CN111914481A - Slope stability prediction method based on improved PSO-RBF algorithm - Google Patents

Slope stability prediction method based on improved PSO-RBF algorithm Download PDF

Info

Publication number
CN111914481A
CN111914481A CN202010729020.8A CN202010729020A CN111914481A CN 111914481 A CN111914481 A CN 111914481A CN 202010729020 A CN202010729020 A CN 202010729020A CN 111914481 A CN111914481 A CN 111914481A
Authority
CN
China
Prior art keywords
neural network
basis function
radial basis
fitness
particle
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010729020.8A
Other languages
Chinese (zh)
Other versions
CN111914481B (en
Inventor
池小波
刘宇韬
贾新春
刘丽红
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanxi University
Original Assignee
Shanxi University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanxi University filed Critical Shanxi University
Priority to CN202010729020.8A priority Critical patent/CN111914481B/en
Publication of CN111914481A publication Critical patent/CN111914481A/en
Application granted granted Critical
Publication of CN111914481B publication Critical patent/CN111914481B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • General Health & Medical Sciences (AREA)
  • Mathematical Physics (AREA)
  • Computational Linguistics (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • Biophysics (AREA)
  • Biomedical Technology (AREA)
  • Data Mining & Analysis (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Computer Hardware Design (AREA)
  • Geometry (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

A slope stability prediction method based on an improved PSO-RBF algorithm is disclosed. The invention discloses a slope stability prediction model based on an improved PSO-RBF algorithm, and belongs to the technical field of slope stability prediction. The slope stability prediction method comprises the steps of initializing the radial basis function neural network, optimizing parameters of the radial basis function neural network by adopting a particle swarm optimization algorithm based on a normal attenuation inertia weight factor, constructing a brand-new radial basis function neural network prediction model according to optimal parameters of the radial basis function neural network calculated by the optimization algorithm, and predicting slope stability by using the improved radial basis function neural network prediction model. According to the invention, on the basis of a Gaussian function used by a traditional hidden layer, a radial basis function expansion speed control factor is added, and the factor can adjust the variation trend of parameters of a neural network in an iteration process, so that mutation in the iteration process is avoided, and the prediction accuracy of a trained model is higher.

Description

Slope stability prediction method based on improved PSO-RBF algorithm
Technical Field
The invention belongs to the technical field of slope stability prediction, and particularly relates to a slope stability prediction method based on an improved PSO-RBF algorithm.
Background
In recent years, natural disasters frequently occur along with the continuous occurrence of extreme weather events in the world, wherein disasters such as landslide and debris flow caused by instability of a side slope cause the loss of lives and properties of a plurality of people. Therefore, it becomes important to be able to effectively predict the stability of the side slope.
The slope stability is predicted mainly by analyzing the landslide condition, the combination of factors which are beneficial to the landslide effect is determined, and the possibility of generating the landslide in the area or in a certain section of slope in the future is predicted according to the combination of the beneficial factors. The first type is a qualitative analysis method, and the evolution stage and the stability condition of the side slope are judged by researching the size and the shape of the side slope, the geological structure of the side slope, the geological environment in which the side slope is positioned, the formed geological history, the deformation damage trace and various factors influencing the stability of the side slope; the second type is a limit balance analysis method, which assumes the rock and soil bodies which can slide as rigid bodies, and calculates the stability coefficient of the side slope by analyzing the possible sliding surface and simplifying the stress on the sliding surface into uniform distribution; the third type is a numerical analysis method, which firstly calculates a slope displacement field and a stress field by using a finite element analysis method, and then calculates the stability coefficient of each element and a possible sliding surface by using a rock and soil strength criterion; the fourth type is an engineering geology analogy method, which is to compare the studied slope or the artificial slope to be designed with the studied or experienced slope to evaluate the stability and propose a reasonable slope height and a reasonable slope angle. With the development of the nonlinear theory, intelligent algorithms such as a fuzzy algorithm, a support vector machine and an artificial neural network bring a new research approach to the problem of slope stability prediction. The radial basis function neural network in the artificial neural network can map any complex nonlinear relation due to the strong nonlinear fitting capability of the radial basis function neural network, has the advantages of simple learning rule, convenience for computer implementation and the like, and is widely applied to slope stability prediction by learners. The traditional RBF network generally uses a clustering method and a gradient descent method for determining the parameters of the hidden layer of the network, and related researchers continuously propose an evolutionary algorithm capable of optimizing a neural network structure in recent decades along with further understanding and research on the natural biological elimination theory: dorigo proposed an Ant Colony algorithm (Ant Colony Optimization, ACO for short); roben proposes a Cultural Algorithm (curtal Algorithm, CA for short); storn and Price propose a Differential Evolution algorithm (DE for short); kennedy and Eberhart propose Particle Swarm Optimization (PSO for short). The PSO algorithm is now widely used for neural network training due to its simple principle, few parameters, and easy implementation. Compared with the traditional PSO algorithm, researchers have proposed some improved methods in recent years: SHI et al propose a linear weight attenuation particle swarm optimization algorithm, which performs linear attenuation inertial weight with the increase of iteration times; YAN, etc., providing an exponential weight attenuation particle swarm optimization algorithm, and attenuating the inertia weight based on an exponential form; the contraction factor x is introduced into the contraction factor particle swarm optimization algorithm provided by CLERC and the like, so that the local and global searching capability of the traditional particle swarm optimization algorithm can be balanced; ZHANG et al propose gaussian distribution attenuation inertia weight particle swarm optimization algorithm, which is inspired by gaussian distribution function and combined with particle swarm optimization algorithm.
Although the PSO algorithm has certain development compared with the initial theory, the PSO algorithm still has the problems of easy falling into local optimization, slow later convergence speed, low accuracy of the optimization result of the algorithm and the like; the RBF neural network also has the problem that the improper parameter setting can cause under-fitting or over-fitting of a training model and the like. Meanwhile, due to a plurality of factors influencing the slope stability, if relevant parameters and quantity cannot be reasonably selected, accurate prediction cannot be achieved. And due to the burstiness and severity of the slope instability disaster, the stability of the slope instability disaster can be quickly and accurately predicted.
Disclosure of Invention
Aiming at the problems, the invention provides a slope stability prediction method based on an improved PSO-RBF algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
a slope stability prediction method based on an improved PSO-RBF algorithm initializes a radial basis function neural network, optimizes parameters of the radial basis function neural network by adopting a particle swarm optimization algorithm based on a normal attenuation inertial weight factor, constructs a brand new radial basis function neural network prediction model according to the optimal parameters of the radial basis function neural network calculated by the optimization algorithm, and predicts the slope stability by using the improved radial basis function neural network prediction model.
Further, the method specifically comprises the following steps:
step S1, initializing the radial basis function neural network, determining the structure of the radial basis function neural network,
step S2, initializing the particle group: setting the scale, the iteration times, the weight factor, the initial value and the end value of learning, the initial speed and the initial position of each particle, the individual optimal position and the global optimal position of the population;
step S3, training radial basis function neural network parameters: calculating the velocity of each particle according to equation (1)
Figure BDA0002602385810000031
Figure BDA0002602385810000032
Wherein the content of the first and second substances,
Figure BDA0002602385810000033
representing the velocity vector of the ith particle after t +1 iterations,
Figure BDA0002602385810000034
is the best position of the particle found by the ith particle after t iterations,
Figure BDA0002602385810000035
is the best position of the population, r, found after the population iterates t times1And r2Take [0, 1]Random number of cells, ωtThe weight factor is defined by the formula:
Figure BDA0002602385810000036
wherein, tmaxIs the maximum iteration number, t is the current iteration number,
Figure BDA0002602385810000037
the golden section ratio is 0.618.
Wherein, c1、c2The formula is defined as the learning factor:
c1＝2-cos(-tπ/2tmax) (3)
c2＝1+cos(-tπ/2tmax) (4)
in finding
Figure BDA0002602385810000041
Then, v is required and setmax、vminMake a comparison
Figure BDA0002602385810000042
Wherein v ismaxUpper limit of velocity, vminTo the lower velocity limit, the position of each particle is then calculated
Figure BDA0002602385810000043
Figure BDA0002602385810000044
Therein, in order to adapt to omegatThe change characteristic of (2) introduces a regulating factor beta into a position formula, and the formula is defined as follows:
Figure BDA0002602385810000045
wherein n is the total number of particles,
Figure BDA0002602385810000046
the fitness of the current particle is defined by the formula:
Figure BDA0002602385810000047
wherein the content of the first and second substances,
Figure BDA0002602385810000048
is a measured value, fi tFor the predicted value, the predicted value definition formula is:
Figure BDA0002602385810000049
wherein the content of the first and second substances,
Figure BDA00026023858100000410
is the connection coefficient of the output layer, obtained from the best position coordinate of the particle at this moment, N is the number of neurons of the hidden layer,
Figure BDA00026023858100000411
is a radial basis function, which is defined by the formula:
Figure BDA0002602385810000051
wherein the content of the first and second substances,
Figure BDA0002602385810000052
as a parameter of the width of the strip,
Figure BDA0002602385810000053
the central value is obtained from the optimal position coordinates of the particle at the moment, and alpha is a radial basis function expansion speed control factor and is defined by the following formula:
Figure BDA0002602385810000054
wherein gamma is an adjusting factor which can be controlled by a worker;
step S4, the fitness obtained for each particle at the current time
Figure BDA0002602385810000055
Fitness with last moment
Figure BDA0002602385810000056
Comparing, if the fitness value of the particle at the moment is better than the fitness value at the previous moment, replacing the value of the individual optimal position with the position at the moment
Figure BDA0002602385810000057
Otherwise, keeping the state unchanged;
step S5, comparing the updated fitness of all the particles at the moment, and selecting the best fitness with the fitness at the last moment
Figure BDA0002602385810000058
The corresponding fitness is compared and if the fitness is better than the fitness
Figure BDA0002602385810000059
Corresponding to the fitness, then will
Figure BDA00026023858100000510
Updated to the position of the particle
Figure BDA00026023858100000511
Otherwise, keeping the state unchanged;
step S6, judging whether the optimal fitness reaches 0.06, if so, stopping iteration and outputting a global optimal position value; otherwise, repeating the steps S3-S5;
and step S7, taking the coordinate value in the global optimum position after meeting the requirement as the optimal solution as the parameter value required in the radial basis function neural network, establishing a radial basis function neural network prediction model, preprocessing the data set collected from the slope of which the stability needs to be predicted, inputting the preprocessed data set into the established prediction model, and obtaining the stability prediction of the model on the slope.
Compared with the prior art, the invention has the following advantages:
compared with a method that the inertia weight and the learning factor in the particle velocity iterative formula in the traditional particle swarm optimization adopt fixed values, the inertia weight and the learning factor in the particle swarm optimization both adopt a nonlinear dynamic iterative strategy, wherein the inertia weight adopts a quasi-normal distribution curve as an attenuation strategy, and the learning factor adopts a trigonometric function curve as an attenuation strategy. By optimizing the parameters, the improved particle swarm optimization obviously improves the problems of easy generation of premature convergence (especially in the process of complex multi-peak search tasks), poor local optimization capability, slow later convergence speed and low accuracy of the optimization result of the algorithm. When iteration begins, because the whole initial solution space is large, improved parameter values are kept at large values, the algorithm searches the whole space by a sufficient step length, the global searching capability is strongest at the moment, and the problem of falling into local optimum is solved by increasing the convergence speed. After a certain number of iterations, the improved parameter value is rapidly reduced, the search step length is reduced, the global search capability is weakened, the local search capability is strengthened, compared with the traditional particle swarm algorithm, the optimal solution can not be omitted to the maximum extent, and meanwhile, in the final iteration stage, the convergence speed cannot be reduced due to the reduction of the solution space and the curve change design of the parameter. Compared with the traditional radial basis function neural network, the radial basis function expansion speed control factor is added on the basis of the Gaussian function used by the traditional hidden layer, the factor can adjust the variation trend of the parameters of the neural network in the iteration process, the mutation in the iteration process is avoided, and the trained model has higher prediction accuracy.
Drawings
FIG. 1 is a schematic diagram of the algorithm steps of the present invention;
FIG. 2 is a comparison graph of a conventional PSO algorithm and an inertia weight optimization alone;
FIG. 3 is a graph comparing a conventional PSO algorithm with a single optimized learning factor;
FIG. 4 is a comparison graph of a conventional PSO algorithm and a PSO algorithm that optimizes two parameters simultaneously;
FIG. 5 is a graph comparing the predicted effect of an alpha-factor-added RBF neural network with that of a conventional RBF neural network;
FIG. 6 is a graph comparing the predicted effects of a conventional RBF neural network, a PSO-RBF neural network, and an improved PSO-RBF neural network.
Detailed Description
A slope stability prediction method based on an improved PSO-RBF algorithm initializes a radial basis function neural network, optimizes parameters of the radial basis function neural network by adopting a particle swarm optimization algorithm based on a normal attenuation inertial weight factor, constructs a brand new radial basis function neural network prediction model according to the optimal parameters of the radial basis function neural network calculated by the optimization algorithm, and predicts the slope stability by using the improved radial basis function neural network prediction model.
Further, the method specifically comprises the following steps:
step S1, initializing the radial basis function neural network, determining the structure of the radial basis function neural network,
step S2, initializing the particle group: setting the scale, the iteration times, the weight factor, the initial value and the end value of learning, the initial speed and the initial position of each particle, the individual optimal position and the global optimal position of the population;
step S3, training radial basis function neural network parameters: calculating the velocity of each particle according to equation (1)
Figure BDA0002602385810000071
Figure BDA0002602385810000072
Wherein the content of the first and second substances,
Figure BDA0002602385810000073
representing the velocity vector of the ith particle after t +1 iterations,
Figure BDA0002602385810000074
is the best position of the particle found by the ith particle after t iterations,
Figure BDA0002602385810000075
is the best position of the population, r, found after the population iterates t times1And r2Take [0, 1]Random number of cells, ωtThe weight factor is defined by the formula:
Figure BDA0002602385810000076
wherein, tmaxIs the maximum iteration number, t is the current iteration number,
Figure BDA0002602385810000077
the golden section ratio is 0.618.
Wherein, c1、c2The formula is defined as the learning factor:
c1＝2-cos(-tπ/2tmax) (3)
c2＝1+cos(-tπ/2tmax) (4)
in finding
Figure BDA0002602385810000081
Then, v is required and setmax、vminMake a comparison
Figure BDA0002602385810000082
Wherein v ismaxUpper limit of velocity, vminTo the lower velocity limit, the position of each particle is then calculated
Figure BDA0002602385810000083
Figure BDA0002602385810000084
Therein, in order to adapt to omegatThe change characteristic of (2) introduces a regulating factor beta into a position formula, and the formula is defined as follows:
Figure BDA0002602385810000085
wherein n is the total number of particles,
Figure BDA0002602385810000086
the fitness of the current particle is defined by the formula:
Figure BDA0002602385810000087
wherein the content of the first and second substances,
Figure BDA0002602385810000088
is a measured value, fi tFor the predicted value, the predicted value definition formula is:
Figure BDA0002602385810000089
wherein the content of the first and second substances,
Figure BDA00026023858100000810
is the connection coefficient of the output layer, obtained from the best position coordinate of the particle at this moment, N is the number of neurons of the hidden layer,
Figure BDA00026023858100000811
is a radial basis function, which is defined by the formula:
Figure BDA0002602385810000091
wherein the content of the first and second substances,
Figure BDA0002602385810000092
as a parameter of the width of the strip,
Figure BDA0002602385810000093
the central value is obtained from the optimal position coordinates of the particle at the moment, and alpha is a radial basis function expansion speed control factor and is defined by the following formula:
Figure BDA0002602385810000094
wherein gamma is an adjusting factor which can be controlled by a worker;
step S4, the fitness obtained for each particle at the current time
Figure BDA0002602385810000095
Fitness with last moment
Figure BDA0002602385810000096
Comparing, if the fitness value of the particle at the moment is better than the fitness value at the previous moment, replacing the value of the individual optimal position with the position at the moment
Figure BDA0002602385810000097
Otherwise, keeping the state unchanged;
step S5, comparing the updated fitness of all the particles at the moment, and selecting the best fitness with the fitness at the last moment
Figure BDA0002602385810000098
The corresponding fitness is compared and if the fitness is better than the fitness
Figure BDA0002602385810000099
Corresponding to the fitness, then will
Figure BDA00026023858100000910
Updated to the position of the particle
Figure BDA00026023858100000911
Otherwise, keeping the state unchanged;
step S6, judging whether the optimal fitness reaches 0.06, if so, stopping iteration and outputting a global optimal position value; otherwise, repeating the steps S3-S5;
and step S7, taking the coordinate value in the global optimum position after meeting the requirement as the optimal solution as the parameter value required in the radial basis function neural network, establishing a radial basis function neural network prediction model, preprocessing the data set collected from the slope of which the stability needs to be predicted, inputting the preprocessed data set into the established prediction model, and obtaining the stability prediction of the model on the slope.
Example 2
Initialization of radial basis function neural network
Selecting six parameters of landform, topography and stratum lithology which affect one engineering geological condition of the slope stability factors, wherein the six parameters are respectively gravity, internal friction angle, cohesive force, slope inclination angle, pore water pressure and slope height, and the six parameters are used as input variables of a neural network; and establishing a training set, carrying out normalized data preprocessing, and keeping the original data by taking the slope stability coefficient as an output parameter.
Landform and terrain parameters:
slope inclination angle: the slope is at the size of space gradient, the acute angle that the slope face of slope and horizontal plane pressed from both sides. Research has shown that 86.72% of landslide occurs on slopes with slopes of 30-45 °, thereby indicating that the magnitude of slope angle is one of the important parameters affecting slope stability.
Height of the side slope: the vertical height from the top of the slope to the horizontal plane of the slope angle. No matter the slope is a soil slope or a rock slope, the higher the height of the slope, the larger the self-weight stress is, and the worse the slope stability is. Therefore, each slope angle has a corresponding upper limit of the slope height, and if the upper limit of the slope height exceeds the upper limit of the slope height, the risk of instability exists, and the two need to be considered together.
Formation lithology:
and (3) severe degree: refers to the weight of the unit volume of accumulated soil. The magnitude of the side slope gliding force is directly influenced by the slope gliding force, and under the condition that other conditions are not changed, the greater the side slope gliding force is, the higher the instability risk is, so severe factors need to be considered.
Pore water pressure: the stress is borne by water and transmitted by communicated pore water under the action of external force. A large amount of data show that water is one of important factors influencing the stability of the side slope, and the soil body can influence the gravity of the soil body under the action of pore water pressure after being soaked, so that the stability of the side slope is changed.
Internal friction angle: the mutual movement and the gluing action among the particles in the soil body form the friction characteristic. The numerical value is the included angle between the strength envelope and the horizontal line, and is one of the shear strength indexes of soil or rock, so that the numerical value is one of the most important factors influencing the slope stability.
Cohesive force: the mutual attraction between adjacent parts in the same substance is the expression of molecular force existing between the molecules of the same substance, is one of the indexes of the shear strength, and is the most important factor influencing the slope stability together with the internal friction angle.
Determining the number N of neurons of a hidden layer of the neural network, simultaneously determining a transfer function in the neurons, and establishing an initial radial basis function neural network architecture by using a Gaussian function added with a radial basis function expansion speed control factor.
Second, adopting improved particle swarm optimization to optimize parameters in radial basis function neural network
Determining the dimension of particles in the particle swarm, wherein the dimension consists of the centers, the widths and the weights of all neurons; the dimension calculation formula is: (6+1+1) N ═ 8N; since there are 6 input parameters, the center is a 6-dimensional value, the width and weight are respectively a value, the sum is multiplied by the total number of neurons, which is the total dimension of the particle, and the expression is:
Figure BDA0002602385810000111
wherein, mukOne of the dimensions, σ, representing the central value of the k-th neuronkDenotes the width, ω, of the k-th neuronkRepresenting the weight of the k-th neuron connected to the output layer.
And initializing the total number of particles in the particle swarm, the maximum iteration times, the upper limit and the lower limit of the particle speed and a fitness value function, and adopting the root mean square error of the actual slope stability coefficient and the predicted slope stability coefficient.
After initialization is completed, according to the algorithm steps of fig. 1, the local and global optimal positions are updated according to the fitness values of the particles obtained by each iteration. And stopping immediately when the required fitness is reached, wherein the global optimal position is the optimal radial basis function neural network parameter obtained through optimization.
Starting to train radial basis function neural network parameters: calculating the velocity of each particle according to equation (1)
Figure BDA0002602385810000112
Figure BDA0002602385810000113
Wherein the content of the first and second substances,
Figure BDA0002602385810000114
representing the velocity vector of the ith particle after t +1 iterations,
Figure BDA0002602385810000115
is the best position of the particle found by the ith particle after t iterations,
Figure BDA0002602385810000116
is the best position of the population, r, found after the population iterates t times1And r2Take [0, 1]Random number of cells, ωtThe weight factor is defined by the formula:
Figure BDA0002602385810000121
wherein, tmaxIs the maximum iteration number, t is the current iteration number,
Figure BDA0002602385810000122
the golden section ratio is 0.618.
Wherein, c1、c2The formula is defined as the learning factor:
c1＝2-cos(-tπ/2tmax) (3)
c2＝1+cos(-tπ/2tmax) (4)
in finding
Figure BDA0002602385810000123
Then, v is required and setmax、vminMake a comparison
Wherein v ismaxUpper limit of velocity, vminTo the lower velocity limit, the position of each particle is then calculated
Figure BDA0002602385810000125
Figure BDA0002602385810000126
Therein, in order to adapt to omegatThe change characteristic of (2) introduces a regulating factor beta into a position formula, and the formula is defined as follows:
Figure BDA0002602385810000127
wherein n is the total number of particles,
Figure BDA0002602385810000128
the fitness of the current particle is defined by the formula:
Figure BDA0002602385810000129
wherein the content of the first and second substances,
Figure BDA00026023858100001210
is a measured value, fi tFor the predicted value, the predicted value definition formula is:
Figure BDA0002602385810000131
wherein the content of the first and second substances,
Figure BDA0002602385810000132
is the connection coefficient of the output layer, obtained from the best position coordinate of the particle at this moment, N is the number of neurons of the hidden layer,
Figure BDA0002602385810000133
is a radial basis function, which is defined by the formula:
Figure BDA0002602385810000134
wherein the content of the first and second substances,
Figure BDA0002602385810000135
as a parameter of the width of the strip,
Figure BDA0002602385810000136
the central value is obtained from the optimal position coordinates of the particle at the moment, and alpha is a radial basis function expansion speed control factor and is defined by the following formula:
Figure BDA0002602385810000137
wherein gamma is an adjusting factor which can be controlled by a worker;
the fitness obtained from the current time of each particle
Figure BDA0002602385810000138
Fitness with last moment
Figure BDA0002602385810000139
Comparing, if the fitness value of the particle at the moment is better than the fitness value at the previous moment, replacing the value of the individual optimal position with the position at the moment
Figure BDA00026023858100001310
Otherwise it remains unchanged.
Comparing the updated fitness of all the particles at the moment, and selecting the best fitness from the updated fitness and the fitness of the particles at the last moment
Figure BDA00026023858100001311
The corresponding fitness is compared and if the fitness is better than the fitness
Figure BDA00026023858100001312
Corresponding to the fitness, then will
Figure BDA00026023858100001313
Updated to the position of the particle
Figure BDA00026023858100001314
Otherwise it remains unchanged.
After the requirement of the optimal fitness is met,
Figure BDA00026023858100001315
i.e. the optimal solution.
And establishing an optimized RBF neural network prediction model to predict the slope stability coefficient, inputting six preprocessed parameters of the slope needing to predict the stability coefficient to obtain the predicted slope stability coefficient, and finishing the algorithm.
Benchmark test validation
1. Verification method
In order to verify the performance of the improved PSO-RBF neural network, this section will perform model training and data prediction on a set of data collected by the actual slope. There were 70 sets of slope data, 55 as training data and 15 as test data. The number of the neurons of the hidden layer in the radial basis function neural network is set to be 30, the number of particle swarm particles is 50, the maximum iteration time is 400, and the RBF neural network, the PSO-RBF neural network and the improved PSO-RBF neural network provided by the patent are compared.
2. Degree of adaptability
First, the conventional PSO algorithm is compared with the PSO algorithm that optimizes the inertial weight alone, the learning factor alone, and both parameters at the same time, as shown in fig. 2, 3, and 4. When the traditional PSO algorithm iterates to about 250 steps, the optimal fitness is 1.07, so that the situation that the traditional algorithm is slow in later convergence and falls into a local optimal solution is not easily seen; the PSO algorithm for independently optimizing the learning factors reaches the optimal fitness of 0.97 when the iteration reaches about 150 steps; the PSO algorithm for independently optimizing the inertia weight reaches the optimal fitness of 0.08 in about 110 steps, so that the improvement on two parameters improves the convergence speed and the search precision of the PSO algorithm, and the inertia weight is more obvious; when two parameters are optimized simultaneously, the PSO algorithm reaches the optimal fitness of 0.6 in about 65 steps, so that the improved combination of the two parameters supplements each other, and the performance of the particle swarm algorithm is further improved.
3. Accuracy of prediction
In order to more accurately evaluate the performance of the model, the following 3 error formulas are used as evaluation indexes, namely, Mean Absolute Error (MAE), Mean Relative Error (MRE), and Mean Square Error (MSE), and the formulas are:
Figure BDA0002602385810000141
Figure BDA0002602385810000151
Figure BDA0002602385810000152
fig. 5 is a graph comparing the predicted effect of the RBF neural network added with the alpha factor with that of the conventional RBF neural network, and table 1 is an error evaluation index comparison.
TABLE 1 error evaluation index COMPARATIVE TABLE
Figure BDA0002602385810000153
It is easily obtained from fig. 5 and table 1 that the conventional RBF neural network has a large error in predicting the slope stability coefficient, and the prediction accuracy of the RBF neural network added with the radial basis function velocity expansion factor is significantly improved.
FIG. 6 is a comparison graph of the predicted effects of the conventional RBF neural network, the PSO-RBF neural network and the improved PSO-RBF neural network, and Table 2 is a comparison of error evaluation indexes.
TABLE 2 error evaluation index comparison table
Figure BDA0002602385810000154
The accuracy of the predicted value of the PSO-optimized RBF neural network is obviously improved, and MSE, MAE and MRE values are all larger than those of the RBF neural network, so that the particle swarm optimization has the optimization capability on the RBF neural network, and meanwhile, compared with the prediction accuracy of the traditional PSO-RBF neural network, the improved PSO-RBF neural network is improved greatly, and the stability of the predicted value is also obviously improved.
Those skilled in the art will appreciate that the invention may be practiced without these specific details. Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (2)

1. The slope stability prediction method based on the improved PSO-RBF algorithm is characterized by comprising the following steps: initializing a radial basis function neural network, optimizing parameters of the radial basis function neural network by adopting a particle swarm optimization algorithm based on a normal attenuation inertia weight factor, constructing a brand new radial basis function neural network prediction model according to optimal parameters of the radial basis function neural network calculated by the optimization algorithm, and predicting slope stability by using the improved radial basis function neural network prediction model.
2. The improved PSO-RBF algorithm-based slope stability prediction method according to claim 1, characterized in that: the method specifically comprises the following steps:
step S1, initializing the radial basis function neural network, determining the structure of the radial basis function neural network,
step S2, initializing the particle group: setting the scale, the iteration times, the weight factor, the initial value and the end value of learning, the initial speed and the initial position of each particle, the individual optimal position and the global optimal position of the population;
step S3, training radial basis function neural network parameters: calculating the velocity of each particle according to equation (1)
Figure FDA0002602385800000011
Figure FDA0002602385800000012
Wherein the content of the first and second substances,
Figure FDA0002602385800000013
representing the velocity vector of the ith particle after t +1 iterations,
Figure FDA0002602385800000014
is the firstThe optimal positions of the particles found by the i particles after t iterations,
Figure FDA0002602385800000015
is the best position of the population, r, found after the population iterates t times1And r2Take [0, 1]Random number of cells, ωtThe weight factor is defined by the formula:
Figure FDA0002602385800000016
wherein, tmaxIs the maximum iteration number, t is the current iteration number,
Figure FDA0002602385800000017
the golden section ratio is 0.618;
wherein, c1、c2The formula is defined as the learning factor:
c1＝2-cos(-tπ/2tmax) (3)
c2＝1+cos(-tπ/2tmax) (4)
in finding
Figure FDA0002602385800000021
Then, v is required and setmax、vminMake a comparison
Figure FDA0002602385800000022
Wherein v ismaxUpper limit of velocity, vminTo the lower velocity limit, the position of each particle is then calculated
Figure FDA0002602385800000023
Figure FDA0002602385800000024
Therein, in order to adapt to omegatThe change characteristic of (2) introduces a regulating factor beta into a position formula, and the formula is defined as follows:
Figure FDA0002602385800000025
wherein n is the total number of particles,
Figure FDA0002602385800000026
the fitness of the current particle is defined by the formula:
Figure FDA0002602385800000027
wherein the content of the first and second substances,
Figure FDA0002602385800000028
is a measured value, fi tFor the predicted value, the predicted value definition formula is:
Figure FDA0002602385800000029
wherein the content of the first and second substances,
Figure FDA00026023858000000210
is the connection coefficient of the output layer, obtained from the best position coordinates of the particle at this moment,
n is the number of neurons in the hidden layer,
Figure FDA00026023858000000211
is a radial basis function, which is defined by the formula:
Figure FDA0002602385800000031
wherein the content of the first and second substances,
Figure FDA0002602385800000032
as a parameter of the width of the strip,
Figure FDA0002602385800000033
the central value is obtained from the optimal position coordinates of the particle at the moment, and alpha is a radial basis function expansion speed control factor and is defined by the following formula:
Figure FDA0002602385800000034
wherein gamma is an adjusting factor which can be controlled by a worker;
step S4, the fitness obtained for each particle at the current time
Figure FDA0002602385800000035
Fitness with last moment
Figure FDA0002602385800000036
Comparing, if the fitness value of the particle at the moment is better than the fitness value at the previous moment, replacing the value of the individual optimal position with the position at the moment
Figure FDA0002602385800000037
Otherwise, keeping the state unchanged;
step S5, comparing the updated fitness of all the particles at the moment, and selecting the best fitness with the fitness at the last moment
Figure FDA0002602385800000038
The corresponding fitness is compared and if the fitness is better than the fitness
Figure FDA0002602385800000039
Corresponding to the fitness, then will
Figure FDA00026023858000000310
Updated to the position of the particle
Figure FDA00026023858000000311
Otherwise, keeping the state unchanged;
step S6, judging whether the optimal fitness reaches 0.06, if so, stopping iteration and outputting a global optimal position value; otherwise, repeating the steps S3-S5;
and step S7, taking the coordinate value in the global optimum position after meeting the requirement as the optimal solution as the parameter value required in the radial basis function neural network, establishing a radial basis function neural network prediction model, preprocessing the data set collected from the slope of which the stability needs to be predicted, inputting the preprocessed data set into the established prediction model, and obtaining the stability prediction of the model on the slope.
CN202010729020.8A 2020-07-27 2020-07-27 Slope stability prediction method based on improved PSO-RBF algorithm Active CN111914481B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010729020.8A CN111914481B (en) 2020-07-27 2020-07-27 Slope stability prediction method based on improved PSO-RBF algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010729020.8A CN111914481B (en) 2020-07-27 2020-07-27 Slope stability prediction method based on improved PSO-RBF algorithm

Publications (2)

Publication Number Publication Date
CN111914481A true CN111914481A (en) 2020-11-10
CN111914481B CN111914481B (en) 2022-03-18

Family

ID=73281124

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010729020.8A Active CN111914481B (en) 2020-07-27 2020-07-27 Slope stability prediction method based on improved PSO-RBF algorithm

Country Status (1)

Country Link
CN (1) CN111914481B (en)

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112710401A (en) * 2021-03-29 2021-04-27 国网江西省电力有限公司供电服务管理中心 Method for detecting temperature of electric energy meter terminal
CN112733423A (en) * 2020-12-03 2021-04-30 重庆邮智机器人研究院有限公司 Industrial robot inverse kinematics solving method based on PSO-RBFNN
CN112945162A (en) * 2021-01-26 2021-06-11 山西大学 Accumulation layer landslide displacement prediction model and prediction method
CN113283183A (en) * 2021-07-08 2021-08-20 国网新源控股有限公司 Waste slag dam deformation prediction method based on DPSO-ANFIS
CN114118365A (en) * 2021-11-08 2022-03-01 北京理工大学 Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network
CN114692441A (en) * 2022-02-17 2022-07-01 成都理工大学 Loess landslide stability prediction method, electronic device and storage medium
CN116579245A (en) * 2023-05-16 2023-08-11 中国兵器装备集团自动化研究所有限公司 Grain density prediction method and device
WO2024001942A1 (en) * 2022-06-30 2024-01-04 西南交通大学 Mountainous area slope displacement prediction method based on mi-gra and improved pso-lstm
CN117494282A (en) * 2023-11-23 2024-02-02 桂林理工大学 Slope stability prediction method, system, equipment and medium based on parameter optimization

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104361393A (en) * 2014-09-06 2015-02-18 华北电力大学 Method for using improved neural network model based on particle swarm optimization for data prediction
CN109919489A (en) * 2019-03-08 2019-06-21 北京工业大学 Business equipment life-span prediction method based on enterprise asset management and GA-BP
CN110708318A (en) * 2019-10-10 2020-01-17 国网湖北省电力有限公司电力科学研究院 Network abnormal flow prediction method based on improved radial basis function neural network algorithm
CN111310902A (en) * 2020-02-24 2020-06-19 石家庄铁道大学 Training method of neural network model, slope displacement prediction method and related device
CN111351668A (en) * 2020-01-14 2020-06-30 江苏科技大学 Diesel engine fault diagnosis method based on optimized particle swarm algorithm and neural network

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104361393A (en) * 2014-09-06 2015-02-18 华北电力大学 Method for using improved neural network model based on particle swarm optimization for data prediction
CN109919489A (en) * 2019-03-08 2019-06-21 北京工业大学 Business equipment life-span prediction method based on enterprise asset management and GA-BP
CN110708318A (en) * 2019-10-10 2020-01-17 国网湖北省电力有限公司电力科学研究院 Network abnormal flow prediction method based on improved radial basis function neural network algorithm
CN111351668A (en) * 2020-01-14 2020-06-30 江苏科技大学 Diesel engine fault diagnosis method based on optimized particle swarm algorithm and neural network
CN111310902A (en) * 2020-02-24 2020-06-19 石家庄铁道大学 Training method of neural network model, slope displacement prediction method and related device

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
NANNAN LI: "A method based on PSO-RBF to the optimization of dam structure", 《2011 CHINESE CONTROL AND DECISION CONFERENCE(CCDC)》 *
张敏敏等: "基于GPS和神经网络的滑坡位移监测算法", 《计算机测量与控制》 *
徐浩天等: "基于正态分布衰减惯性权重的粒子群优化算法", 《深圳大学学报(理工版)》 *
林宇锋等: "基于新的改进粒子群算法的BP神经网络在拟合非线性函数中的应用", 《计算机科学》 *
江龙艳: "基于PSO―BP神经网络的边坡稳定性模型研究", 《有色金属(矿山部分)》 *
胡昊等: "基于PSO-RBF的边坡安全系数预测", 《河南科学》 *

Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112733423A (en) * 2020-12-03 2021-04-30 重庆邮智机器人研究院有限公司 Industrial robot inverse kinematics solving method based on PSO-RBFNN
CN112945162A (en) * 2021-01-26 2021-06-11 山西大学 Accumulation layer landslide displacement prediction model and prediction method
CN112710401A (en) * 2021-03-29 2021-04-27 国网江西省电力有限公司供电服务管理中心 Method for detecting temperature of electric energy meter terminal
CN112710401B (en) * 2021-03-29 2021-08-24 国网江西省电力有限公司供电服务管理中心 Method for detecting temperature of electric energy meter terminal
CN113283183A (en) * 2021-07-08 2021-08-20 国网新源控股有限公司 Waste slag dam deformation prediction method based on DPSO-ANFIS
CN114118365A (en) * 2021-11-08 2022-03-01 北京理工大学 Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network
CN114692441A (en) * 2022-02-17 2022-07-01 成都理工大学 Loess landslide stability prediction method, electronic device and storage medium
CN114692441B (en) * 2022-02-17 2023-05-09 成都理工大学 Loess landslide stability prediction method, electronic equipment and storage medium
WO2024001942A1 (en) * 2022-06-30 2024-01-04 西南交通大学 Mountainous area slope displacement prediction method based on mi-gra and improved pso-lstm
CN116579245A (en) * 2023-05-16 2023-08-11 中国兵器装备集团自动化研究所有限公司 Grain density prediction method and device
CN116579245B (en) * 2023-05-16 2024-05-14 中国兵器装备集团自动化研究所有限公司 Grain density prediction method and device
CN117494282A (en) * 2023-11-23 2024-02-02 桂林理工大学 Slope stability prediction method, system, equipment and medium based on parameter optimization

Also Published As

Publication number Publication date
CN111914481B (en) 2022-03-18

Similar Documents

Publication Publication Date Title
CN111914481B (en) Slope stability prediction method based on improved PSO-RBF algorithm
CN109343505A (en) Gear method for predicting residual useful life based on shot and long term memory network
CN111538076B (en) Earthquake magnitude rapid estimation method based on deep learning feature fusion
CN110807557A (en) Drilling rate prediction method based on BP neural network and drilling rate optimization method based on BP neural network and particle swarm optimization
CN112083498B (en) Multi-wave earthquake oil and gas reservoir prediction method based on deep neural network
CN109614580A (en) Antidetonation bulk testing model update method based on online Xgboost algorithm
CN111784070A (en) Intelligent landslide short-term early warning method based on XGboost algorithm
CN103489039B (en) There is the freeway traffic flow amount fusion forecasting method of online self-tuning optimization ability
CN106483559B (en) A kind of construction method of subsurface velocity model
CN115906675B (en) Well position and injection and production parameter joint optimization method based on time sequence multi-target prediction model
CN112699572A (en) Method for predicting landslide deformation based on time-lag correlation analysis
CN114818076B (en) Machine learning-based fault closed hydrocarbon column height evaluation method
CN107843920A (en) A kind of cluster analysis optimizes population reservoir attribute Forecasting Methodology
CN112487695A (en) Multi-target intelligent comprehensive line selection method for railway in complex environment
CN110119590A (en) A kind of water quality model particle filter assimilation method based on multi-source observation data
CN114722731B (en) Method and system for predicting drag viscous drag resistance of towed body
CN113610945A (en) Ground stress curve prediction method based on hybrid neural network
CN111045080A (en) Coal bed gas content prediction method based on PSO-BP model and seismic attribute parameters
CN105976025A (en) BP neural network gas prediction method based on genetic algorithm optimization
CN116151102A (en) Intelligent determination method for space target ultra-short arc initial orbit
KR102155101B1 (en) System and method for predicting ground layer information, and a recording medium having computer readable program for executing the method
CN116881676B (en) Prediction method for water inflow of open pit
CN111209528B (en) Slope accumulated displacement grading early warning threshold value determination method
CN112819087A (en) Effluent BOD sensor abnormity detection method based on modular neural network
CN116402209A (en) Three gorges reservoir dam front drift prediction method based on improved neural network model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant