A deep foundation pit displacement prediction method combining finite element and data-driven

Abstract

The present invention belongs to the field of intelligent construction and discloses a method for predicting deep foundation pit displacement that combines finite element and data-driven methods. The method includes calculating the theoretical elastic modulus based on the survey report, constructing a sample space using the Latin hypercube sampling method and the orthogonal experimental design method, selecting an appropriate constitutive model, and calculating the corresponding lateral displacement using finite element methods. A global sensitivity analysis based on variance is used to reduce the dimensionality of the dataset to accelerate convergence during subsequent inversion. An ensemble learning method is used to train the SKRR-LSBOOST model to replace the traditional model. An improved Hippo optimization algorithm is combined with the replacement model and applied to parameter inversion. A forward analysis is performed based on the finite element model defined by the inversion parameters to predict the deformation of the deep foundation pit during the next excavation stage. The method of the present invention fully utilizes the advantages of numerical simulation and data-driven methods, reduces computational costs based on geotechnical parameters, achieves higher prediction accuracy, and improves the accuracy of foundation pit deformation prediction.

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 driving. Background Art

[0002] With the continuous advancement of urbanization, foundation pit projects are developing in multiple directions, such as greater depth and larger areas. The influencing factors are complex and changing, and the requirements for related technologies such as monitoring and control are gradually increasing. To ensure the safety and stability of the foundation pit during construction, and to provide an important reference for subsequent construction tasks, the analysis and prediction of lateral displacement within the foundation pit is very important. However, the factors affecting lateral displacement are relatively complex, making multi-parameter inversion difficult to solve. On the other hand, the number of static penetration points on site is also very limited, resulting in insufficient geotechnical parameter acquisition. 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 from 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 computationally expensive and require high precision input parameters, which are difficult to obtain; (3) The data driven nature of machine learning models relies on data quality and lacks a certain degree of physical interpretability. When geotechnical parameters are not yet clear or field conditions deviate from the training data, their effectiveness is 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 response to the above-mentioned 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, and 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 methods includes the following steps:

[0008] S1 Data Preparation: Based on the on-site geotechnical investigation report and the physical information of the soil layer obtained from the field investigation, the parameters were obtained, 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;

[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 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;

[0013] S6 Finite element analysis prediction: The results obtained by multi-parameter inversion in step S5 are 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 void 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 interlayer, 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 of 0.5 times and 2 times the elastic modulus respectively, and the Latin hypercube sampling method and the 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] As an example, 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={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.

[0021] Preferably, in step S3, the specific measurement indicators of the global sensitivity analysis based on variance include: first-order sensitivity index S i and 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. ～i Indicates 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 objects of the AdaBoost integrated optimization algorithm include 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] As a preference, in the integrated optimization algorithm of step S4, the basic model H is selected each time it is updated. 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, 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 ensemble q for:

[0029]

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

[0031] During the ensemble learning process, the updated weight distribution D in the training sample set is 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] Where R 2 The range is [0,1], and 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+1It 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. Its calculation formula is as follows:

[0046]

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

[0048] The position of a female hippopotamus or immature hippopotamus is updated using the following 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; the variables lb and ub represent the lower and upper limits of the decision variable, respectively, and r is a random number ranging 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, h1 consists of random numbers and random vectors, and its calculation formula is as follows:

[0054]

[0055] Here, 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 ranging 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 Phase: The Hippo algorithm remains unchanged in this phase. 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] 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 the better solution is selected through comparison. b1 represents the information exchange control parameter, and its calculation formula is as follows:

[0069]

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

[0071] Cauchy mutation is introduced into the Hippo algorithm, and the random variable obeying the Cauchy distribution is 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 adjust the target position dynamically. 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:

[0075]

[0076] Where r represents a random number in the interval [0,1], η represents a random variable with Cauchy mutation, and b1 represents the information exchange control parameter.

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

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

[0085] (1) A new framework combining finite element analysis with data-driven methods is proposed, which can achieve more accurate predictions while reducing costs, and provides 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 sample weights to form a more suitable alternative model (SKRR-LSBOOST) to replace the machine learning model. This improves the model's ability to capture nonlinear relationships, enhances generalization capabilities, and significantly improves the prediction accuracy of the prediction model, thus overcoming 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 that combines finite element and data-driven methods;

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

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

[0092] To provide a clearer understanding of the objectives, advantages, and features of the present invention, the following detailed description and analysis of the present invention is provided in conjunction with the accompanying drawings and examples. Please note that the specific implementations described herein are intended only to illustrate the present invention and are not intended to limit the present invention. Furthermore, the technical features described in the embodiments of the present invention may be combined with one another as long as they do not conflict with one another.

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

[0094] S1 Data preparation: Parameters are obtained based on the physical information of the soil layer obtained from the on-site geotechnical investigation report and the field survey, 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 (LHS);

[0095] The geotechnical investigation report shall include soil mass, deadweight, layer thickness, porosity and void ratio, permeability, and groundwater level. The soil mass, in descending order of depth, includes: 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 corresponding elastic modulus calculation formula is calculated according to the soil information 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 method (OED) 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 the geotechnical engineering analysis software PLAXIS 3D to perform 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 = {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.

[0104] That is, certain monitoring points are arranged in the supporting piles, and the input elastic modulus E={E1,E2,E3,……,E n}, numerical simulation is performed to obtain the lateral displacement of the foundation pit y={y1,y2,y3,…,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, and representing 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 and total effect index S Ti .

[0107] Perform 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. ～iIndicates 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 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 a cumulative sum exceeding 95% can be used for model training; this method can achieve dimensionality reduction of the 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 dataset used by the S4 ensemble learning optimization algorithm is the synthetic dataset obtained in step S3 after dimensionality reduction based on global sensitivity analysis. The AdaBoost ensemble optimization algorithm targets two separate machine learning algorithms, SKRR and LSBOOST, each with its own advantages, and combines them to form a more suitable surrogate 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, 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 the ensemble learning process, the updated weight distribution D in the training sample set is q+1 for:

[0120]

[0121] 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.

[0122] Finally, different weight coefficients λ q The basic model H q (x) are combined 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] Where R 2 The range is [0,1], and 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 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 based on 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. To represent the potential high-quality optimal solution in the optimization process; the position of the remaining hippopotamus is updated as Compare the current solution with the candidate solutions and take the best solution to proceed to the next stage.

[0134] During the defense strategy phase, the algorithm determines the location of the predator. Calculating the distance between predators and hippo populations According to the distance, the hippo population adopts two different defense strategies, and the position is updated to The candidate solution Compare with the current solution to complete the iterative update.

[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 Compare with the current solution to complete the iterative update.

[0136] The improved Hippo algorithm is characterized by providing corresponding improvement solutions 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 and making it 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: Based on the ergodic and random nature of chaotic mapping, the Hippo population is initialized using the Sin mapping during the initialization phase of the Hippo algorithm. The initial value cannot be set to 0 to avoid generating zeros and fixed points, thereby improving the initial quality of the Hippo population and the efficiency of the algorithm optimization. Specifically, the search space upper and lower bounds up and lp are set. Using chaotic mapping for initialization, a randomly generated vector X0 is generated, with each component of the vector in the interval [0, 1]. N vectors are generated using the 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, which is calculated based on the current number of iterations t and the maximum number of iterations tmax The relationship between the two adaptively adjusts the weighted size, accelerating convergence while improving search accuracy, taking into account the capabilities of global search and local search. The calculation formula is as follows:

[0142]

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

[0144] The position of a female hippopotamus or immature hippopotamus is updated using the following 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; the variables lb and ub represent the lower and upper limits of the decision variable, respectively, and r is a random number ranging 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, h1 consists of random numbers and random vectors, and its calculation formula is as follows:

[0150]

[0151] Here, 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 ranging 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 Phase: The Hippo algorithm remains unchanged in this phase. 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] 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 the better solution is selected through comparison. b1 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 into the Hippo algorithm, and the random variable obeying the Cauchy distribution is 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 adjust the target position dynamically. 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:

[0171]

[0172] Where r represents a random number in the interval [0,1], η represents a random variable with Cauchy mutation, and b1 represents the information exchange control parameter.

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

[0180] Based on R 2 According to the calculation results of SAD, in this embodiment, the IHO-SKRR-LSBOOST framework combining the improved Hippo algorithm (IHO) and the substitution model is superior to the ordinary Hippo algorithm and substitution model combination framework (HO-SKRR-LSBOOST) and other integrated learning model combination frameworks (SSA-SKRR-LSTOOST).

[0181] S6 Finite element analysis prediction: The results obtained by multi-parameter inversion in step S5 are 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 merely 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 scope of protection 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: Based on the on-site geotechnical investigation report and the physical information of the soil layer obtained from the field investigation, the parameters were obtained, 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; 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 replacement model obtained in step S4, the Hippo Algorithm is improved using Sin mapping, reverse learning, and Cauchy mutation and applied to parameter inversion, and the elastic modulus is output through the objective function; in step S5, the basic Hippo optimization algorithm includes population initialization, position update phase, defense strategy phase, and predator avoidance phase, and the specific steps are as follows: 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 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; S5.2 Position update phase: Introduce a dynamic adaptive weighting factor ω to accelerate convergence and improve search accuracy. Its calculation formula is as follows: Among them, t and t max Represent the current number of iterations and the maximum number of iterations respectively; The position of a female hippopotamus or immature hippopotamus is updated using the following 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 bounds of the decision variable, respectively, and r is a random number ranging 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 consists of random numbers and random vectors, and its calculation formula is as follows: Where, 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 ranging 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 Phase: The Hippo algorithm remains unchanged in this phase. 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 Represent the current number of iterations and the maximum number of iterations respectively; A 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 through comparison. b1 represents the information exchange control parameter, and its calculation formula is as follows: Among them, t and t max Represent the current number of iterations and the maximum number of iterations respectively; Cauchy mutation is introduced into the Hippo algorithm, and the random variable η obeying 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 adjust the target position dynamically; when the random number r>P s Select Cauchy mutation; otherwise, use the reverse learning strategy. The candidate solution generated in the predator avoidance phase is calculated as follows: Where r represents a random number in the interval [0,1], η represents a random variable with Cauchy mutation, and b1 represents an information exchange control parameter; After the Hippo algorithm completes the update of this stage, it compares the candidate solution generated in this stage with the final solution of the defense strategy stage, and determines the optimal solution of this iteration. 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 calculation value is H n , w n is the weight of the monitoring point; X best The optimal solution X generated by all iterations i The minimum value in ; S6 Finite element analysis prediction: The results obtained by multi-parameter inversion in step S5 are 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 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, silt-sand interbedded layers, and sand.

3. The method for predicting deep foundation pit displacement by combining finite element and data-driven methods 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 method for predicting deep foundation pit displacement by combining finite element and data-driven methods 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 value and a lower threshold value of 0.5 times and 2 times the elastic modulus respectively, and the Latin hypercube sampling method and the 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 method for predicting deep foundation pit displacement by combining finite element and data-driven methods according to claim 1, characterized in that: The object soil of the Mohr-Coulomb constitutive model constructed 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 deep foundation pit displacement by combining finite element and data-driven methods according to claim 1, characterized in that: In step S3, the specific measurement indicators of the global sensitivity analysis based on variance include: first-order sensitivity index S i and 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. ～i Indicates 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 deep foundation pit displacement by combining finite element and data-driven methods according to claim 1, characterized in that: In step S4, the objects of the AdaBoost integrated optimization algorithm include 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 deep foundation pit displacement by combining finite element and data-driven methods as claimed in claim 7, characterized in that: In the step S4 integrated optimization algorithm, 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, 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 is q+1 for: 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; 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: Where R 2 The range is [0,1], and 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.

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