Soft soil rigidity intelligent prediction method based on machine learning

Abstract

The invention discloses an intelligent soft soil rigidity prediction method based on machine learning, and belongs to the technical field of soft soil rigidity prediction. According to the technical scheme, RVM model parameters are optimized based on ICSSA, and a soft soil rigidity prediction model of ICSSA-RVM is constructed; the method comprises the following steps: initializing a population through Logistic-Tent chaotic mapping so as to enhance the initial diversity of the population; an adaptive weight is introduced to realize the balance of exploratory property and development property in a search process; the position of the sparrow is updated by adopting a mixed method combining Levy flight and a reverse learning strategy, and the capability of getting rid of a local optimal solution of the algorithm is improved. The machine learning-based soft soil rigidity intelligent prediction method has the beneficial effects of improving prediction efficiency and accuracy, enhancing model adaptability and generalization ability, providing a reliable prediction tool, promoting technical innovation, reducing engineering cost and time cost and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of the intersection of civil engineering and artificial intelligence, specifically to the technical field of soft soil stiffness prediction, and in particular to a soft soil stiffness intelligent prediction method based on machine learning. Background Art

[0002] Land reclamation and dockyard projects in soft soil areas have become an important driving force to stimulate economic vitality in coastal areas and open up new paths to prosperity. However, the construction of foundation measures on soft soil faces challenges such as soil settlement and ground instability. Soft soil stiffness (Gs, called Young's modulus) is a key indicator for calculating foundation and pavement settlement. However, soft soil stiffness is affected by many factors, and most of these factors have uncertain characteristics such as randomness and fuzziness. Therefore, the study of soft soil stiffness has always been the focus of attention in the engineering community. For example, PHAM M et al. used different vertical inclusions to study the improvement of soft soil bearing capacity; Wijeyesekera, DC et al. used field emission scanning electron microscopy (FESEM) to study the microstructure of factors affecting soft soil strength and stiffness. However, whether it is a triaxial test in the laboratory, an unconfined compression test, or a cone penetration test, plate load test, and standard penetration test in the field, it is very difficult and time-consuming to measure Gs, especially for large projects that require multiple tests in a short period of time. Therefore, a more reasonable and economical method to obtain Gs is needed.

[0003] In recent years, with the rapid development of computer technology, artificial intelligence algorithms such as support vector machines (SVM), artificial neural networks (ANN), and decision trees (DT) have been proposed, which can improve efficiency and save costs through autonomous learning, and promote technological innovation in civil engineering. For example, Sarat KD et al. used SVM and ANN to predict the maximum dry density and unconfined compressive strength of cement stabilized soil; Mohammadi M et al. verified the feasibility of mixed logistic regression (MLR) and ANN neural network methods in predicting the shear strength parameters of soil; Nawaz MN et al. used gene expression programming (GEP) to predict the liquid limit of soil and achieved good results. Using artificial intelligence algorithms to predict soft soil stiffness has become an inevitable trend. For example, Nawaz et al. proposed three models, namely artificial neural network (ANN), gene expression programming (GEP) and multivariate linear regression (MLR), to predict the stiffness of soft soil. The feasibility of the model was verified by the measured data of samples from different regions, and the prediction results of the ANN model were better than those of GEP and MLR. However, neural networks require a large number of parameters to be set manually, and the learning time is too long, and even the purpose of learning cannot be achieved. Therefore, it is very important to seek a more efficient and reasonable intelligent prediction model for soil stiffness prediction.

[0004] Relevance Vector Machine (RVM) is a machine learning method proposed by Tipping in 2001. It makes up for the defect of SVM that the kernel function selection needs to meet the mercer condition. In addition, RVM has the advantages of simple control parameters and the ability to use fewer related vectors to solve sample fitting problems. It has great advantages in dealing with nonlinear data prediction problems and has been verified in many fields. The kernel function width is a key parameter of the RVM model. In the past, it often required manual attempts to determine it, which was subjective and blind, affecting the accuracy and prediction ability of RVM. The sparrow optimization algorithm has good global optimization ability, convergence speed and stability, and has obvious advantages in solving complex optimization problems. It can achieve good results when combined with other models, but the traditional SSA has poor group diversity and insufficient exploration in the initial search stage. The sparrow optimization algorithm improved by the hybrid strategy overcomes the above shortcomings, optimizes the model kernel function width, seeks the optimal parameters, and improves the prediction efficiency and accuracy of the RVM model. Therefore, combining ICSSA and RVM to predict soft soil stiffness provides a new way to solve the problem of soft soil stiffness. Summary of the invention

[0005] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for intelligent prediction of soft soil stiffness based on machine learning. The method uses soft soil samples from different areas of Islamabad, Pakistan as a data set of the model, and takes water content (w), liquid limit (LL), plastic limit (PL), bulk density (d), sand content (S) and fine content (FC) as model input variables, and Gs as model output variable; based on ICSSA optimization of RVM model parameters, an ICSSA-RVM soft soil stiffness prediction model is constructed. First, the population is initialized by Logistic-Tent chaotic mapping to enhance the initial diversity of the population; at the same time, adaptive weights are introduced to achieve a balance between exploration and development in the search process; in addition, a hybrid method combining Levy flight and reverse learning strategies is used to update the sparrow position, thereby improving the algorithm's ability to escape from the local optimal solution. In order to verify the superiority of the combination of ICSSA optimization algorithm and RVM, the prediction results of RVM, PSO-RVM, SSA-RVM and ICSSA-RVM models were compared under the same conditions; and an in-depth comparative analysis was carried out with the GEP model, MLR model and ANN model (application) in the engineering case to prove the reliability and accuracy of the ICSSA-RVM prediction model.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for intelligent prediction of soft soil stiffness based on machine learning, the steps are as follows:

[0008] S1. Optimize the RVM model parameters based on ICSSA and build the ICSSA-RVM soft soil stiffness prediction model;

[0009] S2, initializing the population through Logistic-Tent chaotic mapping to enhance the initial diversity of the population;

[0010] S3, introduce adaptive weights to achieve a balance between exploration and exploitation in the search process;

[0011] S4. A hybrid method combining Levy flight and reverse learning strategies is used to update the position of sparrows to improve the algorithm's ability to escape from the local optimal solution.

[0012] Furthermore, the RVM model performs the following steps:

[0013] S1.1, Assume that the sample set is {x n , t n |n=1,2,......,N},where x n represents the input sample value, t n Represents the output value; assuming t n Independent distribution with Gaussian white noise ξn , and establish about t n

[0014] t n =y(x n :ω)+ξ n (1)

[0015]

[0016] Where: ω is the weight vector ω=[ω0,ω1……ω n ] T ,ξ n is the additional Gaussian noise, K(x,x n ) is the kernel function;

[0017] S1.2. Assumed parameter ω i The mean is 0 and the variance is α i -1 Gauss conditional probability distribution of:

[0018]

[0019] In the Bayesian framework, by using the conjugate prior of the Gaussian normal distribution, we obtain equations (4) and (5); solving for α and σ 2 The partial derivative of is set to zero, and then solved to obtain equation (6); using equation (6), the hyperparameters α and σ 2 is updated, thus completing the learning process of RVM; in addition, the predicted value t* of a given sample x* can be predicted by formula (7);

[0020]

[0021] P(t|α,σ 2 )=∫p(t|ω,σ 2 )p(ω|α)dω~N(0,C) (5)

[0022]

[0023] Where C = σ 2 I+ΦA -1 Φ T , I is the unit matrix.

[0024] Furthermore, the RVM model parameters are optimized by particle swarm optimization algorithm, and the following steps are performed:

[0025] T1, initialize the position, fitness and speed of the particle swarm;

[0026] T2. Determine the optimal position and fitness of the particle swarm

[0027] T3, when the number of iterations is less than the maximum number of iterations, use formula (8) to update the particle's velocity and position;

[0028]

[0029] Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors, which are often used to adjust the optimal weights, and r1 and r2 are random numbers between [0,1];

[0030] T4. Calculate the fitness of the next generation population;

[0031] T5. Update the optimal position and fitness of the particle swarm.

[0032] Furthermore, the RVM model parameters are optimized by using the sparrow search algorithm, and the following steps are performed:

[0033] U1, initialize the position and fitness of the sparrow population;

[0034] U2, sort the fitness values ​​and determine the first generation of discoverers, followers and scouts;

[0035] U3. When the number of iterations is less than the maximum number of iterations, for each discoverer, i from 1 to DN, a random number R2 is generated and the discoverer position is updated using formula (9):

[0036]

[0037] Where: DN is the number of discoverers, t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1;

[0038] U4. For each follower, i from 1 to FN, update the follower position using formula (10):

[0039]

[0040] Where: FN is the number of followers, X B The finder obtains the optimal position, X w Represents the global worst value; A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food;

[0041] U5. For each detector, i from 1 to VN, update the detector position using formula (11):

[0042]

[0043] Where: VN is the number of detectors, X gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, ε is a constant to avoid the denominator being 0, f i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively;

[0044] U6. Update the optimal fitness and position of the sparrow population.

[0045] Furthermore, in step S2, the population is initialized by the expression equation (12) of the Logistic-Tent mapping:

[0046]

[0047] Among them, r∈(0,4].

[0048] Furthermore, in step S3, an adaptive weight adjustment mechanism is introduced, and the improved finder position update formula is shown in formula (13):

[0049]

[0050] The calculation formula of γ is shown in formula (14):

[0051]

[0052] Among them, t0 is the number of iterations, γ0 is a number, and t is the current iteration number.

[0053] Further, in step S4, the position of the sparrow is adjusted according to the Levy and reverse learning strategies, and the Levy flight and reverse learning are used alternately with a certain probability to update the position;

[0054] The sparrow position updates for the Levy flight strategy and reverse learning strategy are detailed in equations (15) and (16), respectively, while the dynamic selection strategy is given in equation (17):

[0055]

[0056]

[0057] in: r∈(0,1), ub is the upper limit of the particle, and lb is the lower limit of the particle.

[0058] Furthermore, in step S1, the ICSSA-RVM model prediction steps are as follows:

[0059] V1. Divide the collected soil data set into three parts: training set, validation set and test set, and normalize the samples. The processing formula is:

[0060]

[0061] Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, s is the sample standard deviation;

[0062] V2. Initialization, setting the parameters of the ICSSA algorithm; optimizing the kernel function width of the RVM model through the ICSSA algorithm, taking the global optimal solution in the ICSSA algorithm as the kernel function width parameter of the RVM model, and establishing the soil stiffness modulus G that meets the requirements based on this. s Predictive models;

[0063] V3. Substitute the test data and verification data into the body stiffness modulus G s The prediction model is used to compare and analyze the prediction results with the actual values ​​to verify the feasibility of the model.

[0064] Furthermore, the method further includes step V4, using MATLAB software to compile the ICSSA-RVM soil stiffness modulus G according to the above modeling steps. s Predictive models.

[0065] Beneficial effects of the present invention:

[0066] Compared with the prior art, the intelligent prediction method for soft soil stiffness based on machine learning described in the present invention has the following technical characteristics and beneficial effects:

[0067] (1) Significantly improve prediction efficiency and accuracy:

[0068] By combining the improved sparrow optimization algorithm (ICSSA) and the relevance vector machine (RVM), this method can automatically optimize the kernel function width of the RVM model to find the optimal parameters. This optimization process not only reduces manual intervention, but also significantly improves the prediction efficiency and accuracy of the model.

[0069] Under the same sample conditions, the relative error of the prediction results of the ICSSA-RVM model is greatly reduced compared with the RVM, PSO-RVM, SSA-RVM and other models, verifying its excellent performance.

[0070] (2) Enhance the adaptability and generalization ability of the model:

[0071] This method uses Logistic-Tent chaotic mapping to initialize the population, which enhances the initial diversity of the population and helps the model better adapt to different soft soil sample data.

[0072] The adaptive weight adjustment mechanism and the hybrid update mechanism combined with the Levy flight reverse learning strategy enable the model to better balance exploration and development during the search process and improve the generalization ability of the model.

[0073] (3) Provide reliable soft soil stiffness prediction tools:

[0074] Compared with the GEP model, MLR model and ANN model in actual engineering cases, the ICSSA-RVM model showed the best performance in the prediction result indicators on both the validation set and the test set, providing a new and powerful analysis tool for the prediction of soft soil stiffness.

[0075] (4) Promoting technological innovation in the field of civil engineering:

[0076] This method applies artificial intelligence algorithms to the prediction of soft soil stiffness, promoting technological innovation in the field of civil engineering. It improves the efficiency and safety of infrastructure construction in soft soil areas through automation and intelligence.

[0077] (5) Reduce engineering costs and time costs:

[0078] Compared with traditional laboratory testing methods, this method can predict soft soil stiffness more quickly and accurately, thereby reducing engineering costs and time costs.

[0079] In large-scale projects, especially when multiple tests need to be carried out in a short period of time, this prediction method has significant economic and social benefits.

[0080] In summary, the intelligent prediction method of soft soil stiffness based on machine learning in the present invention shows significant beneficial effects in improving prediction efficiency and accuracy, enhancing model adaptability and generalization ability, providing reliable prediction tools, promoting technological innovation, and reducing engineering costs and time costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0082] Figure 1 Schematic diagram of the RVM algorithm of the present invention;

[0083] Figure 2 Schematic diagram of the sparrow algorithm of the present invention;

[0084] Figure 3 ICSSA algorithm flow chart of the present invention;

[0085] Figure 4 It is a statistical characteristic diagram of the data set of the present invention;

[0086] Figure 5 It is the Pearson correlation coefficient matrix diagram of the data set of the present invention;

[0087] Figure 6 ICSSA-RVM flow chart of the present invention;

[0088] Figure 7 Optimization curve diagram for validation set and test set of each model (a) validation set (b) test set;

[0089] Figure 8 Fitting curves for validation and test sets of each model;

[0090] Fig. 9 The scatter plots are the distribution characteristics of the relative errors of the test set and validation set of the three models;

[0091] Fig.10 Radar distribution diagram of evaluation indicators of each model: (a) R 2 ; (b) RMSE; (c) MAE;

[0092] Fig.11 This is a sensitive factor analysis chart. DETAILED DESCRIPTION

[0093] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Figure 1-11 The intelligent prediction method of soft soil stiffness based on machine learning is further explained.

[0094] Example 1

[0095] This embodiment provides an introduction to the RVM principle and optimization algorithm.

[0096] 1.1 RVM Principle

[0097] RVM is based on the Bayesian principle and is applied to regression problems. After data training, a sparse model is obtained, and the relevant vectors and weights are obtained by maximizing the marginal likelihood. Assume that the sample set is {x n , t n |n=1,2,......,N},where x n represents the input sample value, t n represents the output value. Assume that t n Independent distribution with Gaussian white noise ξ n , and establish about t n

[0098] t n =y(x n :ω)+ξ n (1)

[0099]

[0100] Where: ω is the weight vector ω=[ω0,ω1……ω n ] T ,ξ n is the additional Gaussian noise, K(x,x n ) is the kernel function.

[0101] Assuming the parameter ω i The mean is 0 and the variance is α i -1 Gauss conditional probability distribution of:

[0102]

[0103] In the Bayesian framework, by using the conjugate prior of the Gaussian normal distribution, we can derive equations (4) and (5). Solving for α and σ 2 The partial derivative of , set its value to zero, and then solve it to get equation (6). Using equation (6), the hyperparameters α and σ 2 is updated, thus completing the learning process of RVM. In addition, the predicted value t* of a given sample x* can be predicted by formula (7).

[0104]

[0105] P(t|α,σ 2 )=∫p(t|ω,σ 2 )p(ω|α)dω~N(0,C)(5)

[0106]

[0107] Where C = σ 2 I+ΦA -1 ΦT , I is the unit matrix,

[0108] The principle of RVM is as follows Figure 1 As shown, it includes input layer, hidden layer, non-zero weights and output layer.

[0109] 1.2. Introduction to optimization algorithms

[0110] 1.2.1 Particle Swarm Optimization Algorithm

[0111] Particle Swarm Optimization (PSO) is an evolutionary computing technology based on swarm intelligence. This method randomly initializes a group of particles in the feasible solution range. Each particle will become an optimal solution to the problem to be solved. The initial position and initial velocity of the group of random particles are iteratively calculated to finally find the optimal solution. PSO is widely used in pattern recognition and parameter optimization due to its advantages such as few parameters, intelligent optimization, and fast convergence.

[0112] The basic principle of PSO is to search for the best result based on the competition and cooperation between particle groups. The particle group is continuously updated during the flight through formula (8):

[0113]

[0114] Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors, which are often used to adjust the optimal weights, r1 and r2 are random numbers between [0,1]. The code running steps are shown in Table 1.

[0115] Table 1 Pseudo code of particle swarm algorithm

[0116]

[0117] 1.2.2 Sparrow Search Algorithm

[0118] 1.2.2.1 Basic Mahjong Search Algorithm

[0119] Sparrow Search Algorithm (SSA) is a new type of intelligent optimization algorithm that emerged in 2020. The algorithm does not require gradient information and has the advantages of easy implementation, high optimization efficiency and fast search speed. It is widely used to solve complex optimization problems with excellent global search capabilities and fast convergence characteristics. In the algorithm, the sparrow population is divided into discoverers, followers and scouts according to a certain proportional coefficient.

[0120] The discoverer is mainly responsible for finding food for the sparrow population and providing the participants with the optimal search direction. During the search process, food with good fitness will be more popular. The discoverer's position update formula is as follows:

[0121]

[0122] Where: t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1.

[0123] In order to obtain high-quality food, the follower closely follows the finder, searches for food after the finder, and searches around the finder's location. The position update formula of the participant is as follows:

[0124]

[0125] Where: X B The finder obtains the optimal position, X w Represents the global worst value. A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food.

[0126] Sparrows have excellent ability to avoid predators. During the foraging process, they will select some members as scouts to avoid being detected by predators. The scout position update formula is as follows:

[0127]

[0128] Where: X gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, and ε is a constant to avoid the denominator being 0. i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively. The code running steps are shown in Table 1; the algorithm principle is shown in Figure 2 shown.

[0129] Table 2 Pseudocode of sparrow optimization algorithm

[0130]

[0131] 1.2.2.2 Improved sparrow search algorithm

[0132] As an emerging swarm intelligence optimization technology, the sparrow search algorithm (SSA) has attracted attention for its excellent global search capability, less parameter adjustment requirements and simple algorithm structure, and has been applied in many fields. However, the existing sparrow search algorithm still has some shortcomings, including poor population diversity and insufficient exploration in the initial search stage, which may lead to a decrease in the accuracy of the algorithm in later iterations and increase the risk of falling into a local optimal solution. In view of the above shortcomings, this paper makes the following improvements to SSA.

[0133] Chaotic mapping has been applied by many scholars to improve the performance of swarm intelligence algorithms due to its ergodic and random characteristics, especially to enhance the ergodicity of individuals in the algorithm. Logistic and tent are classic mappings of chaotic systems. Compared with the individual Logistic mapping and Tent mapping, the Logistic-Tent mapping that combines the characteristics of both shows superior ergodic properties and uniformity of distribution. Therefore, the Logistic-Tent mapping is introduced to initialize the population, enhance the initial diversity of the population, and improve the overall optimization performance of the algorithm. The expression equation of the Logistic-Tent mapping (12) is:

[0134]

[0135] Among them, r∈(0,4].

[0136] In order to achieve extensive global search and quickly approach the global optimal solution in the initial iteration, the discoverer should perform large-scale exploration actions, which requires a larger inertia weight to expand its search range. As the iteration enters the later stage, reducing the inertia weight helps to enhance the discoverer's search ability in the local area, which can not only improve the convergence rate of the algorithm, but also reduce the possibility of falling into the local optimum. Based on this, this paper improves the update formula (9) of the discoverer position and introduces an adaptive weight adjustment mechanism. The improved producer position update formula is shown in formula (13)

[0137]

[0138] The calculation formula of γ is shown in formula (14):

[0139]

[0140] Among them, t0 is the number of iterations, γ0 is a number, and t is the current iteration number.

[0141] In order to enhance the search performance of SSA, this paper introduces a dynamic selection mechanism, which adjusts the position of sparrows according to Levy and reverse learning strategies, and updates the position by alternating Levy flight and reverse learning with a certain probability. When implementing the Levy flight strategy, the search range is broadened by adjusting the step factor, and the algorithm is helped to get rid of the limitation of local optimality. At the same time, the reverse learning strategy aims to enrich the diversity of the population by introducing reverse solutions, thereby improving the global search and optimization capabilities of the algorithm. The ICSSA algorithm process is as follows Figure 3 shown.

[0142] The sparrow position updates for the Levy flight strategy and reverse learning strategy are detailed in equations (15) and (16), respectively, while the dynamic selection strategy is given in equation (17).

[0143]

[0144] in: r∈(0,1), ub is the upper limit of the particle, and lb is the lower limit of the particle.

[0145] Example 2

[0146] This embodiment provides specific implementation methods such as constructing data sources, correlation coefficients, and model establishment.

[0147] 2.1 Data Source

[0148] The soil samples are 199 undisturbed soil samples and 20 additional samples for testing collected by Nawaz et al. in several soil survey projects in different areas of Islamabad, Pakistan, for a total of 219 samples. In order to facilitate comparative analysis with the model, this paper uses the same parameters as the model in Nawaz et al., that is, the input parameters are sand content (S), fine particle content (FC), liquid limit (LL), plastic limit (PL), water content (w) and density (d), and the output parameter is Gs. 139 sample data of the 199 soil samples are used as training sets, the remaining 60 sample data are used as validation sets, and the additional 20 samples are used as test sets. Table 3, Figure 4 A basic description of the intrinsic characteristics of soft soils in the datasets is given respectively.

[0149] Table 3 Statistical characteristics of the dataset

[0150]

[0151]

[0152] from Figure 4The box plot shows that the data of sand content (S) 25% to 75% are mainly concentrated in 5.85% to 16.30%, the data of fine particle content (FC) 25% to 75% are mainly concentrated in 80.40% to 93.70%, the data of liquid limit (LL) 25% to 75% are mainly concentrated in 24.63% to 30.00%, the data of plastic limit (PL) 25% to 75% are mainly concentrated in 16.65% to 20.00%, the data of water content (w) 25% to 75% are mainly concentrated in 14.43% to 19.86% and the data of density (d) 25% to 75% are mainly concentrated in 1.78 to 2.02 g / cm 3 The output parameter is Gs, 25% to 75% of the data is mainly concentrated in 62.75 to 83.72 kg / cm 2 .

[0153] 2.2 Correlation coefficient

[0154] The Pearson correlation coefficient is a symbol of the degree of linear correlation between elements. It ranges from -1 to +1. The closer the absolute value is to 1, the higher the correlation. The mathematical formula for the Pearson correlation coefficient is as follows:

[0155]

[0156] Where: X and Y are two variables, cov(X,Y) is the covariance of X and Y; and are the standard deviations of X and Y respectively.

[0157] Figure 5 The correlation between Gs and various factors is shown, where orange represents negative correlation, blue represents positive correlation, and the larger the circle area, the stronger the correlation. Figure 5 It can be seen that Gs has a certain positive correlation with S and LL, and a certain negative correlation with FC, PL, w, and d. Some scholars have also made similar findings on soft soil. Therefore, the data set in this paper is representative and has research value.

[0158] 2.3 Model establishment

[0159] In this paper, ICSSA is used to optimize the kernel width parameters of the RVM model, and the optimal parameter value is obtained adaptively. The optimized RVM is used to establish the relationship between the six influencing factors of sand content (S), fine particle content (FC), liquid limit (LL), plastic limit (PL), water content (w) and density (d) and the soil stiffness modulus G. s The nonlinear mapping relationship of soil stiffness modulus G is established s Prediction model. The prediction steps of the ICSSA-RVM model are as follows:

[0160] Step 1: Divide the collected soil data set into three parts: training set, validation set and test set to prevent the dimensional differences of influencing factors from affecting the results. Normalize the samples. The processing formula is:

[0161]

[0162] Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, and s is the sample standard deviation.

[0163] Step 2: Initialization, setting the parameters of the ICSSA algorithm. The kernel function width of the RVM model is optimized through the ICSSA algorithm, and the global optimal solution in the ICSSA algorithm is used as the kernel function width parameter of the RVM model. Based on this, the soil stiffness modulus G that meets the requirements is established. s Predictive models.

[0164] Step 3: Substitute the test data and verification data into the body stiffness modulus G s Prediction model, compare and analyze the prediction results with the actual values ​​to verify the feasibility of the model.

[0165] With the help of MATLAB software, according to the above modeling steps, the ICSSA-RVM soil stiffness modulus G is compiled s Prediction model.ICSSA-RVM model process is as follows Figure 6 as shown.

[0166] Example 3

[0167] This embodiment provides specific instructions for optimizing RVM model comparison, model accuracy evaluation, and analysis of the impact of various factors on prediction results.

[0168] 3.1. Comparison of optimized RVM models

[0169] This paper constructs the currently popular PSO algorithm and the traditional SSA algorithm to optimize the RVM model and verify the superiority of the ICSSA-RVM model. The parameters of the PSO, SSA and ICSSA models are shown in Table 4. The optimization curves of the PSO-RVM, SSA-RVM and ICSSA-RVM models are shown in Figure 7 As shown, the fitting curves of RVM, PSO-RVM, SSA-RVM and ICSSA-RVM models are shown in Figure 8 shown.

[0170] Table 4 Optimization model parameter values

[0171]

[0172] Figure 7 It can be seen that the optimization effect of the SSA algorithm is better than that of the PSO algorithm, whether it is the validation set or the test set. Therefore, the SSA algorithm has better optimization ability than the PSO algorithm. Figure 7 In (a), the SSA algorithm fell into a local minimum value after 10 to 20 cycles and did not jump out of the minimum value. The ICSSA algorithm fell into a local minimum value after 10 to 60 cycles, but jumped out of the local minimum value after 60 to 70 cycles. Figure 7 There is a similar phenomenon in (b), which shows that the ICSSA algorithm has a higher ability to escape from local extreme values ​​than the SSA algorithm, so the ICSSA algorithm has stronger optimization ability. Figure 8 It shows how well the predicted values ​​fit the actual values.

[0173] Fig. 9 The scatter plot intuitively shows the distribution characteristics of the relative errors of the test and validation sets of the three models. It can be seen from the figure that 93% of the relative error data of the RVM model validation set are distributed in the range of 39.00% to 45.00%; 91% of the relative errors of the PSO-RVM model validation set are in the range of 0.00% to 4.00%, but the maximum relative error exceeds 22.00%; 90% of the relative errors of the SSA-RVM and ICSSA-RVM model validation sets are in the range of 0.00% to 3.00%. The maximum relative error does not exceed 20.00%. The relative errors of the test sets of the RVM, PSO-RVM, SSA-RVM, and ICSSA-RVM models are mainly concentrated between 0.00% and 6.00%.

[0174] Fig. 9 The relative error distribution diagrams of each model can be seen from Appendix 1 and 2: the average relative errors of the validation set and test set of the RVM model are 42.28% and 4.784% respectively; the average relative errors of the validation set and test set of the PSO-RVM model are 1.33% and 2.125% respectively; the average relative errors of the validation set and test set of the SSA-RVM model are 1.22% and 2.051% respectively, and the average errors of the validation set and test set of the ICSSA-RVM model are 1.20% and 2.048% respectively. The ICSSA-RVM model is compared with the relative errors of the validation set and test set of RVM, PSO-RVM, and SSA-SSA-RVM respectively: the relative error of the validation set is reduced by 97.16%, 9.77%, and 1.64%; the relative error of the test set is reduced by 57.19%, 3.62%, and 0.15%. Therefore, the ICSSA-RVM model is significantly better than the SSA-RVM, PSO-RVM model and RVM model in terms of accuracy.

[0175] 3.2. Model Accuracy Evaluation

[0176] In order to better highlight the efficiency of ICSS-RVM in solving the practical problem of predicting soft soil stiffness, the RMSE, MAE and R of the GEP model, MLR model and ANN model are compared with the engineering example. 2 Conduct comparative analysis.

[0177] As MAE and RMSE are closer to 0, R 2 The closer it is to 1, the better the prediction effect.

[0178]

[0179] Where y 0，i represents the actual value of the i-th sample, y i represents the predicted value of the i-th sample. n represents the total number of samples. represents the average value of the sample actual value, Represents the mean of the sample prediction values.

[0180] Table 5 Evaluation indicators of each model

[0181]

[0182] Depend on Fig.10 As shown in Table 5, the ICSSA-RVM model is compared with the GEP, MLR and ANN models in terms of evaluation indicators: R 2 The R of the test set was improved by 5.32%, 37.5% and 1.01%, the RMSE was reduced by 61.82%, 83.36% and 13.12%, and the MAE was reduced by 80.50%, 88.09% and 48.52%. 2 The performance of the ICSSA-RVM model was improved by 7.95%, 33.80% and 5.55%, the RMSE was reduced by 8.29%, 38.39% and 4.78%, and the MAE was reduced by 20.98%, 37.64% and 6.28%. The ICSSA-RVM model was the best among the four models in terms of both the evaluation indicators of the test set and the evaluation indicators of the validation set.

[0183] In summary, in the prediction of soft soil stiffness, the ICSSA-RVM model has the best results compared with the GEP model, MLR model, and ANN model: 2 The R 2 The accuracy was improved by 5.55%, the RMSE was reduced by 4.78%, and the MAE was reduced by 6.28%. Therefore, the ICSSA-RVM soft soil stiffness modulus prediction model proposed in this paper is superior to the GEP model, MLR model, and ANN model in terms of overall prediction accuracy, and the sample prediction value is more stable, so it is more credible.

[0184] 3.3 Analysis of the impact of various factors on prediction results

[0185] Sand content (S), fine particle content (FC), liquid limit (LL), plastic limit (PL), water content (w) and density (d) have different effects on soft soil stiffness (Gs). To explore the sensitivity of the six influencing factors, the R 2 , RMSE and MAE, the influence of the influencing factors is evaluated. The formula is as follows:

[0186]

[0187] In the formula, R 2 , RMSE and MAE represent the three indicators of the initial model test set, respectively. j corresponds to the six factors (S, FC, LL, PL, w, d) that are not considered in turn by the new model. RMSE j and MAE j is an index without this factor, R 1j , R 2j , R 3j R 2 , the ratio of RMSE and MAE, R 1j The smaller the ratio, the 2j , R 3j The larger the ratio, the greater the impact.

[0188] Fig.11 Table 6 shows the prediction index of the model without this factor in the test set and the three indicators and the comparison results. 1j , R 2j , R 3j The values ​​of are not equal to 1, indicating that each factor has different degrees of influence on the prediction results of soft soil stiffness. 1j Although the value is greater than 1, its R 2j The ratio of R3j is greater than 1, indicating that although the correlation between the predicted value and the actual value of the model without d is better than that of the initial model, its accuracy is not as accurate as that of the initial model, and the R 1j The values ​​are all smaller than 1, R 2j , R 3jThe values ​​are all greater than 1, which indicates that the 6-factor model is superior to the 5-factor model and more credible. The ranking of sensitive factors further compares the influence of each factor, and the water content ranks first. This is because in soil mechanics, the presence of water increases the porosity of the soil, thereby reducing the contact and friction between soil particles, and reducing the shear strength and bearing capacity of the soil. At the same time, as the pore water pressure increases, the effective stress decreases, resulting in greater deformation of the soil when subjected to the same load. In addition, high water content may also increase the compressibility and permeability of the soil, slow down the consolidation process, and further affect the stiffness and stability of the soil.

[0189] Table 6 Sensitivity analysis of the test set

[0190]

[0191] 1. This paper uses Logistic-Tent chaotic mapping to initialize the population, adaptively adjusts the weights to balance exploration and development, combines the Levy flight reverse learning strategy and hybrid update mechanism, improves the traditional sparrow algorithm, optimizes the width of the RVM model kernel function, seeks the optimal parameters, improves the prediction efficiency and accuracy of the RVM model, and constructs the ICSSA-RVM soft soil stiffness prediction model.

[0192] 2. Under the same sample conditions, the prediction results of the ICSSA-RVM model were compared with those of the RVM, PSO-RVM, and SSA-RVM models. The relative error of the ICSSA-RVM model validation set was reduced by 97.16%, 9.77%, and 1.64%, respectively; the relative error of the test set was reduced by 57.19%, 3.62%, and 0.15%.

[0193] This verifies the excellent performance of the combination of the ICSSA optimization algorithm and the RVM model.

[0194] 3. Compared with the best model among the GEP model, MLR model and ANN model in actual engineering cases, the R of the ICSSA-RVM validation set is 2 The R 2 The accuracy was improved by 5.55%, the RMSE was reduced by 4.78%, and the MAE was reduced by 6.28%. Whether in the prediction result indicators of the validation set or the test set, the indicators of the ICSSA-RVM model are the best, which highlights the high efficiency of ICSS-RVM in solving the complex problem of predicting soft soil stiffness, and provides a new and powerful analysis tool for related fields, which has important theoretical significance and application value.

[0195] The entire sample set of this study is from Islamabad, Pakistan, which has certain regional limitations. In future research work, it is planned to collect soft soil samples outside Islamabad to fully evaluate the promotion potential of the ICSSA-RVM model. In addition, similar models can be developed for other types of special soils (such as loess).

[0196] The stiffness modulus (Gs) of soft soil is a key indicator for calculating the settlement of foundation and pavement, while traditional measurement methods often consume a lot of manpower and time. Based on soil samples from different areas of Islamabad, Pakistan, this paper establishes a soft soil stiffness prediction model based on the hybrid strategy improved chaos sparrow search algorithm (ICSSA) optimized relevance vector machine (RVM), and realizes the rapid prediction of the stiffness modulus of soft soil. In the model, ICSSA can enrich the diversity of the population and enhance the global search and optimization capabilities of the algorithm. RVM has great advantages in dealing with nonlinear data prediction problems. The combination of the two improves the prediction efficiency and accuracy of the RVM model. By comparing the prediction results of RVM, PSO-RVM (Particle Swarm Optimization-RVM), and SSA-RVM (sparrow search algorithm-RVM), it is found that the relative error of the ICSSA-RVM model validation set is reduced by 97.16%, 9.77%, and 1.64%, respectively. In order to further verify the applicability and reliability of the ICSSA-RVM model, we conducted a comparative analysis of the application with the gene expression programming (GEP) model, the multivariate linear regression (MLR) model and the artificial neural network (ANN) model under the same conditions in actual engineering cases. The results show that in practical applications, the ICSSA-RVM model has the best prediction results compared with the ANN, GEP and MLR models: the ICSSA-RVM model has a better prediction accuracy than the ANN, GEP and MLR models. 2 The ICSSA-RVM model can provide a more reliable guarantee for the quality and safety of soft soil engineering and help improve the accuracy and efficiency of engineering design and construction.

[0197] Appendix 1 Prediction results of the validation set

[0198]

[0199]

[0200] Appendix 2 Prediction results of the test set

[0201]

[0202] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for intelligent prediction of soft soil stiffness based on machine learning, characterized in that: Here are the steps: S1. Optimize the RVM model parameters based on ICSSA and build the ICSSA-RVM soft soil stiffness prediction model; S2, initializing the population through Logistic-Tent chaotic mapping to enhance the initial diversity of the population; S3, introduce adaptive weights to achieve a balance between exploration and exploitation in the search process; S4. A hybrid method combining Levy flight and reverse learning strategies is used to update the position of sparrows to improve the algorithm's ability to escape from the local optimal solution.

2. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: The RVM model performs the following steps: S1.1, Assume that the sample set is {x n , t n |n=1,2,......,N},where x n represents the input sample value, t n Represents the output value; assuming t n Independent distribution with Gaussian white noise ξ n , and establish about t n t n =y(x n :ω)+ξ n (1) Where: ω is the weight vector ω=[ω0,ω1……ω n ] T ,ξ n is the additional Gaussian noise, K(x,x n ) is the kernel function; S1.2, assuming parameter ω i The mean is 0 and the variance is α i -1 Gauss conditional probability distribution of: In the Bayesian framework, by using the conjugate prior of the Gaussian normal distribution, we obtain equations (4) and (5); solving for α and σ 2 The partial derivative of is set to zero, and then solved to obtain equation (6); using equation (6), the hyperparameters α and σ 2 Get updated, thus completing the RVM learning process; In addition, the predicted value t* of a given sample x* can be predicted by formula (7); P(t|α,σ 2 )=∫p(t|ω,σ 2 )p(ω|α)dω~N(0,C) (5) Where C = σ 2 I+ΦA -1 Φ T , I is the unit matrix.

3. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: The RVM model parameters are optimized by particle swarm optimization algorithm, and the following steps are performed: T1, initialize the position, fitness and speed of the particle swarm; T2. Determine the optimal position and fitness of the particle swarm T3, when the number of iterations is less than the maximum number of iterations, use formula (8) to update the particle's velocity and position; Among them, w is a non-negative inertia factor used for algorithm convergence, c1 and c2 are learning factors, which are often used to adjust the optimal weights, and r1 and r2 are random numbers between [0,1]; T4. Calculate the fitness of the next generation population; T5. Update the optimal position and fitness of the particle swarm.

4. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: The RVM model parameters are optimized by using the sparrow search algorithm. The following steps are performed: U1, initialize the position and fitness of the sparrow population; U2, sort the fitness values ​​and determine the first generation of discoverers, followers and scouts; U3. When the number of iterations is less than the maximum number of iterations, for each discoverer, i from 1 to DN, a random number R2 is generated and the discoverer position is updated using formula (9): Where: DN is the number of discoverers, t is the current iteration number, T max is the maximum number of iterations, α is a random number and α∈(0,1], R2∈[0,1] and ST∈[0.5,1] are the warning and safety values ​​respectively, Q is a normally distributed random number, and L is a 1×d matrix whose elements are all 1; U4. For each follower, i from 1 to FN, update the follower position using formula (10): Where: FN is the number of followers, X B The finder obtains the optimal position, X w Represents the global worst value; A is a one-dimensional vector of length d, A + =A T (AA T ) -1 ,When i>N / 2, it means that the sparrows with low fitness are very hungry and need to fly to other places to find food; U5. For each detector, i from 1 to VN, update the detector position using formula (11): Where: VN is the number of detectors, X gB is the current global optimal value, β is the step size control parameter that obeys the (0,1) normal distribution, K∈[-1,1] is a random number, ε is a constant to avoid the denominator being 0, f i is the fitness value of the sparrow individual, f g and f w are the current global optimal and worst fitness values ​​respectively; U6. Update the optimal fitness and position of the sparrow population.

5. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: In step S2, the population is initialized by the expression equation (12) of the Logistic-Tent mapping: Among them, r∈(0,4].

6. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: In step S3, an adaptive weight adjustment mechanism is introduced, and the improved finder position update formula is shown in formula (13): The calculation formula of γ is shown in formula (14): Among them, t0 is the number of iterations, γ0 is a number, and t is the current iteration number.

7. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: In step S4, the position of the sparrow is adjusted according to the Levy and reverse learning strategies, and the Levy flight and reverse learning are used alternately with a certain probability to update the position; The sparrow position updates for the Levy flight strategy and reverse learning strategy are detailed in equations (15) and (16), respectively, while the dynamic selection strategy is given in equation (17): in: ub is the upper limit of the particle size, and lb is the lower limit of the particle size.

8. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 1, characterized in that: In step S1, the ICSSA-RVM model prediction steps are as follows: V1. Divide the collected soil data set into three parts: training set, validation set and test set, and normalize the samples. The processing formula is: Where: x i is the i-th influencing factor among the influencing factors, is the sample data mean, s is the sample standard deviation; V2. Initialization, setting the parameters of the ICSSA algorithm; optimizing the kernel function width of the RVM model through the ICSSA algorithm, taking the global optimal solution in the ICSSA algorithm as the kernel function width parameter of the RVM model, and establishing the soil stiffness modulus G that meets the requirements based on this. s Predictive models; V3. Substitute the test data and verification data into the body stiffness modulus G s The prediction model is used to compare and analyze the prediction results with the actual values ​​to verify the feasibility of the model.

9. The method for intelligent prediction of soft soil stiffness based on machine learning according to claim 8, characterized in that: The step V4 is to use MATLAB software to compile the ICSSA-RVM soil stiffness modulus G according to the above modeling steps. s Predictive models.

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