CN115130772A - Ground surface settlement prediction method based on PSO (particle swarm optimization) optimization BP (back propagation) neural network - Google Patents
Ground surface settlement prediction method based on PSO (particle swarm optimization) optimization BP (back propagation) neural network Download PDFInfo
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Abstract
The invention provides a ground surface subsidence prediction method based on a PSO (particle swarm optimization) optimized BP (back propagation) neural network, which comprises the following steps of: collecting historical settlement data of a target area, generating a data set, dividing a training set and a testing set, carrying out data normalization treatment, using the buried depth of a waterproof curtain, the well diameter of a water collecting well, the water level depth, the distance between the waterproof curtain and the water collecting well, the permeability coefficient of soil and the thickness of a water-containing layer as input variables, using the settlement value corresponding to the input variables as output variables to construct a BP neural network prediction model, using the model to input hydrogeological parameters of a to-be-constructed area into an earth surface settlement model, calculating prediction data of the surrounding earth surface settlement caused by different construction methods and construction strengths of the to-be-constructed area, being beneficial to accurately judging the effective influence radius of foundation pit precipitation, selecting the optimal position of the water collecting well and the buried depth of a water-stopping structure, reducing the construction cost, accelerating the construction efficiency and ensuring the safe construction of a project.
Description
Technical Field
The invention belongs to the technical field of foundation pit precipitation ground settlement, and particularly relates to a ground surface settlement prediction method based on a PSO (particle swarm optimization) optimization BP (back propagation) neural network.
Background
With the development of economic technology in China, high-rise buildings and urban subways are continuously increased, deep foundation pit engineering is also increased in a leap manner, in cities with abundant underground water, the construction of the foundation pit engineering is greatly influenced by abundant underground water resources and high underground water level, and foundation pit dewatering becomes an essential measure in underground construction. Along with the continuous promotion of the precipitation process, the problems of the settlement and the lateral inclination of the surrounding terrain, underground pipelines and adjacent buildings caused by the continuous promotion of the precipitation process are solved, the damage caused by the problems is not small, the settlement caused by the precipitation of foundation pits is reduced by adopting a recharge technology in engineering, but the construction period is certainly prolonged, and the cost is also increased. The method is characterized in that a falling funnel is formed around the precipitation of the foundation pit, when the precipitation exceeds a certain distance, the water level falling value is extremely small and gradually approaches to zero, namely the influence radius, the influence radius is determined in the current engineering mainly by adopting an empirical formula method and based on a stable flow basis, the precipitation in the actual engineering basically belongs to unstable flow, and the calculated influence radius has uncertainty.
The BP neural network adopts a gradient descent method, and continuously corrects random initial weight and threshold value through back propagation of an error function until the accuracy requirement of convergence error or the maximum iteration number is met.
The existing BP neural network is adopted to predict the settlement of the surrounding earth surface caused by foundation pit precipitation, but the BP neural network has the problems of low training efficiency and falling into a local optimal value in the prediction process, so that the error between the prediction result and the actual result is large, the influence radius of the precipitation cannot be accurately determined, and the optimal position of a water collecting well cannot be selected and the embedding depth of a water stopping structure cannot be determined.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to provide a method for predicting the surface subsidence by optimizing a BP neural network based on PSO, which can solve the problems that the BP neural network has low training efficiency in the prediction process, falls into a local optimal value, so that the error between the prediction result and the actual result is large, the influence radius of precipitation cannot be accurately determined, the optimal position of a water collecting well cannot be selected, and the embedding depth of a water stopping structure cannot be determined.
In order to solve the above problems, the present invention provides a method for predicting surface subsidence based on a PSO optimized BP neural network, comprising the following steps:
s1: collecting each set of settlement data including the depth H of the waterproof curtain and the water level depth S w Well diameter r of water collecting well w And a distance r from the water collecting well o Permeability coefficient K and water-containing layer thickness H 0 ；
S2: normalizing the collected settlement data to obtain input variables and output variables of a settlement prediction model to form normalized data sets X and Y, wherein X represents influence factors, Y represents final settlement, and the normalized data sets are processed according to the following steps of 7: dividing 3 columns into a training sample set and a test sample set;
s3: establishing a BP neural network model according to the sedimentation data after normalization processing, and determining the neuron number, the activation function and the loss function of an input layer, a hidden layer and an output layer;
s4: based on the established BP neural network model, the following parameters of PSO are initialized: the space dimension D of the particle swarm, the number N of the particle swarm, the iteration times g, the inertia weight omega, the self-learning factor C1, the parameter of the group learning factor C2 and the random variable r 1 、r 2 ；
S5: based on the parameters of the initialized POS in S4, the current particle fitness P of each particle in the particle swarm is i Calculating by comparing the current particle fitness P of each particle in the particle swarm i Obtaining the historical optimal value P of the individual particles in the particle swarm best Individuals in a population of comparison-based particlesParticle history optimum P best Obtaining the current group particle optimal value G best Based on individual particle history optimal values P best And the current group particle optimum value G best Updating the speed Vi and the position Xi of the current particle in the particle swarm, and if the optimal value G of the current swarm particle is best If the convergence error precision is satisfied, outputting the current group particle optimal value G best Otherwise, if the current group particle optimal value G is best If the convergence error precision requirement is not met, circularly iterating according to the characteristic of feedback propagation of the BP neural network, namely, reacquiring the updated individual particle optimal value P in the particle swarm best(new) Updating the optimal value P based on the individual particles in the population of comparison particles best(new) Until an updated population particle optimum value G is obtained best If the convergence error precision is satisfied, outputting an updated group particle optimal value G best ；
S6: based on the population particle optimal value G output in S5 best And calculating to obtain a mean square error as an initial weight and a threshold of the BP model, judging whether the mean square error meets the precision range of the convergence error, if so, outputting a predicted settlement result, if not, correcting the weight and the threshold of each layer in the BP model by adopting a gradient descent method, calculating the corrected mean square error, and performing circular iteration until the mean square error meets the convergence error or reaches the maximum iteration number.
Optionally, in step S2, the collected sedimentation data is normalized, and the following formula (1) is used:
wherein X is a normalized numerical value; x is any number in the dataset; x is the number of max 、x min Respectively a maximum value in the data set and a minimum value in the data set.
Optionally, step S3 includes:
step S3.1: determining the number of hidden layer neurons by the number of input layer neurons and output layer neurons, as shown in the following formula (2):
wherein, L, m and n are the number of neurons of an input layer, a hidden layer and an output layer respectively; α is an adjustment parameter α ∈ (1, 2, 3.... 10);
step S3.2: the activation function is a nonlinear Sigmoid function delta, and the loss function is a mean square error function MSE, the activation function being expressed by equation (3) and the mean square error function being expressed by equation (4):
wherein n is the number of neurons;
is a target sedimentation value; y is i To predict the output settling volume, E is a natural constant, x represents a constant in the input layer activation, x represents the output of the input layer in the hidden layer activation, and E is the mean square error.
Optionally, in step S4, parameters of the PSO particle group are initialized, where a spatial dimension calculation formula of the particle group is as follows formula (5), and an inertia weight calculation formula is as follows formula (6):
D＝L×m+m×n+m+n (5)
wherein, L, m and n are the neuron numbers of an input layer, a hidden layer and an output layer respectively; the inertia weight omega is in a linear relationship with the iteration number g, g max Maximum inertia weight ω for maximum number of iterations max Minimum inertia weightHeavy omega min 。
Optionally, the updating formula for updating the speed Vi and the position Xi of the current particle in the particle swarm in step S5 is as follows, wherein the updating formula for updating the position of the current particle in the particle swarm is as follows (7), and the updating formula for updating the speed of the current particle in the particle swarm is as follows (8):
V i+1 ＝ωv i +c 1 r 1 (P best -x i )+c 2 r 2 (G best -x i ) (7)
X i+1 ＝V i+1 +x i (8)
wherein r is 1 、r 2 ∈[0，1]Is a random variable; x i 、V i Respectively the current particle position and the current particle velocity, V, at the current iteration number i+1 Expressed as the updated particle velocity, X i+1 Indicating the updated position, X i ＝(x i1 ,x i2 ,......x iD ),i∈(1，2，3，……，N)；V i ＝(v i1 ,v i2 ,......v iD ),i∈(1，2，3，……，N)；
In step S5, the current particle fitness P of each particle in the particle group i Calculating, realizing information sharing in the group, and obtaining the optimal value P of the individual particles best And the group particle optimum value G best The formula is as follows (9),
wherein, P best ＝(p i1 ,p i2 ,......p iD ),i∈(1，2，3，......，N)，P best Historical optima for individual particles;
G best ＝(p b1 ,p b2 ,......p bD ),b∈(1，2，3，......，N)，G best for the current population particle optimum, P best(new) For updated individual particle optima, P i Is the current fitness.
Advantageous effects
The method for predicting the surface subsidence based on the PSO optimized BP neural network provided by the embodiment of the invention takes 6 factors of the embedding depth of the waterproof curtain, the well diameter of the water collecting well, the water level depth, the distance between the waterproof curtain and the water collecting well, the permeability coefficient of soil and the thickness of the water-bearing layer into consideration, and measures the surface subsidence amount caused by different distances between the waterproof curtain and the water collecting well and under the condition of the water level depth. The method is different from the initial weight and threshold randomization generated by the traditional BP neural network algorithm, adopts the PSO particle swarm optimization to further optimize the BP neural network algorithm, and effectively solves the problems that the iteration speed of the traditional algorithm is low, the local optimal value is easy to fall into, and the error between the predicted result and the actual result is large. The method has the advantages of good generalization, high prediction precision, high convergence speed and the like, has a good effect on prediction of surrounding ground surface settlement caused by foundation pit precipitation, is favorable for accurately judging the influence radius of the foundation pit precipitation, selects the optimal water collecting well position and the embedding depth of the water stopping structure, reduces the construction cost, accelerates the construction efficiency and ensures the safe implementation of construction engineering. The PSO (particle swarm optimization) is utilized to optimize the BP neural network, accurately predict the surrounding ground surface settlement caused by the foundation pit precipitation, and judge the effective influence radius of the foundation pit precipitation, so that the optimal position of the water collecting well and the embedding depth of the water stopping structure are determined, and the method has great significance in reducing the construction cost, improving the construction efficiency and ensuring the construction engineering safety.
The PSO is one of biological intelligent optimization algorithms, simulates foraging behavior of bird groups, continuously shares own optimal positions among particle swarms, finds a global optimal solution, and gives the optimal solution to initial weights and thresholds among layers in a BP neural network structure, so that iteration times can be effectively reduced, and prediction rate and accuracy are improved. Therefore, in order to solve the defects of the traditional BP neural network in predicting the settlement, the PSO (particle swarm optimization) is utilized to optimize the BP neural network to accurately predict the settlement of the surrounding ground surface caused by the foundation pit precipitation so as to determine the influence radius of the precipitation, and the selection of the optimal water collecting well position and the embedding depth of the water stopping structure is very important.
Drawings
FIG. 1 is a diagram of a prediction system of a prediction method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a prediction method according to an embodiment of the present invention;
FIG. 3 is a BP neural network topology model diagram of the prediction method of the embodiment of the present invention;
FIG. 4 is a diagram of a convergence process of the adaptive PSO algorithm value of the prediction method in the iterative process according to the embodiment of the present invention;
FIG. 5 is a diagram of a PSO optimized BP neural network training process of the prediction method according to the embodiment of the present invention;
FIG. 6 is a graph comparing PSO-BP predicted settling amount, conventional BP predicted settling amount, and actual settling amount of a prediction method according to an embodiment of the present invention.
Detailed Description
The settlement of the surrounding earth surface caused by precipitation can be summarized into two reasons, on one hand, the water head difference caused by the water level depth reduction causes the hydrodynamic pressure of seepage in the earth body; on the other hand, the pressure of pore water is dispersed by the reduction of underground water level due to the precipitation of foundation pit, and the effective stress on the soil framework is increased under the condition that the total stress is kept unchanged according to the effective stress principle. Both stresses cause compaction of the soil particles, resulting in an increase in the amount of settling. However, the physical properties of different soils, hydrological conditions and water stopping structures are all closely related to the radius of influence of precipitation. Therefore, the embodiments of the present invention will be described by the following specific examples.
In this embodiment, a first line of a shenyang subway is used to start a station segment, and data of monitoring ground surface settlement by construction precipitation are obtained, and 50 monitoring points are provided in the segment, so as to generate 50 sets of original data, as follows:
referring to fig. 1 to fig. 6 in combination, according to an embodiment of the present invention, a method for optimizing a surface subsidence prediction of a BP neural network based on PSO, please refer to fig. 1 and fig. 2, includes the following steps:
s1: collect the sediment of each groupData of settlement including the depth H of water-stop curtain and the water level S w Well diameter r of water collecting well w And a distance r from the water collecting well o Permeability coefficient K and water-containing layer thickness H 0 And a corresponding amount of sedimentation.
S2: carrying out normalization processing on the collected settlement data to obtain input variables and output variables of a settlement prediction model, forming a normalized data set X and Y, wherein X represents influence factors, Y represents final settlement, and the processed data set is subjected to normalization processing according to the following steps of 7: the 3 columns are divided into a training sample set and a test sample set.
Furthermore, the problems of long network training time, incapability of convergence and the like of the acquired settlement data due to different unit dimensions and orders of magnitude cannot be directly input into a network model, so that the acquired settlement data set needs to be normalized to be unified in a range, wherein X belongs to [0, 1], and the normalization formula is as follows (1):
wherein X is a normalized numerical value; x is any number in the dataset; x is the number of max 、x min Respectively, a maximum and a minimum in the data set.
S3: and establishing a BP neural network model according to the sedimentation data after the normalization processing, and determining the neuron number, the activation function and the loss function of the input layer, the hidden layer and the output layer.
Further, establishing a BP neural network model:
the input layer, the hidden layer and the output layer jointly form a BP neural network model, and in the network model, the 6 sedimentation influence factors are used as the number x of neurons in the input layer to be 6; the sedimentation amount corresponding to the influence factors is the number y of neurons in the output layer is 1; since there is no fixed way to determine the number of neurons contained in the hidden layer, an empirical formula is used in this invention to calculate, as shown in the following formula (2):
wherein, L, m and n are the number of neurons of the input layer, the hidden layer and the output layer respectively; α is an adjusting parameter α ∈ (1, 2, 3.. said., 10), where α ═ 6 is taken in the present invention; therefore, the number of hidden layer neurons is m-9. Presetting a maximum iteration time t as 100; the preset learning rate is equal to 0.1; the predetermined convergence error μ is 1 × 10 -4 。
The activation function is a nonlinear Sigmoid function delta, and the loss function is a mean square error function MSE, the activation function being expressed by equation (3) and the mean square error function being expressed by equation (4):
wherein n is the number of neurons;
is a target sedimentation value; y is i Outputting the settlement for prediction; e is a natural constant; x represents a constant in the input layer activation and x represents the output of the input layer in the hidden layer activation; e denotes the mean square error.
S4: based on the established BP neural network model, the following parameters of PSO are initialized: spatial dimension D of particle swarm, population number N, iteration times g, inertia weight omega, self-learning factor C1, population learning factor C2 parameter and random variable r 1 、r 2 。
Further, initializing PSO particle swarm algorithm model parameters:
the particle swarm optimization is an optimization algorithm for the BP network model, wherein the maximum optimization iteration number g is 100; the population size N is 20; the inertia weight ω is 0.8; the individual particle learning factor and the group particle learning factors C1 and C2 are 1.2; seed of a species of riceGroup space dimension D73; range of positions x of particles i ∈[-5，5](ii) a Velocity range v of the particles i ∈[-1，1](ii) a The calculation formula of the inertia weight of the particle is as follows (6):
the inertia weight omega of the particle and the iteration times g are in a linear relation, and the maximum inertia weight omega in the formula max 0.9; minimum inertial weight ω min ＝0.2。
The space dimension is the number of optimal solutions to be sought, namely the number of all weights and thresholds between all layers in a BP neural network model, and the space dimension calculation formula of the particle swarm is as follows (5):
D＝L×m+m×n+m+n (5)
in the formula, L, m and n are the numbers of neurons of an input layer, a hidden layer and an output layer in the BP neural network model, and are respectively 6, 9 and 1. The above parameters are entered into MATLAB by binary coding.
S5: based on the parameters of the initialized POS in S4, the current particle fitness P of each particle in the particle swarm is i Calculating by comparing the current particle fitness P of each particle in the particle swarm i Obtaining the historical optimal value P of the individual particles in the particle swarm best Based on comparing historical optimal values P of individual particles in the particle swarm best Obtaining the current group particle optimal value G best Based on individual particle history optimal values P best And the current population particle optimum G best Updating the speed Vi and the position Xi of the current particle in the particle swarm, and if the optimal value G of the current swarm particle is best If the convergence error precision is met, outputting the current group particle optimal value G best Otherwise, if the current group particle optimal value G is best If the requirement of convergence error precision is not met, carrying out circular iteration according to the characteristic of feedback propagation of the BP neural network, namely, re-acquiring the updated optimal value P of the individual particles in the particle swarm best(new) Updating the optimal value P based on the individual particles in the population of comparison particles best(new) Until an updated population particle optimum value G is obtained best If the convergence error precision is satisfied, the updated group particle optimal value G is output best 。
Calculating the particle swarm fitness:
in order to find a local optimal solution in the given range, the fitness of the population particles is calculated, and the calculation method takes the mean square error of the predicted settlement amount and the target settlement amount as the fitness of the particle swarm, and the formula (9) is as follows:
wherein n is the number of neurons;
is a target sedimentation amount; y is i The amount of sedimentation is output for prediction.
Referring to fig. 4, by comparing the particle fitness, the individual optimal value and the group optimal value in the particle group are obtained, and the position and the velocity of each particle in the particle group are updated in this way.
If the current particle fitness P i Lower than the historical optimum P of the individual particle best I.e. P i ＜P best Then the individual particle history optimum value P best Keeping the original shape;
if the current particle fitness P i Superior to the historical optimum P of the individual particles best I.e. P i ≥P best Then the current individual particle fitness P is used i Updated to a new individual particle history optimum value P best(new) 。
Thirdly, if the current individual particle fitness P after updating is up to the maximum best(new) Particle optimum value G superior to historical population best I.e. P best(new) ≥G best Then the current individual particle fitness P is used best(new) Updating to the optimal value G of the population particles best 。
Wherein: as shown in formula (9):
wherein, P best ＝(p i1 ,p i2 ,......p iD ),i∈(1，2，3，......，N)，P best Historical optima for individual particles;
G best ＝(p b1 ,p b2 ,......p bD ),b∈(1，2，3，......，N)，G best for the current population particle optimum, P best(new) For updated individual particle optima, P i Is the current fitness.
P best ＝(p i1 ,p i2 ,......p iD ),i∈[1,N]；
G best ＝(p b1 ,p b2 ,......p bD ),b∈[1,N]
Updating the position and the speed of each particle, and updating the following formula (10):
in the formula r 1 、r 2 ∈[0，1]For random variables, in the invention r is taken 1 、r 2 ＝1；X i 、V i Respectively the position and the speed of the particle under the current iteration times; the updated particle position is X i+1 Indicates the velocity V for the particle after the update i+1 And (4) showing.
Recalculating the updated particle fitness and comparing the recalculated particle fitness with the fitness before updating iteration so as to continuously optimize the optimal values of the individual particles and the group particles in the particle swarm until the accuracy range of the convergence error is met or the requirement of the maximum iteration times, namely 100 times is met, terminating the iterative operation and outputting the optimal value G of the group particles which meets the accuracy of the convergence error best Otherwise, performing loop iteration to obtain the group particle optimal value G which does not meet the convergence error precision best Then calculate the current fitness P again i And are combinedComparing, updating, and outputting the optimal value G of the population particles again best If the convergence error is satisfied, the output is performed, and if the convergence error is not satisfied, the loop iteration is continued.
And giving the optimal parameters after the iterative optimization to initial weight values and threshold values among layers in the BP neural network model.
S6: based on the population particle optimal value G output in S5 best And calculating to obtain a mean square error as an initial weight and a threshold of the BP model, judging whether the mean square error meets the accuracy range of the convergence error, if so, outputting a predicted settlement result, if not, correcting the weight and the threshold of each layer in the BP model by adopting a gradient descent method, calculating the corrected mean square error, and performing circular iteration until the mean square error meets the convergence error or reaches the maximum iteration number.
Referring to fig. 3, a BP neural network model is perfected:
forward propagation: input variable X 1 To X 6 For the buried depth of the waterproof curtain, the water level deepening, the well diameter of the water collecting well, the distance between the water collecting well and the water collecting well, the permeability coefficient of soil and the thickness of a water containing layer, the output variable Y is the earth surface settlement amount corresponding to the influence factors, u1 to u9 are output functions of a hidden layer, and delta is the mapping relation of an activation function, the activation function is selected to be a sigmoid function, the activation function is expressed as a formula (3), and the hidden layer output function uj (j belongs to [1, 9 ], is the element of [ 1], and is the element of [ 9 ]]) Is expressed by the following formula (11):
in the formula, n belongs to (1, 2, 3, … …, 6) as the number of neurons in the input layer;
the jth neuron threshold for the hidden layer uj; w is a ij For the ith input variable and the jth implicitThe weight of the neurons in the layer; in the input layer activation x represents a constant and in the hidden layer activation x represents the output of the input layer.
Taking the first neuron u1 as an example, the output function is the following equation (12):
the output layer function y is expressed as the following equation (13):
in the formula, m is the number of neurons in the hidden layer as the element (1, 2, 3, … …, 9); w is a jk Is the weight of the j-th neuron connected with the output layer, θ k For the threshold value of the output layer, the output function y is the following formula (14):
and y is the predicted settling amount of the BP neural network.
And (4) reverse propagation: verifying the settlement prediction model by the following formula, and predicting the settlement y and the target settlement
Calculating the node output error e, as shown in equation (15):
the total error E is calculated as equation (16):
in the formula (I); p is the total number of neurons; e.g. of the type q Is the qth node error (q ═ 1, 2, 3, … …, p); mu isConvergence error.
Referring to fig. 6, the optimized mean square error E is 0.4656, and the non-optimized mean square error E is 0.7363, which improves the prediction accuracy of POS-BP by 36.8% compared to the conventional BP.
If the mean square error E is less than mu, the requirement of error precision is met, a predicted settlement value is output, otherwise, the weight and the threshold of each layer are corrected by adopting a gradient descent method, and forward propagation is carried out again until the calculation error is less than the convergence error or the maximum iteration number is met.
Updating the weight and the threshold value between the connected layers by a gradient descent method:
the formula for correcting the connection weight and the threshold between the output layer and the hidden layer is as follows (17):
the weight between the output layer and the hidden layer is graded as follows from equation (18) to equation (20):
wherein t e (1, 2, 3, … …, 100) is iteration number; uj is a hidden layer output function; η is 0.1 as the learning rate.
Similarly, a calculation formula of a connection weight value between the hidden layer and the input layer and a threshold value can be obtained, wherein the weight value is as shown in the following formula (21), and the threshold value is as shown in the following formula (22):
wherein,
for the implicit layer to output layer error, the following formula (23) is calculated:
and when the calculation error meets the convergence error requirement or reaches the maximum iteration times, outputting a result to obtain a prediction model of the surrounding earth surface settlement under the characteristics of different hydrogeological conditions, different water stopping structures and the like.
Referring to fig. five, the PSO optimization process, the R values of the prediction results of the training samples, the verification samples, the test samples, and the total data set are all closer to 1, and the closer the R value is to 1, the higher the prediction accuracy of the model is, which proves the feasibility of the subsidence prediction model.
The invention discloses a method for predicting surface subsidence based on a PSO (particle swarm optimization) optimized BP (back propagation) neural network, which takes 6 factors of the embedding depth of a waterproof curtain, the well diameter of a water collecting well, the water level depression, the distance between the waterproof curtain and the water collecting well, the permeability coefficient of soil and the thickness of a water-bearing layer into consideration, and measures the surface subsidence quantity caused by different distances between the waterproof curtain and the water collecting well and under the condition of the water level depression. The method is different from the initial weight and threshold randomization generated by the traditional BP neural network algorithm, adopts the PSO particle swarm optimization to further optimize the BP neural network algorithm, and effectively solves the problems that the traditional algorithm is low in iteration speed and easy to fall into a local optimal value, and the error between a prediction result and an actual result is large. The method has the advantages of good generalization, high prediction precision, high convergence speed and the like, has a good effect on prediction of surrounding ground surface settlement caused by foundation pit precipitation, is favorable for accurately judging the influence radius of the foundation pit precipitation, selects the optimal water collecting well position and the embedding depth of the water stopping structure, reduces the construction cost, accelerates the construction efficiency and ensures the safe implementation of construction engineering.
It is readily understood by a person skilled in the art that the advantageous ways described above can be freely combined, superimposed without conflict.
Claims (5)
1. The method for predicting the surface subsidence of the BP neural network based on PSO optimization is characterized by comprising the following steps:
s1: collecting each set of settlement data including the depth H of the waterproof curtain and the water level depth S w Well diameter r of water collecting well w And a distance r from the water collecting well o Permeability coefficient K and water-containing layer thickness H 0 ；
S2: normalizing the collected settlement data to obtain input variables and output variables of a settlement prediction model to form normalized data sets X and Y, wherein X represents influence factors, Y represents final settlement, and the normalized data sets are processed according to the following steps of 7: dividing 3 columns into a training sample set and a test sample set;
s3: establishing a BP neural network model according to the sedimentation data after normalization processing, and determining the neuron number, the activation function and the loss function of an input layer, a hidden layer and an output layer;
s4: based on the established BP neural network model, the following parameters of PSO are initialized: the space dimension D of the particle swarm, the number N of the particle swarm, the iteration times g, the inertia weight omega, the self-learning factor C1, the parameter of the group learning factor C2 and the random variable r 1 、r 2 ；
S5: based on the parameters of the initialized POS in S4, the current particle fitness P of each particle in the particle swarm is i Performing calculation by comparing the current particle fitness P of each particle in the particle swarm i Obtaining the historical optimal value P of the individual particles in the particle swarm best Based on comparing historical optimal values P of individual particles in the particle swarm best Obtaining the current group particle optimal value G best Based on individual particle history optimal values P best And the current population particle optimum G best For the velocity Vi and bit of the current particle in the particle swarmSetting Xi for updating, if the current group particle optimal value G best If the convergence error precision is satisfied, outputting the current group particle optimal value G best On the contrary, if the current group particle optimal value G best If the convergence error precision requirement is not met, circularly iterating according to the characteristic of feedback propagation of the BP neural network, namely, reacquiring the updated individual particle optimal value P in the particle swarm best(new) Updating the optimal value P based on the individual particles in the population of comparison particles best(new) Until an updated population particle optimum value G is obtained best If the convergence error precision is satisfied, the updated group particle optimal value G is output best ；
S6: based on the population particle optimal value G output in S5 best And calculating to obtain a mean square error as an initial weight and a threshold of the BP model, judging whether the mean square error meets a convergence error precision range, if so, outputting a predicted settlement result, if not, correcting the weight and the threshold of each layer in the BP model by adopting a gradient descent method, calculating the corrected mean square error, and performing circular iteration until the mean square error meets the convergence error or reaches a preset maximum iteration number.
2. The method for predicting the ground surface subsidence based on the PSO optimized BP neural network of claim 1, wherein the collected subsidence data is normalized in step S2, and the formula (1) is as follows:
wherein X is a normalized numerical value; x is any number in the dataset; x is a radical of a fluorine atom max 、x min Respectively the maximum value in the data set and the minimum value in the data set.
3. The method for predicting the surface subsidence based on the PSO optimized BP neural network of claim 1, wherein the step S3 comprises:
step S3.1: determining the number of hidden layer neurons by the number of input layer neurons and output layer neurons, as shown in the following formula (2):
wherein, L, m and n are the number of neurons of the input layer, the hidden layer and the output layer respectively; α is an adjustment parameter α ∈ (1, 2, 3.... 10);
step S3.2: the activation function is a nonlinear Sigmoid function delta, and the loss function is a mean square error function MSE, the activation function being expressed by equation (3) and the mean square error function being expressed by equation (4):
wherein n is the number of neurons;
is a target sedimentation value; y is i To predict the output settling volume, E is the natural constant, x is the input volume, and E is the mean square error.
4. The method for ground subsidence prediction based on the PSO optimized BP neural network of claim 1, wherein the parameters of the PSO particle swarm are initialized in step S4, wherein the spatial dimension of the particle swarm is calculated as shown in formula (5), and the inertial weight is calculated as shown in formula (6):
D＝L×m+m×n+m+n (5)
wherein, L, m and n are the neuron numbers of an input layer, a hidden layer and an output layer respectively; the inertia weight omega is in a linear relationship with the iteration number g, g max Maximum number of iterations, maximum inertial weight ω max Minimum inertial weight ω min 。
5. The method for PSO-optimized BP neural network-based surface subsidence prediction according to claim 1, wherein the updating formula for updating the velocity Vi and the position Xi of the current particle in the particle swarm in step S5 is as follows, wherein the updating formula for the position of the current particle in the particle swarm is as following formula (7), and the updating formula for the velocity of the current particle in the particle swarm is as following formula (8):
V i+1 ＝ωv i +c 1 r 1 (P best -x i )+c 2 r 2 (G best -x i ) (7)
X i+1 ＝V i+1 +x i (8)
wherein r is 1 、r 2 ∈[0，1]Is a random variable; x i 、V i Respectively the current particle position and the current particle velocity, V, at the current iteration number i+1 Expressed as the updated particle velocity, X i+1 Indicating the updated position, X i ＝(x i1 ,x i2 ,......x iD ),i∈(1，2，3，……，N)；V i ＝(v i1 ,v i2 ,......v iD ),i∈(1，2，3，……，N)；
In step S5, the current particle fitness P of each particle in the particle group i Calculating, realizing information sharing in the group, and obtaining the optimal value P of the individual particles best And the optimal value G of population particles best The formula is as follows (9),
wherein, P best ＝(p i1 ,p i2 ,......p iD ),i∈(1，2，3，......，N)，P best Historical optima for individual particles;
G best ＝(p b1 ,p b2 ,……p bD ),b∈(1，2，3，……，N)，G best for the current population particle optimum, P best(new) For updated individual particle optima, P i Is the current fitness.
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| CN117260379A (en) * | 2023-11-21 | 2023-12-22 | 靖江市恒友汽车部件制造有限公司 | On-line control method for machining diameter of automobile part |
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| CN116401749B (en) * | 2023-06-09 | 2023-09-01 | 吉林大学 | Method, system, electronic equipment and storage medium for determining circulation well parameters |
| CN117260379A (en) * | 2023-11-21 | 2023-12-22 | 靖江市恒友汽车部件制造有限公司 | On-line control method for machining diameter of automobile part |
| CN117260379B (en) * | 2023-11-21 | 2024-02-23 | 靖江市恒友汽车部件制造有限公司 | On-line control method for machining diameter of automobile part |
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