippopotamus. is the position of the male hippopotamus, and Fit is the appropriate evaluation function.

[0158] S5.3 Defense strategy stage: The Hippo algorithm is unchanged in this stage. After the update, the new candidate solution is compared with the current candidate solution, and the optimal solution is selected for iteration. The calculation formula is as follows:

[0159]

[0160] in, is the new candidate solution in the defense strategy phase, X i is the current candidate solution.

[0161] S5.4 Predator avoidance stage: Introduce a dynamic selection strategy to update the target position, based on the selection probability P s The calculation formula is as follows:

[0162]

[0163] Among them, t and t max Represent the current number of iterations and the maximum number of iterations respectively.

[0164] Introducing the reverse learning strategy into the Hippo algorithm, the algorithm space is expanded, the corresponding inverse solution is obtained by reversing the current solution, and a better solution is selected by comparison. 1 It represents the information exchange control parameter, and its calculation formula is as follows:

[0165]

[0166] Among them, t and t max Represent the current number of iterations and the maximum number of iterations respectively.

[0167] Cauchy mutation is introduced in the Hippo algorithm, and the random variables obeying the Cauchy distribution are calculated according to the following formula.

[0168] η=tan[(ξ-0.5)π]

[0169] Here, ξ represents a random number in the interval [0,1].

[0170] According to the selection probability, the reverse learning strategy and the Cauchy mutation strategy are used alternately to dynamically adjust the target position. s Select Cauchy mutation; otherwise use the reverse learning strategy. The candidate solution generated in the predator avoidance phase is calculated as follows:

[0171]

[0172] Among them, r represents a random number in the interval [0,1], η represents a random variable with Cauchy mutation, and b 1 Indicates information exchange control parameters.

[0173] After the Hippo algorithm completes the update of this stage, it compares the candidate solution generated in this stage with the final solution (current candidate solution) of the defense strategy stage, and determines the optimal solution of this iteration. The calculation formula is as follows:

[0174]

[0175] in, represents the candidate solution generated in the predator avoidance phase, X i is the current candidate solution.

[0176] The improved Hippo algorithm is applied to parameter inversion, and its inversion objective function is:

[0177]

[0178] F(X best )=minF(X i )

[0179] In the formula, the lateral displacement value measured at the nth monitoring point is The corresponding model calculated value is H n , w n is the weight of the monitoring point, X best is the optimal solution X generated by all iterations i The minimum value in .

[0180] Based on R 2The calculation results of SAD show that in this embodiment, the IHO-SKRR-LSBOOST framework, which is a combination of the improved Hippo algorithm (IHO) and the substitution model, has better accuracy and efficiency than the ordinary Hippo algorithm and the substitution model combination framework (HO-SKRR-LSBOOST) and other integrated learning model combination frameworks (SSA-SKRR-LSTOOST).

[0181] S6 Finite element analysis prediction: The result obtained by multi-parameter inversion in step S5 is input into the finite element model for forward analysis. The output lateral displacement is the predicted value for the next stage, so as to realize the prediction of deep foundation pit displacement.

[0182] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A deep foundation pit displacement prediction method combining finite element and data-driven, characterized in that: The following steps are involved: S1 Data preparation: Parameters are obtained based on the on-site geotechnical investigation report and soil physical information obtained from the field investigation, the theoretical value of the elastic modulus is calculated, and the sample space is determined and optimized using orthogonal experimental design and Latin hypercube sampling; S2 numerical simulation: construct a Mohr-Coulomb constitutive model, input the theoretical value of the elastic modulus obtained in step S1 into the finite element model and output the horizontal displacement; S3 global sensitivity analysis: Perform variance-based global sensitivity analysis based on the horizontal displacement output in step S2, remove measurement points with low sensitivity, and achieve dimensionality reduction of the synthetic data set; S4 ensemble learning alternative model: Based on the data set of the global sensitivity analysis in step S3, the weight of each sample is adjusted using the AdaBoost ensemble optimization algorithm, and multiple machine learning algorithms are trained and integrated to form an alternative model; S5 Improved Hippo Algorithm: Based on the substitute model obtained in step S4, the Hippo Algorithm is improved by using Sin mapping, reverse learning and Cauchy mutation and applied to parameter inversion, and the elastic modulus is output through the objective function; S6 Finite element analysis prediction: The result obtained by multi-parameter inversion in step S5 is input into the finite element model for forward analysis. The output lateral displacement is the predicted value for the next stage, so as to realize the prediction of deep foundation pit displacement.

2. The deep foundation pit displacement prediction method combining finite element and data-driven as claimed in claim 1, characterized in that: The parameters in step S1 include soil, deadweight, layer thickness, porosity and porosity ratio, permeability, and groundwater level; the soil includes, in order of depth, miscellaneous fill, plain fill, silt, clay, silty clay, silt, silt-sand interlayer, and sand.

3. The deep foundation pit displacement prediction method combining finite element and data-driven as claimed in claim 2, characterized in that: In step S1, the elastic modulus calculation formula corresponding to the soil information is calculated as follows: Where v is Poisson's ratio, E S is the compression modulus.

4. The deep foundation pit displacement prediction method combining finite element and data-driven as claimed in claim 3, characterized in that: In step S1, the size of the data sampling space is determined by adopting an upper threshold and a lower threshold which are 0.5 times and 2 times of the elastic modulus respectively, and a Latin hypercube sampling method and an orthogonal experimental design method are used to generate sample data from the specified sampling space, and the sample data are evenly and comprehensively distributed.

5. The deep foundation pit displacement prediction method combining finite element and data-driven as claimed in claim 1, characterized in that: The object soil for constructing the Mohr-Coulomb constitutive model in step S2 includes all soil types, and the input value of the finite element model is the theoretical elastic modulus: E = {E1, E2, E3, ..., E n }, where n is the number of inverted soil layers; the output value is the lateral displacement of the foundation pit: y = {y1, y2, y3, …, y m }, where m is the number of measuring points for detecting horizontal displacement.

6. The method for predicting displacement of deep foundation pits combining finite element and data-driven as claimed in claim 1, characterized in that: In step S3, the specific measurement indicators for the variance-based global sensitivity analysis include: first-order sensitivity index S i Total effect index S Ti , the calculation formula is as follows: In the formula, Y and X are related by the model Y = f(X), and the i-th variable X i The sensitivity of is given by Var, where Var and E are operators representing variance and expectation, respectively, and X ～i Indicates the division by X i The set of all input variables except i Measured the contribution to uncertainty, S Ti Provides the total variance of Y.

7. The method for predicting displacement of deep foundation pits combining finite element and data-driven as claimed in claim 1, characterized in that: In step S4, the object of the AdaBoost integrated optimization algorithm includes two single machine learning algorithms, SKRR and LSBOOST, and the two are combined to form a proxy model SKRR-LSBOOST.

8. The method for predicting displacement of deep foundation pits combining finite element and data-driven as claimed in claim 7, characterized in that: In the integrated optimization algorithm of step S4, each time the iteration is updated, the basic model H is selected. q , according to the current distribution of sample weights, its error e q The calculation formula is: Among them, x i represents the training set, represents the true result of the training set, I represents the error calculation function, and w qi is the weight of the qth training sample of the i-th basic model; The weight coefficient λ of the basic model in the ensemble q for: Among them, e q represents the calculated error; During the ensemble learning process, the updated weight distribution D in the training sample set q+1 for: Among them, w qi represents the weight of the qth training sample of the i-th basic model; q Represents the basic model weight coefficient calculated by the above formula; For the above ensemble learning, each basic model is combined with its weight coefficient, and the sign function is used to obtain the final comprehensive prediction value H final , the calculation formula is: Among them, Q represents the total amount of the basic model, H q represents the selected base model; For the replacement model formed by the above ensemble learning, the basis for quantifying the accuracy of the model is two important indicators in regression prediction: the coefficient of determination R 2 The calculation formula for the sum of absolute differences (SAD) is: In the formula, R 2 The range of y is [0,1]. The value closer to 1 means that the model prediction value is closer to the actual value. i is the result of model parameter inversion, is the average value of the inversion results.

9. The method for predicting displacement of deep foundation pits combining finite element and data-driven as claimed in claim 1, characterized in that: In step S5, the basic hippopotamus optimization algorithm includes population initialization, position update phase, defense strategy phase and predator avoidance phase.

10. The deep foundation pit displacement prediction method combining finite element and data-driven as claimed in claim 9, characterized in that: The basic Hippo algorithm includes the following specific steps: S5.1 Population initialization: Initialize the hippo population through Sin mapping. The initial value cannot be set to 0 to avoid zero points and fixed points. The mapping equation is as follows: Among them, X i+1 represents the position of the i-th candidate solution in the population after Sin chaotic mapping, and C represents the size of the population; S5.2 Position update phase: Introduce a dynamic adaptive weighting factor ω to accelerate convergence and improve search accuracy. The calculation formula is as follows: Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations; The position of a female hippopotamus or an immature hippopotamus is updated using the following calculation formula: Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; variables lb and ub represent the lower and upper limits of the decision variable, respectively, and r is a random number from 0 to 1; The male hippopotamus position is updated, and the calculation formula is as follows: Where E is the position of the female hippopotamus or immature hippopotamus, h1 is composed of random numbers and random vectors, and its calculation formula is as follows: Among them, I represents 1 or 2, Q represents 0 or 1; The position of the male leader hippopotamus is updated, and the calculation formula is as follows: Among them, MG i represents the average of several randomly selected candidate solutions in the population; besthippo represents the best known candidate solution in the population; r is a random number from 0 to 1; The optimal solution for this stage is calculated as follows: in, The location of the male leader hippopotamus. is the position of the male hippopotamus, and Fit is the appropriate evaluation function; S5.3 Defense strategy stage: The Hippo algorithm is unchanged in this stage. After the update, the new candidate solution is compared with the current candidate solution, and the optimal solution is selected for iteration. The calculation formula is as follows: in, is the new candidate solution in the defense strategy phase, X i is the current candidate solution; S5.4 Predator avoidance stage: Introduce a dynamic selection strategy to update the target position, based on the selection probability P S The calculation formula is as follows: Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations; The reverse learning strategy is introduced into the Hippo algorithm to expand the algorithm space. The corresponding inverse solution is obtained by reversing the current solution, and a better solution is selected by comparison. b1 represents the information exchange control parameter, and its calculation formula is as follows: Among them, t and t max Respectively represent the current number of iterations and the maximum number of iterations; The Cauchy mutation is introduced in the Hippo algorithm, and the random variable η that obeys the Cauchy distribution is calculated according to the following formula; η=tan[(ξ-0.5)π] Where ξ represents a random number in the interval [0,1]; According to the selection probability, the reverse learning strategy and the Cauchy mutation strategy are used alternately to dynamically adjust the target position; when the random number r>P s Select Cauchy mutation; otherwise use the reverse learning strategy. The calculation formula for the candidate solution generated in the predator avoidance phase is as follows: Where r represents a random number in the interval [0,1], η represents a random variable of Cauchy mutation, and b1 represents an information exchange control parameter; After the Hippo algorithm completes the update of this stage, the candidate solution generated in this stage is compared with the final solution of the defense strategy stage, and the optimal solution of this iteration is determined. The calculation formula is as follows: in, represents the candidate solution generated in the predator avoidance phase, X i is the current candidate solution; The improved Hippo algorithm is applied to parameter inversion, and its inversion objective function is: F(X best )=minF(X i ) In the formula, the lateral displacement value measured at the nth monitoring point is The corresponding model calculated value is H n , w n is the weight of the monitoring point; X best is the optimal solution X generated by all iterations i The minimum value in .

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