CN113821863B - Method for predicting vertical ultimate bearing capacity of pile foundation - Google Patents

Abstract

The invention provides a method for predicting the vertical ultimate bearing capacity of a pile foundation, which includes step S1, establishing an initial population; step S2, calculating the fitness value of each individual in the initial population by using the fitness function of the improved radial movement algorithm, The fitness values of the individuals are compared one by one to determine the contemporary optimal position and define it as the initial center position; step S3, adopt the update condition at ±0.5 ( x _{j max} ‑ x _{j min} ) w ^k of the center position of the kth generation Generate a new pre-position point within the range, calculate the fitness value, and update the position information; step S4, determine the global optimal position, and calculate the fitness value of the global optimal position; step S5, calculate the weight of the global optimal position And the threshold is assigned to the BP neural network model, and the BP neural network model is trained and simulated to obtain the optimal prediction value of the vertical ultimate bearing capacity of the pile foundation. The present invention facilitates ensuring that the predicted value is closer to the true value.

Description

A method for predicting the vertical ultimate bearing capacity of pile foundations

technical field

The invention relates to the technical field of pile foundation bearing capacity prediction, in particular to a method for predicting the vertical ultimate bearing capacity of a pile foundation.

Background technique

Pile foundation is a foundation form with high bearing capacity, wide application range and long history. With the continuous development of social economy, pile foundations are widely used in high-rise buildings, ports and bridge projects. In application, the vertical ultimate bearing capacity of pile foundation is an important index to measure the quality of pile foundation. The vertical ultimate bearing capacity of the pile foundation is related to many factors such as the strength of the pile body, the properties of the soil surrounding the pile and the construction technology. There is no theoretical formula and numerical calculation method that can fully consider all factors. Static load test is the most direct and reliable method to measure the bearing capacity of pile foundation. However, due to the long time and high cost, static load tests are generally used in important projects and cannot be widely used. In addition, the load-settlement curve of some pile foundations is slow, and it is difficult to reach the limit state during the static load test, and the ultimate bearing capacity of the pile foundation cannot be measured. However, the test principle of the dynamic test method is inconsistent with the load transfer mechanism of the pile foundation. If the dynamic test method is used to measure the bearing capacity of the pile foundation, certain measurement errors will occur.

Artificial neural network is the earliest method for predicting the bearing capacity of pile foundations based on measured data. BP (BackPropagation) algorithm, also known as error back propagation algorithm, is a supervised learning algorithm in artificial neural network. It has strong nonlinear mapping ability, can approximate any function in theory, and is very flexible, and the parameters can be adjusted according to different situations. However, it is easy to fall into local minima during prediction, and cannot effectively search for multi-peak functions, with slow convergence speed and poor stability of search results.

To sum up, a method for predicting the vertical ultimate bearing capacity of pile foundation is needed to solve the problems that the BP neural network in the prior art is easy to fall into a local minimum value, the convergence speed is slow, and the search results are unstable.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for predicting the vertical ultimate bearing capacity of a pile foundation, and the specific technical scheme is as follows:

A method for predicting the vertical ultimate bearing capacity of a pile foundation, comprising the following steps:

Step S1, using the weights and thresholds of the BP neural network model as the position point information of the improved radial movement algorithm, and establishing an initial population;

In step S2, the fitness function of the improved radial movement algorithm is used to calculate the fitness value of each individual in the initial population, and the contemporary optimal position is determined by comparing the fitness value of the individual one by one, and it is defined as the initial center position; The fitness function is the performance function of the BP neural network model, specifically:

式（1），

Formula 1),

Wherein, N is the number of test samples of the BP neural network model; t _i is the predicted value of the output variable of the ith test sample of the BP neural network model; y _i is the true value of the output variable of the ith test sample of the BP neural network model;

Step S3, using the update condition to generate a new pre-position point within the range of ±0.5 ( x _{j max} - x _{j min} ) w ^k of the center position of the kth generation, and calculate the fitness value, and update the position information; wherein, k refers to The current number of iterations; x _{j min} is the minimum value of the j -th weight or threshold; x _{j max} is the maximum value of the j -th weight or threshold, and w ^k is the inertia weight;

Step S4: Determine the global optimal position from the position information updated in step S3, and calculate the fitness value of the global optimal position; if the number of iterations reaches the upper limit or the fitness value of the global optimal position is less than 0.001, the update ends; otherwise , then repeat steps S3-S4 until the update ends;

Step S5, assign the weight and threshold of the global optimal position to the BP neural network model, train and simulate the BP neural network model to obtain the optimal prediction value of the vertical ultimate bearing capacity of the pile foundation, and the algorithm ends.

Preferably, the step S1 includes the following steps:

Step S1.1, calculate the total number of weights and thresholds of the BP neural network model, which is specifically obtained by the following formula:

nod = w ₁ + w ₂ + w ₃ Equation (2)

w ₁ = n ₁ × n ₂ Equation (3)

w ₂ = n ₂ × n ₃ Equation (4)

w ₃ = n ₂ + n ₃ Equation (5)

Among them, nod is the total number of weights and thresholds; w1 is the number _of weights from the input layer to the hidden layer _; w2 is the number of weights from the hidden layer to the output layer; w3 is the total number _of thresholds ; n ₁ is the number of input layers; n ₂ is the number of hidden layers; n ₃ is the number of output layers;

Step S1.2, determine the value ranges x _{j max} and x _{j min} of the weights and thresholds, where 1 ≤ j ≤ nod ;

Step S1.3, randomly generate nop initial position points within the value range of step S1.2, establish an initial population from the nop initial position points, and the numerical information of the initial position points is obtained by calculating formula (6);

The calculation formula (6) is X _i,j = x _{j min} + rand (0, 1) ( x _{j max} - x _{j min} )

Among them, X _i,j is the j -th weight or threshold of the generated i -th initial position point; rand (0, 1) is a random number between 0 and 1.

Preferably, the step S3 includes the following steps:

Step S3.1, determine the update condition for generating a new pre-position point, specifically,

，

,

，

,

是指第k代新生成的第i个位置点的第j个权值或阈值；Centre _j ^k 是指第k代中心位置的第j个权值或阈值；G是指最大迭代次数；in,

refers to the jth weight or threshold of the i -th position point newly generated in the kth generation; Centre _j ^k refers to the jth weight or threshold of the center position of the kth generation; G refers to the maximum number of iterations;

Step S3.2, using the update condition to generate a new pre-position point Y _i ^k , and calculating the fitness value corresponding to each pre-position point Y _i ^k by calculating the fitness function of formula (1);

Step S3.3, update the position information, specifically, compare the fitness value fitness ( Y _i ^k ) of the k -th generation pre-position point with the fitness value ( X _i ^{k -1} ) of the k -1 generation position point. For comparison, if fitness ( Y _i ^k ) < fitness ( X _i ^{k -1} ), the location point information needs to be updated, let fitness ( X _i ^k ) = fitness ( Y _i ^k ), X _i ^k = Y _i ^k ; otherwise , let fitness ( X _i ^k ) = fitness ( X _i ^{k -1} ), X _i ^k = X _i ^{k -1} ; where X _i ^k is the i -th position point of the k -th generation; X _i ^{k -1} is the ith position k - the i -th position point of the generation; Y _i ^k is the i -th pre-position point generated by the k -th generation.

Preferably, the step S4 includes the following steps:

Step S4.1, determine the contemporary optimal position Rbestx ^k and the global optimal position Gbestx ^k , specifically, take the position point of the minimum value in the fitness ( X _i ^k ) in the updated k -th generation as the contemporary optimal position Rbestx ^k ; when k = 1, the contemporary optimal position Rbestx ¹ is the global optimal position Gbestx ¹ of the first generation;

Step S4.2, when k = 2, update the global optimal position, specifically, compare the fitness value fitness ( Rbestx ^k ) of the contemporary optimal position Rbestx ^k with the fitness value of the global optimal position Gbestx ^{k -1} fitness ( Gbestx ^{k -1} ); if fitness ( Rbestx ^k ) < fitness ( Gbestx ^{k -1} ), you need to update the global optimal position, let fitness ( Gbestx ^k ) = fitness ( Rbestx ^k ), Gbestx ^k = Rbestx ^k ; Otherwise, let fitness ( Gbestx ^k ) = fitness ( Gbestx ^{k -1} ), Gbestx ^k = Gbestx ^{k -1} .

Preferably, in step S3, the center position moves with the movement of the contemporary optimal position Rbestx ^k and the global optimal position Gbestx ^k . Specifically,

Centre ^{k +1} = Centre ^k +0.4( Gbestx ^k - Centre ^k )+0.5( Rbestx ^k - Centre ^k ),

Among them, Centre ^k is the center position of the k -th generation; Centre ^{k +1} is the center position of the k -1th generation.

Apply the technical scheme of the present invention, at least have the following beneficial effects:

，并将由径向移动算法获得的全局最优位置的权值和阈值赋值给BP神经网络模型，对BP神经网络模型进行训练和仿真得到最优的桩基竖向极限承载力预测值，既可以改善BP神经网络模型易陷入局部极小值、收敛速度慢且搜索结果不稳定的缺点，也便于确保预测值更加接近真实值。The present invention uses the BP neural network model in combination with the improved radial movement algorithm. Specifically, the performance function of the BP neural network model is used as the fitness function of the improved radial movement algorithm.

, and assign the weights and thresholds of the global optimal position obtained by the radial movement algorithm to the BP neural network model, and train and simulate the BP neural network model to obtain the optimal prediction value of the vertical ultimate bearing capacity of the pile foundation, which can be either To improve the shortcomings of the BP neural network model, which is easy to fall into local minimum value, slow convergence speed and unstable search results, it is also convenient to ensure that the predicted value is closer to the real value.

In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail below with reference to the drawings.

Description of drawings

The accompanying drawings constituting a part of the present application are used to provide further understanding of the present invention, and the exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the attached image:

1 is a schematic flowchart of a method for predicting the vertical ultimate bearing capacity of a pile foundation in Embodiment 1 of the present invention;

Figure 2 is a comparison chart of the actual value and the predicted value of the test sample.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art fall within the protection scope of the present invention.

Example 1:

Referring to Figure 1, a method for predicting the vertical ultimate bearing capacity of a pile foundation includes the following steps:

Step S1, using the weights and thresholds of the BP neural network model as the position point information of the improved radial movement algorithm, and establishing an initial population;

In step S2, the fitness function of the improved radial movement algorithm is used to calculate the fitness value of each individual in the initial population, and the contemporary optimal position is determined by comparing the fitness value of the individual one by one, and it is defined as the initial center position; The fitness function is the performance function of the BP neural network model, specifically:

式（1），

Formula 1),

Among them, N is the number of test samples of the BP neural network model; t _i is the predicted value of the output variable of the ith test sample of the BP neural network model, specifically, t _i is the individual in the ith test sample of the BP neural network model The weights and thresholds are assigned to the predicted value obtained by the BP neural network model after running; y _i is the true value of the output variable of the ith test sample of the BP neural network model;

Step S3, using the update condition to generate a new pre-position point within the range of ±0.5 ( x _{j max} - x _{j min} ) w ^k of the center position of the kth generation, and calculate the fitness value, and update the position information; wherein, k refers to The current number of iterations; x _{j min} is the minimum value of the j -th weight or threshold; x _{j max} is the maximum value of the j -th weight or threshold, and w ^k is the inertia weight;

Step S4: Determine the global optimal position from the position information updated in step S3, and calculate the fitness value of the global optimal position; if the number of iterations reaches the upper limit or the fitness value of the global optimal position is less than 0.001, the update ends; otherwise , then repeat steps S3-S4 until the update ends;

Step S5, assign the weight and threshold of the global optimal position to the BP neural network model, train and simulate the BP neural network model to obtain the optimal prediction value of the vertical ultimate bearing capacity of the pile foundation, and the algorithm ends.

The step S1 includes the following steps:

Step S1.1, calculate the total number of weights and thresholds of the BP neural network model, which is specifically obtained by the following formula:

nod = w ₁ + w ₂ + w ₃ Equation (2)

w ₁ = n ₁ × n ₂ Equation (3)

w ₂ = n ₂ × n ₃ Equation (4)

w ₃ = n ₂ + n ₃ Equation (5)

Among them, nod is the total number of weights and thresholds; w1 is the number _of weights from the input layer to the hidden layer _; w2 is the number of weights from the hidden layer to the output layer; w3 is the total number _of thresholds ; n ₁ is the number of input layers; n ₂ is the number of hidden layers; n ₃ is the number of output layers;

Step S1.2, determine the value ranges x _{j max} and x _{j min} of the weights and thresholds, where 1 ≤ j ≤ nod ;

Step S1.3, randomly generate nop initial position points within the value range of step S1.2, establish an initial population from the nop initial position points, and the numerical information of the initial position points is obtained by calculating formula (6);

The calculation formula (6) is X _i,j = x _{j min} + rand (0, 1) ( x _{j max} - x _{j min} )

Among them, X _i,j is the j -th weight or threshold of the generated i -th initial position point; rand (0, 1) is a random number between 0 and 1.

The step S3 includes the following steps:

Step S3.1, determine the update condition for generating a new pre-position point, specifically,

，

,

，

,

是指第k代新生成的第i个位置点的第j个权值或阈值；Centre _j ^k 是指第k代中心位置的第j个权值或阈值；w ^k 为惯性权值，随迭代次数递减，用于决定算法的收敛速度；in,

is the j -th weight or threshold of the i -th position point newly generated in the k -th generation; Centre _j ^k refers to the j -th weight or threshold of the center position of the k -th generation; w ^k is the inertia weight, which changes with the iteration The number of times decreases, which is used to determine the convergence speed of the algorithm;

Step S3.2, using the update condition to generate a new pre-position point Y _i ^k , and calculating the fitness value corresponding to each pre-position point Y _i ^k by calculating the fitness function of formula (1);

Step S3.3, update the position information, specifically, compare the fitness value fitness ( Y _i ^k ) of the k -th generation pre-position point with the fitness value ( X _i ^{k -1} ) of the k-1 generation position point. For comparison, if fitness ( Y _i ^k ) < fitness ( X _i ^{k -1} ), the location point information needs to be updated, let fitness ( X _i ^k ) = fitness ( Y _i ^k ), X _i ^k = Y _i ^k ; otherwise , let fitness ( X _i ^k ) = fitness ( X _i ^{k -1} ), X _i ^k = X _i ^{k -1} ; where X _i ^k is the i -th position point of the k -th generation; X _i ^{k -1} is the ith position k - the i -th position point of the generation; Y _i ^k is the i -th pre-position point generated by the k -th generation.

The step S4 includes the following steps:

Step S4.1, determine the contemporary optimal position Rbestx ^k and the global optimal position Gbestx ^k , specifically, take the position point of the minimum value in the fitness ( X _i ^k ) in the updated k -th generation as the contemporary optimal position Rbestx ^k ; when k = 1, the contemporary optimal position Rbestx ¹ is the global optimal position Gbestx ¹ of the first generation;

Step S4.2, when k = 2, update the global optimal position, specifically, compare the fitness value fitness ( Rbestx ^k ) of the contemporary optimal position Rbestx ^k with the fitness value of the global optimal position Gbestx ^{k -1} fitness ( Gbestx ^{k -1} ); if fitness ( Rbestx ^k ) < fitness ( Gbestx ^{k -1} ), you need to update the global optimal position, let fitness ( Gbestx ^k ) = fitness ( Rbestx ^k ), Gbestx ^k = Rbestx ^k ; Otherwise, let fitness ( Gbestx ^k ) = fitness ( Gbestx ^{k -1} ), Gbestx ^k = Gbestx ^{k -1}

In step S3, the center position moves with the movement of the contemporary optimal position Rbestx ^k and the global optimal position Gbestx ^k . Specifically,

Centre ^{k +1} = Centre ^k +0.4( Gbestx ^k - Centre ^k )+0.5( Rbestx ^k - Centre ^k ),

Among them, Centre ^k is the center position of the k -th generation; Centre ^{k +1} is the center position of the k -1th generation.

The parameters adopted by the BP neural network model in the step S5 include prediction accuracy, maximum number of iterations and learning rate, the prediction accuracy is 10 ⁻⁶ , the maximum number of iterations is 1000, and the learning rate is 0.01.

The topology structure of the BP neural network model adopted in Example 1 is 4-10-1, and the optimal value of the number of hidden layer nodes is 10 determined according to the trial algorithm. In Example 1, the parameters nod was 61, nop was 50, and G was 100.

Comparative Example 1:

Only the BP neural network model is used to predict the vertical ultimate bearing capacity of the pile foundation.

Comparative Example 2:

Only the genetic algorithm is used to optimize the BP neural network model to predict the vertical ultimate bearing capacity of the pile foundation.

A total of 32 sets of static load test data were collected for the vertical ultimate bearing capacity of the pile foundation, of which 27 sets of data were used as training sets and 5 sets of data were used as test sets. The static load test data were run 10 times respectively using the prediction methods in Example 1 and Comparative Examples 1-2, and the analysis results are shown in Table 1.

Table 1

grouping Relative error Mean Squared Error (MSE) Comparative Example 1 25.86%-0.42% 0.0049 Comparative Example 2 8.55%~0.48% 0.0036 Example 1 0.01%~2.42% 1.12×10^-7

As can be seen from Table 1, the relative error between the predicted value of the BP neural network model used in Comparative Example 1 and the actual value of the test sample is 25.86%~0.42%, and the MSE is 0.0049, and the prediction result is very unstable. , the relative deviation from the true value. The relative error between the predicted value of the test sample and the actual value of the BP neural network model optimized by the genetic algorithm adopted in Comparative Example 2 is 8.55%~0.48%, and the MSE is 0.0036. The predicted result has good stability and is relatively close to the actual value. . The relative error between the predicted value of the test sample and the actual value obtained by the method for predicting the vertical ultimate bearing capacity of the pile foundation adopted in Example 1 is 0.01%~2.42%, the MSE is 1.12×10 ^-7 , and the maximum relative error is 3%. Below, the predicted result is very close to the true value. It can be seen that the method for predicting the vertical ultimate bearing capacity of the pile foundation adopted in Example 1 has good predictability. At the same time, it can be seen from Figure 2 that the 10-time predicted value of the test sample (that is, the 5 sets of data in the test set) is not much different from the real value, and the results of the 10-time prediction are almost the same. Therefore, the pile foundation used in Example 1 The vertical ultimate bearing capacity prediction method has good stability.

，并将由径向移动算法获得的全局最优位置的权值和阈值赋值给BP神经网络模型，对BP神经网络模型进行训练和仿真得到最优的桩基竖向极限承载力预测值，既可以改善BP神经网络模型易陷入局部极小值、收敛速度慢且搜索结果不稳定的缺点，也便于确保预测值更加接近真实值。In summary, the present invention uses the BP neural network model in combination with the improved radial movement algorithm. Specifically, the performance function of the BP neural network model is used as the fitness function of the improved radial movement algorithm.

, and assign the weights and thresholds of the global optimal position obtained by the radial movement algorithm to the BP neural network model, and train and simulate the BP neural network model to obtain the optimal prediction value of the vertical ultimate bearing capacity of the pile foundation, which can be either To improve the shortcomings of the BP neural network model, which is easy to fall into local minimum value, slow convergence speed and unstable search results, it is also convenient to ensure that the predicted value is closer to the real value.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (3)

1. The method for predicting the vertical ultimate bearing capacity of the pile foundation is characterized by comprising the following steps of:

step S1: acquiring test data of the vertical ultimate bearing capacity of the pile foundation, and dividing a data set into a training set and a test set;

s2, taking the weight and the threshold of the BP neural network model as position point information of a predicted value of the vertical ultimate bearing capacity of the pile foundation in the improved radial movement algorithm, and establishing an initial population;

step S3, calculating the fitness value of each individual in the initial population by adopting a fitness function of an improved radial movement algorithm, determining the optimal position of the predicted value of the vertical ultimate bearing capacity of the current pile foundation by comparing the fitness values of the individuals one by one, and defining the optimal position as the initial central position; the fitness function is a performance function of the BP neural network model, and specifically comprises the following steps:

wherein N is the number of test sets in the BP neural network model data set; t is t_iOutputting a predicted value of a variable for the ith test set in the BP neural network model data set; y is_iOutputting the true value of the variable for the ith test set in the BP neural network model data set;

step S4, adopting the updating condition to be +/-0.5 (x) of the k generation center position_jmax-x_jmin)w^kGenerating a new pre-position point in the range, calculating a fitness value, and updating position information; wherein k refers to the current iteration number; x is the number of_jminIs the minimum value of the jth weight or threshold; x is the number of_jmaxIs the maximum value of the jth weight or threshold, w^kIs the inertia weight;

step S5, determining the global optimal position according to the position information updated in the step S4, and calculating the fitness value of the global optimal position; if the iteration times reach the upper limit or the fitness value of the global optimal position is less than 0.001, ending the updating; otherwise, repeating the steps S4-S5 until the updating is finished;

step S6, assigning the weight and the threshold value of the global optimal position to a BP neural network model, training and simulating the BP neural network model by adopting a training set to obtain an optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, and ending the algorithm;

wherein the step S4 includes the steps of:

step S4.1, determining the update conditions for generating new pre-location points, specifically,

wherein,

is the jth weight or threshold of the ith position point newly generated by the kth generation; centre_j ^kThe weight or threshold of the jth generation center position is referred to as the jth weight or threshold; g refers to the maximum number of iterations;

step S4.2, generating a new preset point Y by adopting the updating condition_i ^kAnd calculating each pre-position point Y by the fitness function of the calculation formula (1)_i ^kA corresponding fitness value;

step S4.3, updating the position information, specifically, updating the fitness value fitness (Y) of the k-th generation pre-position point_i ^k) Fitness value fitness (X) with the k-1 th generation location point_i ^k-1) Making a comparison if fitness (Y)_i ^k)<fitness(X_i ^k-1) Then the location point information needs to be updated, let fitness (X)_i ^k)＝fitness(Y_i ^k)，X_i ^k＝Y_i ^k(ii) a Otherwise, let fitness (X)_i ^k)＝fitness(X_i ^k-1)，X_i ^k＝X_i ^k-1(ii) a Wherein, X_i ^kIs the ith position point of the kth generation; x_i ^k-1Is the ith position point of the k-1 generation; y is_i ^kGenerating an ith pre-position point for the kth generation;

the step S5 includes the steps of:

step S5.1, determining the current generation optimal position Rbestx^kAnd global optimum position Gbest x^kSpecifically, the updated fixness (X) in the k-th generation_i ^k) The position point of the minimum value in (b) is taken as the current generation optimum position Rbestx^k(ii) a When k is 1, the current generation optimum position Rbestx¹Global optimum position Gbestx for first generation¹；

Step S5.2, when k is 2, updating the global optimal position, specifically, comparing Rbestx of the current optimal position^kFitness value of (Rbestx)^k) And global optimum position Gbest x^k-1Fitness value of (Gbestx)^k-1) (ii) a If fitness (Rbestx)^k)<fitness(Gbestx^k-1) Then the global optimum location needs to be updated, let fitness (Gbesx)^k)＝fitness(Rbestx^k)，Gbestx^k＝Rbestx^k(ii) a Otherwise, let fitness (Gbesx)^k)＝fitness(Gbestx^k-1)，Gbestx^k＝Gbestx^k-1。

2. The method for predicting pile foundation vertical ultimate bearing capacity according to claim 1, wherein the step S2 includes the steps of:

s2.1, calculating the total number of the weight values and the threshold values of the BP neural network model, and specifically obtaining the weight values and the total number of the threshold values through the following calculation formula:

nod＝w₁+w₂+w₃formula (2)

w₁＝n₁×n₂Formula (3)

w₂＝n₂×n₃Formula (4)

w₃＝n₂+n₃Formula (5)

Wherein, nod is the total number of the weight and the threshold; w is a₁The number of the weights from the input layer to the hidden layer; w is a₂The number of weights from the hidden layer to the output layer; w is a₃Is the total number of the threshold values; n is₁The number of input layers; n is₂The number of hidden layers; n is₃The number of output layers;

s2.2, determining the value range x of the weight and the threshold value_jmaxAnd x_jminWherein j is more than or equal to 1 and less than or equal to nod;

s2.3, randomly generating nop initial position points in the value range of the step S1.2, establishing an initial population by the nop initial position points, and obtaining the numerical information of the initial position points through a calculation formula (6);

the calculation formula (6) is X_i,j＝x_jmin+rand(0，1)(x_jmax-x_jmin)

Wherein, X_i,jGenerating a jth weight or threshold of the ith initial position point; rand (0, 1) is a random number between 0 and 1.

3. The method for predicting pile foundation vertical ultimate bearing capacity according to claim 2, wherein in step S4, Rbestx with its center position following the current generation optimal position^kAnd global optimum position Gbest x^kThe movement of (a) is moved, in particular,

Centre^k+1＝Centre^k+0.4(Gbestx^k-Centre^k)+0.5(Rbestx^k-Centre^k),

wherein, Centre^kIs the central position of the k generation; centre^k+1Is the central position of the k-1 generation.

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