CN113821863A - Method for predicting vertical ultimate bearing capacity of pile foundation - Google Patents
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Abstract
The invention provides a method for predicting the vertical ultimate bearing capacity of a pile foundation, which comprises the following steps of S1, establishing an initial population; step S2, calculating the fitness value of each individual in the initial population by adopting the fitness function of the improved radial movement algorithm, determining the current optimal position by comparing the fitness values of the individuals one by one, and defining the current optimal position as the initial central position; step S3, adopting the update condition at the firstk. + -. 0.5 of the center position (x jmax‑x jmin）w k Generating a new pre-position point in the range, calculating a fitness value, and updating position information; step S4, determining a global optimal position, and calculating a fitness value of the global optimal position; step by stepAnd S5, assigning the weight and the threshold value of the global optimal position to the BP neural network model, and training and simulating the BP neural network model to obtain the optimal predicted value of the vertical ultimate bearing capacity of the pile foundation. The invention is convenient for ensuring that the predicted value is closer to the true value.
Description
Technical Field
The invention relates to the technical field of pile foundation bearing capacity prediction, in particular to a method for predicting vertical ultimate bearing capacity of a pile foundation.
Background
The pile foundation is a foundation form with high bearing capacity, wide application range and long history. With the continuous development of social economy, the pile foundation is widely applied to high-rise buildings, ports and bridge engineering. When the method is applied, the vertical ultimate bearing capacity of the pile foundation is an important index for measuring the quality of the pile foundation. The vertical ultimate bearing capacity of the pile foundation is related to various factors such as the strength of a pile body, the property of soil around the pile, the construction process and the like, and a theoretical formula and a numerical calculation method which can comprehensively consider all the factors are not available. The static load test is the most direct and reliable method for measuring the bearing capacity of the pile foundation. However, because of the long time and high cost, the static test is generally used in important engineering and cannot be generally used. In addition, the load-settlement curve of some pile foundations is slow, and the limit state is difficult to reach during static load test, so that the limit bearing capacity of the pile foundations cannot be measured. And the dynamic measurement method testing principle is inconsistent with the load transmission mechanism of the pile foundation, and if the dynamic measurement method is adopted to measure the bearing capacity of the pile foundation, a certain measurement error can be generated.
The artificial neural network is the earliest method for predicting the bearing capacity of the pile foundation based on measured data. The bp (back propagation) algorithm is also called an error back propagation algorithm, and is a supervised learning algorithm in an artificial neural network. The method has strong nonlinear mapping capability, can approach any function theoretically, has strong flexibility, and can adjust parameters according to different conditions. However, the method is easy to fall into a local minimum value during prediction, cannot effectively search for the multi-peak function, and is low in convergence speed and poor in search result stability.
In summary, a method for predicting the vertical ultimate bearing capacity of the 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 rate is low, and the search result is unstable.
Disclosure of Invention
The invention aims to provide a method for predicting the vertical ultimate bearing capacity of a pile foundation, which has the following specific technical scheme:
a method for predicting the vertical ultimate bearing capacity of a pile foundation comprises the following steps:
s1, taking the weight and the threshold of the BP neural network model as position point information of an improved radial movement algorithm, and establishing an initial population;
step S2, calculating the fitness value of each individual in the initial population by adopting the fitness function of the improved radial movement algorithm, determining the current optimal position by comparing the fitness values of the individuals one by one, and defining the current 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 the content of the first and second substances,Nthe number of test samples for the BP neural network model;t i for BP neural network modeliThe predicted value of the output variable of each test sample;y i for BP neural network modeliThe actual value of each test sample output variable;
step S3, adopting the update condition at the firstk. + -. 0.5 of the center position (x jmax - x jmin）w k Generating a new pre-position point in the range, calculating a fitness value, and updating position information; wherein the content of the first and second substances,krefers to the current iteration number;x jminis as followsjThe minimum value of the individual weights or thresholds;x jmaxis as followsjThe maximum value of the individual weights or thresholds,w k is the inertia weight;
step S4, determining the global optimal position according to the position information updated in the step S3, 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 S3-S4 until the updating is finished;
and step S5, assigning the weight and the threshold value of the global optimal position to the BP neural network model, training and simulating the BP neural network model to obtain an optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, and ending the algorithm.
Preferably, the step S1 includes the steps of:
s1.1, 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=w 1+w 2+w 3formula (2)
w 1=n 1 × n 2 Formula (3)
w 2=n 2 × n 3 Formula (4)
w 3=n 2 + n 3 Formula (5)
Wherein the content of the first and second substances,nodthe total number of the weight and the threshold value;w 1the number of the weights from the input layer to the hidden layer;w 2the number of weights from the hidden layer to the output layer;w 3is the total number of the threshold values;n 1the number of input layers;n 2the number of hidden layers;n 3the number of output layers;
step S1.2, determining value ranges of weight and thresholdx jmaxAndx jminwherein, 1 is less than or equal to j ≤ nod；
Step S1.3, randomly generating in the value range of the step S1.2nopAn initial position point ofnopEstablishing an initial population by using initial position points, wherein the numerical information of the initial position points is obtained by a calculation formula (6);
the calculation formula (6) isX i,j =x jmin + rand（0，1）（x jmax - x jmin）
Wherein the content of the first and second substances,X i,j to generate the firstiAt the first initial positionjIndividual weights or thresholds;rand(0, 1) is a random number between 0 and 1.
Preferably, the step S3 includes the steps of:
step S3.1, determining an update condition for generating a new pre-location point, specifically,
wherein the content of the first and second substances,
is referred to askIs newly generatediA first of the position pointsjIndividual weights or thresholds;Centre j k is referred to askIn the place of the centerjIndividual weights or thresholds;Grefers to the maximum number of iterations;
step S3.2, generating a new preset point by adopting the updating conditionY i k And calculating each pre-position point by the fitness function of the calculation formula (1)Y i k A corresponding fitness value;
step S3.3, updating the position information, in particularkFitness value of substitute location pointfitness（Y i k ) And a firstkFitness value of-1 generation location pointsfitness（X i k-1) Make a comparison iffitness（Y i k ）<fitness（X i k-1) Then the location point information needs to be updated, orderfitness（X i k ）=fitness（Y i k ），X i k =Y i k (ii) a Otherwise, it ordersfitness（X i k ）=fitness（X i k-1），X i k =X i k-1(ii) a Wherein the content of the first and second substances,X i k is as followskGeneration by generationiA plurality of location points;X i k-1is as followskGeneration 1iA plurality of location points;Y i k is as followskGeneration of the firstiA pre-position point.
Preferably, the step S4 includes the steps of:
step S4.1, determining the current generation optimal positionRbestx k And global optimal positionGbestx k And, in particular, the updatedkIn generationfitness（X i k ) The position point of the minimum value in (1) is taken as the current generation optimum positionRbestx k (ii) a When in usekWhen =1, the current generation optimum positionRbestx 1Global optimum position for first generationGbestx 1；
Step S4.2 whenkWhen =2, the global optimum position is updated, in particular, the current generation optimum position is comparedRbestx k Fitness value offitness（Rbestx k ) And global optimum positionGbestx k-1Fitness value offitness（Gbestx k-1) (ii) a If it isfitness（Rbestx k ）<fitness（Gbestx k-1) Then the global optimum location needs to be updated, orderfitness（Gbestx k ）=fitness（Rbestx k ），Gbestx k =Rbestx k (ii) a Otherwise, it ordersfitness（Gbestx k ）=fitness（Gbestx k-1），Gbestx k =Gbestx k-1。
Preferably, in step S3, the center position follows the current generation optimum positionRbestx k And global optimal positionGbestx k The 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 the content of the first and second substances,Centre k is as followskThe center position of the generation;Centre k+1is as followsk-central position of generation 1.
The technical scheme of the invention at least has the following beneficial effects:
the invention adopts a BP neural network model and an improved radial movement algorithm to be combined for use, and particularly, a performance function of the BP neural network model is taken as a fitness function of the improved radial movement algorithm
And assigning the weight and the threshold of the global optimal position obtained by the radial movement algorithm to the BP neural network model, training and simulating the BP neural network model to obtain the optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, so that the defects that the BP neural network model is easy to fall into a local minimum value, the convergence speed is low and the search result is unstable can be improved, and the predicted value is convenient to be ensured to be closer to the true value.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic flowchart of a method for predicting vertical ultimate bearing capacity of a pile foundation in embodiment 1 of the present invention;
FIG. 2 is a comparison of real and predicted values for a test sample.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments that can be derived by one of ordinary skill in the art from the embodiments given herein are intended to be within the scope of the present invention.
Example 1:
referring to fig. 1, a method for predicting vertical ultimate bearing capacity of a pile foundation includes the following steps:
s1, taking the weight and the threshold of the BP neural network model as position point information of an improved radial movement algorithm, and establishing an initial population;
step S2, calculating the fitness value of each individual in the initial population by adopting the fitness function of the improved radial movement algorithm, determining the current optimal position by comparing the fitness values of the individuals one by one, and defining the current 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 the content of the first and second substances,Nthe number of test samples for the BP neural network model;t i for BP neural network modeliThe predicted values of the output variables of the individual test samples, in particular,t i to model BP neural networkiAssigning the weight and the threshold value of the individual in each test sample to a predicted value obtained after the BP neural network model is operated;y i for BP neural network modeliThe actual value of each test sample output variable;
step S3, adopting the update condition at the firstk. + -. 0.5 of the center position (x jmax - x jmin）w k Generating new pre-position points in the range and calculating the fitness valueUpdating the position information; wherein the content of the first and second substances,krefers to the current iteration number;x jminis as followsjThe minimum value of the individual weights or thresholds;x jmaxis as followsjThe maximum value of the individual weights or thresholds,w k is the inertia weight;
step S4, determining the global optimal position according to the position information updated in the step S3, 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 S3-S4 until the updating is finished;
and step S5, assigning the weight and the threshold value of the global optimal position to the BP neural network model, training and simulating the BP neural network model to obtain an optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, and ending the algorithm.
The step S1 includes the steps of:
s1.1, 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=w 1+w 2+w 3formula (2)
w 1=n 1 × n 2 Formula (3)
w 2=n 2 × n 3 Formula (4)
w 3=n 2 + n 3 Formula (5)
Wherein the content of the first and second substances,nodthe total number of the weight and the threshold value;w 1the number of the weights from the input layer to the hidden layer;w 2the number of weights from the hidden layer to the output layer;w 3is the total number of the threshold values;n 1the number of input layers;n 2the number of hidden layers;n 3the number of output layers;
step S1.2, determining value ranges of weight and thresholdx jmaxAndx jminwherein, 1 is less than or equal toj ≤ nod；
Step S1.3, randomly generating in the value range of the step S1.2nopAn initial position point ofnopEstablishing an initial population by using initial position points, wherein the numerical information of the initial position points is obtained by a calculation formula (6);
the calculation formula (6) isX i,j =x jmin + rand（0，1）（x jmax - x jmin）
Wherein the content of the first and second substances,X i,j to generate the firstiAt the first initial positionjIndividual weights or thresholds;rand(0, 1) is a random number between 0 and 1.
The step S3 includes the steps of:
step S3.1, determining an update condition for generating a new pre-location point, specifically,
wherein the content of the first and second substances,
is referred to askIs newly generatediA first of the position pointsjIndividual weights or thresholds;Centre j k is referred to askIn the place of the centerjIndividual weights or thresholds;w k the inertia weight is decreased with the iteration times and is used for determining the convergence speed of the algorithm;
step S3.2, generating a new preset point by adopting the updating conditionY i k And calculating each pre-position point by the fitness function of the calculation formula (1)Y i k A corresponding fitness value;
step S3.3, updating position informationSpecifically, the fitness value of the k-th generation pre-position pointfitness（Y i k ) And a firstkFitness value of-1 generation location pointsfitness（X i k-1) Make a comparison iffitness（Y i k ）<fitness（X i k-1) Then the location point information needs to be updated, orderfitness（X i k ）=fitness（Y i k ），X i k =Y i k(ii) a Otherwise, it ordersfitness（X i k ）=fitness（X i k-1），X i k =X i k-1(ii) a Wherein the content of the first and second substances,X i k is as followskGeneration by generationiA plurality of location points;X i k-1is as followskGeneration 1iA plurality of location points;Y i k is as followskGeneration of the firstiA pre-position point.
The step S4 includes the steps of:
step S4.1, determining the current generation optimal positionRbestx k And global optimal positionGbestx k And, in particular, the updatedkIn generationfitness（X i k ) The position point of the minimum value in (1) is taken as the current generation optimum positionRbestx k (ii) a When in usekWhen =1, the current generation optimum positionRbestx 1Global optimum position for first generationGbestx 1；
Step S4.2 whenkWhen =2, the global optimum position is updated, in particular, the current generation optimum position is comparedRbestx k Fitness value offitness（Rbestx k ) And global optimum positionGbestx k-1Fitness value offitness（Gbestx k-1) (ii) a If it isfitness（Rbestx k ）<fitness（Gbestx k-1) Then the global optimum location needs to be updated, orderfitness（Gbestx k ）=fitness（Rbestx k ），Gbestx k =Rbestx k (ii) a Otherwise, it ordersfitness（Gbestx k ）=fitness（Gbestx k-1），Gbestx k =Gbestx k-1
In step S3, the center position follows the current generation optimum positionRbestx k And global optimal positionGbestx k The 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 the content of the first and second substances,Centre k is as followskThe center position of the generation;Centre k+1is as followsk-central position of generation 1.
The parameters adopted by the BP neural network model in the step S5 include prediction accuracy, maximum iteration number and learning rate, and the prediction accuracy is 10-6The maximum iteration number is 1000, and the learning rate is 0.01.
The topological structure of the BP neural network model adopted in the embodiment 1 is 4-10-1, and the number of hidden layer nodes is 10 according to the optimal value determined by a trial algorithm. Reference numerals in example 1nodIs 61,nopIs 50 percent,GIs 100.
Comparative example 1:
and predicting the vertical ultimate bearing capacity of the pile foundation only by adopting a BP neural network model.
Comparative example 2:
and (3) predicting the vertical ultimate bearing capacity of the pile foundation by only adopting a genetic algorithm to optimize the BP neural network model.
32 groups of static load test data are collected for the vertical ultimate bearing capacity of the pile foundation, wherein 27 groups of data serve as a training set, and 5 groups of data serve as a test set. The static load test data were run 10 times using the prediction methods in example 1 and comparative examples 1-2, and the analysis results are detailed in table 1.
TABLE 1
| Grouping | Relative error | Mean Square 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 and the actual value of the BP neural network model test sample adopted in comparative example 1 is 25.86% -0.42%, the MSE is 0.0049, and the prediction result has great instability and relatively deviates from the actual value. The relative error between the predicted value and the true value of the BP neural network model test sample optimized by the genetic algorithm adopted in the comparative example 2 is 8.55-0.48%, the MSE is 0.0036, and the prediction result is relatively highGood stability, and is relatively close to the true value. The relative error between the predicted value and the true value of the test sample obtained by the method for predicting the vertical ultimate bearing capacity of the pile foundation adopted in the embodiment 1 is 0.01-2.42%, and the MSE is 1.12 multiplied by 10-7The maximum relative error is below 3%, and the prediction 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 the embodiment 1 has good predictability. Meanwhile, as can be seen from fig. 2, the difference between the 10 predicted values and the true values of the test samples (i.e., 5 groups of data in the test set) is not large, and the 10 prediction results are almost the same, so that the method for predicting the vertical ultimate bearing capacity of the pile foundation adopted in embodiment 1 has good stability.
In summary, the invention combines the BP neural network model with the improved radial movement algorithm, and specifically, the performance function of the BP neural network model is used as the fitness function of the improved radial movement algorithm
And assigning the weight and the threshold of the global optimal position obtained by the radial movement algorithm to the BP neural network model, training and simulating the BP neural network model to obtain the optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, so that the defects that the BP neural network model is easy to fall into a local minimum value, the convergence speed is low and the search result is unstable can be improved, and the predicted value is convenient to be ensured to be closer to the true value.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The method for predicting the vertical ultimate bearing capacity of the pile foundation is characterized by comprising the following steps of:
s1, taking the weight and the threshold of the BP neural network model as position point information of an improved radial movement algorithm, and establishing an initial population;
step S2, calculating the fitness value of each individual in the initial population by adopting the fitness function of the improved radial movement algorithm, determining the current optimal position by comparing the fitness values of the individuals one by one, and defining the current 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 the content of the first and second substances,Nthe number of test samples for the BP neural network model;t i for BP neural network modeliThe predicted value of the output variable of each test sample;y i for BP neural network modeliThe actual value of each test sample output variable;
step S3, adopting the update condition at the firstk. + -. 0.5 of the center position (x jmax- x jmin）w k Generating a new pre-position point in the range, calculating a fitness value, and updating position information; wherein the content of the first and second substances,krefers to the current iteration number;x jminis as followsjThe minimum value of the individual weights or thresholds;x jmaxis as followsjThe maximum value of the individual weights or thresholds,w k is the inertia weight;
step S4, determining the global optimal position according to the position information updated in the step S3, 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 S3-S4 until the updating is finished;
and step S5, assigning the weight and the threshold value of the global optimal position to the BP neural network model, training and simulating the BP neural network model to obtain an optimal predicted value of the vertical ultimate bearing capacity of the pile foundation, and ending the algorithm.
2. The method for predicting pile foundation vertical ultimate bearing capacity according to claim 1, wherein the step S1 includes the steps of:
s1.1, 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=w 1+w 2+w 3formula (2)
w 1=n 1 × n 2 Formula (3)
w 2=n 2 × n 3 Formula (4)
w 3=n 2 + n 3 Formula (5)
Wherein the content of the first and second substances,nodthe total number of the weight and the threshold value;w 1the number of the weights from the input layer to the hidden layer;w 2the number of weights from the hidden layer to the output layer;w 3is the total number of the threshold values;n 1the number of input layers;n 2the number of hidden layers;n 3the number of output layers;
step S1.2, determining value ranges of weight and thresholdx jmaxAndx jminwherein, 1 is less than or equal to j ≤ nod；
Step S1.3, randomly generating in the value range of the step S1.2nopAn initial position point ofnopEstablishing an initial population by using initial position points, wherein the numerical information of the initial position points is obtained by a calculation formula (6);
the calculation formula (6) isX i,j =x jmin+ rand（0，1）（x jmax- x jmin）
Wherein the content of the first and second substances,X i,j to generate the firstiAt the first initial positionjIndividual weights or thresholds;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 the step S3 includes the steps of:
step S3.1, determining an update condition for generating a new pre-location point, specifically,
wherein the content of the first and second substances,
is referred to askIs newly generatediA first of the position pointsjIndividual weights or thresholds;Centre j k is referred to askIn the place of the centerjIndividual weights or thresholds;Grefers to the maximum number of iterations;
step S3.2, generating a new preset point by adopting the updating conditionY i k And calculating each pre-position point by the fitness function of the calculation formula (1)Y i k A corresponding fitness value;
step S3.3, updating the position information, in particularkFitness value of substitute location pointfitness（Y i k ) And a firstkFitness value of-1 generation location pointsfitness（X i k-1) Make a comparison iffitness（Y i k ）<fitness（X i k-1) Then the location point information needs to be updated, orderfitness（X i k ）=fitness（Y i k ），X i k =Y i k (ii) a Otherwise, it ordersfitness（X i k ）=fitness（X i k -1），X i k =X i k-1(ii) a Wherein the content of the first and second substances,X i k is as followskGeneration by generationiA plurality of location points;X i k-1is as followskGeneration 1iA plurality of location points;Y i k is as followskGeneration of the firstiA pre-position point.
4. The method for predicting pile foundation vertical ultimate bearing capacity according to claim 3, wherein the step S4 includes the steps of:
step S4.1, determining the current generation optimal positionRbestx k And global optimal positionGbestx k And, in particular, the updatedkIn generationfitness（X i k ) The position point of the minimum value in (1) is taken as the current generation optimum positionRbestx k (ii) a When in usekWhen =1, the current generation optimum positionRbestx 1Global optimum position for first generationGbestx 1；
Step S4.2 whenkWhen =2, the global optimum position is updated, in particular, the current generation optimum position is comparedRbestx k Fitness value offitness（Rbestx k ) And global optimum positionGbestx k-1Fitness value offitness（Gbestx k-1) (ii) a If it isfitness（Rbestx k ）<fitness（Gbestx k-1) Then the global optimum location needs to be updated, orderfitness（Gbestx k ）=fitness（Rbestx k ），Gbestx k =Rbestx k (ii) a Otherwise, it ordersfitness（Gbestx k ）=fitness（Gbestx k-1），Gbestx k =Gbestx k-1。
5. The method for predicting pile foundation vertical ultimate bearing capacity of claim 4, wherein in step S3, the central position follows the current generation optimal positionRbestx k And global optimal positionGbestx k The 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 the content of the first and second substances,Centre k is as followskThe center position of the generation;Centre k+1is as followsk-central position of generation 1.
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