CN111444569A - Beam structure measuring point optimization method based on improved particle swarm optimization - Google Patents

Beam structure measuring point optimization method based on improved particle swarm optimization Download PDF

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CN111444569A
CN111444569A CN202010250782.XA CN202010250782A CN111444569A CN 111444569 A CN111444569 A CN 111444569A CN 202010250782 A CN202010250782 A CN 202010250782A CN 111444569 A CN111444569 A CN 111444569A
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陆观
刘宏林
徐一鸣
邱自学
邓勇
袁江
邵建新
蔡婷
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Abstract

The invention discloses a beam structure measuring point optimizing method based on an improved particle swarm algorithm. The method provides an improved particle swarm algorithm based on a simulated annealing thought and a genetic algorithm, comprehensively considers stress state identification errors and measurement point optimization, and screens measurement points. Firstly, the initialization, selection, crossing and variation of the genetic algorithm are integrated into the particle swarm algorithm, and secondly, the idea of simulated annealing is introduced into the variation part. The improved particle swarm algorithm improves the problems of 'precocity' of the standard particle swarm algorithm, poor local optimization capability and the like. The algorithm has higher efficiency in the measuring point selection process of stress state identification, can reasonably reduce the number of measuring points, effectively improves the identification accuracy of the measuring point selection scheme, and provides a better measuring point optimization method for the beam structure stress state identification.

Description

Beam structure measuring point optimization method based on improved particle swarm optimization
Technical Field
The invention relates to screening of measuring points in a stress process of a beam structure, in particular to a beam structure measuring point optimizing method based on an improved particle swarm algorithm.
Background
The I-shaped beam can save materials and obtain the moment of inertia of a rectangular section with the length close to the same as that of the outer contour so as to resist bending; the web and the width of the beam are approximately the same, so that the beam can bear larger load; the beam can balance external force in the directions parallel to and vertical to the web plate, so that the beam is widely applied in the engineering field and has important significance in identifying the stress state of the beam. In the measuring process, the selection of measuring points is taken as a key link, and the measuring precision of the stress state is directly influenced. The selection of the measuring point is an extremely important link in the stress state measurement, and especially for various stress state identification problems such as axial force, shearing force, bending moment, torsion and the like, how to obtain a better identification result by using fewer sensors is of great importance in the whole stress state measurement process.
At present, a great deal of research is carried out on a sensing point network optimization method at home and abroad, and commonly used sensing point optimization methods comprise a sensing point network optimization method based on a state recognition probability criterion, an effective independent method, a sensing point network construction method based on an information theory, a classical optimization algorithm and a heuristic algorithm based on an optimization criterion. With the continuous development of computer information technology and the continuous improvement of computer computing efficiency, a heuristic algorithm based on optimization criteria is in compliance with the trend of the times and gradually enters the sight of researchers. For the optimization problem of modern large-scale industrial structure sensing points, the advantage of a heuristic algorithm based on an optimization criterion is increasingly highlighted. In recent years, genetic algorithm or particle swarm algorithm is applied to the engineering to screen the sensing point network of the structure to be measured.
The genetic algorithm refers to a natural world competitive selection mechanism, simulates species evolution, realizes population evolution through operators such as selection, intersection, variation and the like, and has strong optimizing capacity. In both articles, namely a Sensor arrangement method based On multiple optimization strategies in structural health monitoring and a Sensor development for On-Orbit model identification vision, the position arrangement of sensing points is optimized by using operation modes such as selection, intersection and variation of genetic algorithms.
The particle swarm optimization is widely applied to various research fields, for example, in the technical field of automation of electric power systems, a patent of 'an economic dispatching optimization strategy of a micro-grid based on improved particle swarm optimization' adopts the particle swarm optimization of an improved equality constraint processing method, within a constraint range, the dispatching output of a generator set and the energy of energy storage charging and discharging are continuously adjusted, and the optimal particles are searched, so that the running cost of the micro-grid system is lowest; in the patent of 'a wheel profile multi-target optimization method based on an improved particle swarm optimization', the improved particle swarm optimization is used for carrying out iterative solution on a multi-target optimization model, and finally, an optimized low-wear wheel profile is obtained. The improved particle swarm optimization is based on the improved particle swarm optimization, the optimized profile has good vehicle running safety, running stability and curve passing performance, and meanwhile, the wheel track abrasion is reduced; in the patent of an under-actuated mechanical arm joint angle optimizing method based on an improved particle swarm algorithm, a difference value between the tail end position of an under-actuated mechanical arm and a target position is taken as an objective function, a Metropolis acceptance criterion of simulated annealing and a crowding factor of an artificial fish swarm algorithm are introduced based on an optimizing principle of the particle swarm algorithm, and an optimal joint angle corresponding to the target position is solved. According to the technical scheme, when the position of the mechanical arm is under-driven, the probability of the optimization algorithm falling into local optimization can be reduced, and the solving precision is improved. The particle swarm optimization method improves the particle swarm optimization according to different research directions, so that the optimization of the result is realized.
The two algorithms can objectively and effectively optimize the measuring point network, but the problems of 'precocity' and poor local optimization capability still exist in the actual operation process, so that the phenomenon that the selected position of the measuring point is not optimal is caused.
Disclosure of Invention
In view of the above, the invention provides a genetic and particle swarm hybrid algorithm with a simulated annealing thought, which overcomes the defect that the particle swarm algorithm is easy to fall into local minimum, and comprehensively considers two factors of the number of measuring points and the identification error of a stress state to screen the measuring points, so that the beam structure measuring points can be conveniently screened.
In order to solve the technical problems, the invention adopts the following technical scheme:
s1, a measuring point optimizing model of an I-beam structure is constructed in advance, and the measuring point optimizing model comprises an objective function and constraint conditions;
s2, randomly generating N populations according to the constraint conditions; each of the N populations comprises M particles, each particle forms a solution space of the mathematical model, and both N and M are positive integers;
s3, performing iteration updating on each current population for S times respectively to obtain N updated populations, wherein S is a positive integer;
s4, screening out global optimal particles from the updated N populations, and determining all solutions in a solution space corresponding to the global optimal particles as optimal measuring point parameters of the I-beam structure;
wherein, in the process of performing iteration update for each current population for S times, each iteration in the iteration for S times includes:
s31: calculating the fitness value and the temperature of the population according to the simulated annealing idea;
s32: updating the speed and position of each particle in the population, screening each particle by adopting an improved roulette method according to a genetic algorithm, and then crossing and mutating the screened particles;
wherein, adopt an improved roulette method to carry out the screening, specifically do:
using fitness function maximum FtmaxSubtracting the fitness function value F corresponding to each particle in the populationtAnd screening all particles in the population by a first probability, wherein a calculation formula of the first probability is as follows:
Figure BDA0002435402540000021
wherein, Ft′=Ftmax-Ft,FtIs the vector of fitness in the current population, t represents the current population algebra, FtmaxIs the maximum value of fitness in the current population, PiIs the first probability that the ith particle is screened.
Further, in step S32, the crossing and mutation of the screened particles includes the following steps:
selecting a certain number of particles from the particles obtained by screening, placing the particles into a hybridization pool, randomly performing cross operation on the particles in the hybridization pool to obtain cross-mutated daughter particles, selecting the cross-mutated daughter particles according to a second probability, and constructing a new population together with parent particles which do not enter the hybridization pool, wherein the second probability has the following calculation formula:
Figure BDA0002435402540000022
where, dE ═ f '-f, f' is the value of fitness corresponding to the cross-mutated particle, dE is the difference between the fitness value after cross-mutation and the fitness value corresponding to the previous generation particle, and p is the second probability of selecting the cross-mutated child particle.
Further, in step S32, the updating the speed and the position of each particle in the population is specifically performed according to the following formula:
Vi(k+1)=ωVi(k)+c1rand(pbesti(k)-Vi(k))+c2rand(gbest(k)-Xi(k)),
Xi(k+1)=Xi(k)+Vi(k+1),
wherein, Xi(k +1) is the position vector of the i-th generation iteration particle of k +1, Vi(k +1) is the velocity vector of the (k +1) th generation iterative particle i, ω is the inertial weight, c1And c2As a learning factor, pbesti(k) For the optimal solution found by the k-th iteration particle i itself, gbest (k) is the optimal solution found by the whole population in the k-th iteration.
Further, the objective function is determined according to the strain magnitude and the position of each measuring point, and the constraint condition is determined according to the strain and the position change range of the measuring points.
In summary, the following beneficial effects of the invention are:
(1) aiming at the conditions of various stress of a beam structure, the invention provides an improved particle swarm algorithm based on simulated annealing and a genetic algorithm for measuring point selection, and a more optimal measuring point combination is found by checking the relation among the positions, the number and the errors of the measuring points through errors, thereby providing a measuring point optimization method basis for the identification process of various stress states in the operation process.
(2) The improved algorithm provided by the invention integrates the annealing thought of the simulated annealing algorithm and the selection, intersection and variation method in the genetic algorithm. The performance test of the algorithm shows that the minimum value searched by the improved particle swarm algorithm is much smaller than that of the standard particle swarm algorithm, and the improved particle swarm algorithm tends to be stable earlier than that of the standard particle swarm algorithm, so that the improved particle swarm algorithm not only maintains the rapid reduction of the early function value of the particle swarm algorithm, but also overcomes the defect of 'prematurity' of the original algorithm, and the searching performance of the algorithm is greatly improved.
(3) According to the invention, the experimental results of the optimization at the measuring point by comparing the improved particle swarm algorithm with the standard particle swarm algorithm show that the improved algorithm has higher precision and shorter time consumption than the standard particle swarm algorithm; compared with the traditional measuring point selection method, the improved particle swarm optimization has little deviation in measuring point selection but small difference between an exhaustion method and a fast descent method, but greatly improves the efficiency, and overcomes the defect that only the stress state identification error and the beam type adjustment measuring point number are considered in the traditional measuring point optimization method.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of a standard particle swarm algorithm in an embodiment of the present invention;
FIG. 2 is a flow chart of an improved particle swarm algorithm in the embodiment of the invention.
Detailed description of the preferred embodiments
For a further understanding of the invention, reference will now be made to the preferred embodiments of the present invention by way of example, and it is to be understood that the description is intended to further illustrate features and advantages of the present invention and is not intended to limit the scope of the claims which follow.
Referring to fig. 2, the invention provides a beam structure measuring point optimizing method based on an improved particle swarm optimization algorithm, which comprises the following steps:
s1, a measuring point optimizing model of an I-beam structure is constructed in advance, and the measuring point optimizing model comprises an objective function and constraint conditions;
in the embodiment, a measuring point optimizing model is established according to the positions and the strain information of I-beam measuring points, an objective function in the model is determined according to the strain magnitude and the positions of the measuring points, and constraint conditions are determined according to the strain and the position change range of the measuring points.
S2, randomly generating N populations according to constraint conditions; each of the N populations comprises M particles, each particle forms a solution space of the mathematical model, and both N and M are positive integers;
in this embodiment, the nature of the population is a solution set of the objective function, and the nature of the particle is a solution of the objective function. In this embodiment, any one population includes M particles, that is, M solutions. Both the N value and the M value may be set according to actual application requirements, and for example, the N value may be set to 10 and the M value may be set to 100.
It is understood that, in the present embodiment, when any particle of any population is generated, the solution formed by the particle needs to satisfy the constraint condition.
S3, performing iteration updating on each current population for S times respectively to obtain N updated populations, wherein S is a positive integer;
wherein, in the process of performing iteration update for each current population for S times, each iteration in the iteration for S times includes:
s31: calculating the fitness value and the temperature of the population according to the simulated annealing idea;
s32: updating the speed and position of each particle in the population, screening each particle by adopting an improved roulette method according to a genetic algorithm, and then crossing and mutating the screened particles;
in an embodiment of the present invention, the velocity and position of each particle in the population may be updated according to the following formula, specifically:
Vi(k+1)=ωVi(k)+c1rand(pbesti(k)-Vi(k))+c2rand(gbest(k)-Xi(k)),
Xi(k+1)=Xi(k)+Vi(k+1),
wherein, Xi(k +1) is the position vector of the i-th generation iteration particle of k +1, Vi(k +1) is the velocity vector of the (k +1) th generation iterative particle i, ω is the inertial weight, c1And c2As a learning factor, pbesti(k) For the optimal solution found by the K-th iteration particle i itself, gbest (K) is the optimal solution found by the whole population in the K-th iteration.
In the embodiment of the invention, an improved roulette method is adopted for screening, and the method specifically comprises the following steps:
using fitness function maximum FtmaxSubtracting the fitness function value F corresponding to each particle in the populationtAnd screening all particles in the population by a first probability, wherein a calculation formula of the first probability is as follows:
Figure BDA0002435402540000031
wherein, Ft′=Ftmax-Ft,FtIs the vector of fitness in the current population, t represents the current population algebra, FtmaxIs the maximum value of fitness in the current population, PiIs the first probability that the ith particle is screened.
In the embodiment of the invention, the crossing and variation of the particles obtained by screening comprises the following steps:
selecting a certain number of particles from the particles obtained by screening, placing the particles into a hybridization pool, randomly performing cross operation on the particles in the hybridization pool to obtain cross-mutated progeny particles, selecting the cross-mutated progeny particles according to a second probability, and constructing a new population together with parent particles which do not enter the hybridization pool, so as to improve the global optimum searching capability of the particles. The calculation formula of the second probability is as follows:
Figure BDA0002435402540000041
where, dE ═ f '-f, f' is the value of fitness corresponding to the cross-mutated particle, dE is the difference between the fitness value after cross-mutation and the fitness value corresponding to the previous generation particle, and p is the second probability of selecting the cross-mutated child particle.
S4, screening out global optimal particles from the updated N populations, and determining all solutions in a solution space corresponding to the global optimal particles as optimal measuring point parameters of the I-beam structure.
Examples
Selecting an I-beam structure as a simplified model of a complex structure, carrying out statics analysis on the I-beam structure in ANSYS finite element analysis software, selecting A L as a material parameter of the I-beam structure in order to make the strain expression of the structure more obvious, selecting axial force as a loading force for stress state identification, preliminarily selecting 60 measuring points on the surface of the I-beam according to ANSYS simulation results, structural characteristics and an FBG strain sensing effective area, using the positions and strain information of the 60 measuring points as the positions and speeds of particles, and then carrying out measuring point optimization on the 60 measuring points according to an improved particle swarm algorithm.
And establishing a measuring point optimizing model by taking the positions and strain information of the 60 measuring points as the positions and the speeds of the particles, wherein an object function in the model is determined according to the strain magnitude and the positions of the measuring points, constraint conditions are determined according to the strain range (1-400 micro strains) and the position change range (1-60) of the measuring points, and a fitness function is set as fitness ═ inline ('(x (1) ^2+ x (2) ^2)/1000', 'x').
According to the constraint condition, if the number of required mesh mapping points is 2, randomly generating 2 populations, wherein each population in the 2 populations comprises 30 particles, and each particle forms a solution space of the mathematical model; if the number of required mesh points is 3, 3 populations are randomly generated, wherein each population of the 3 populations comprises 20 particles, each particle constituting a solution space of the mathematical model.
Then, we set the maximum iteration number maxnum to 100, the argument number narvs of the objective function to 2, the maximum velocity vmax of the particle to 5, the position information to the entire search space, we randomly initialize the velocity and position in the velocity interval and the search space, set the particle swarm size to 60, and randomly initialize one flight velocity for each particle.
And each current population is respectively subjected to 100 times of iterative updating according to the following formula, the speed and the position of each particle in the population are updated,
Vi(k+1)=ωVi(k)+c1rand(pbesti(k)-Vi(k))+c2rand(gbest(k)-Xi(k)),
Xi(k+1)=Xi(k)+Vi(k+1),
wherein, Xi(k +1) is the position vector of the i-th generation iteration particle of k +1, Vi(k +1) is the iterative particle i velocity vector of the (k +1) th generation, ω is the inertial weight set to 0.6, c1And c2For learning factor settingIs set as 2, pbesti(k) For the optimal solution found by the K-th iteration particle i itself, gbest (K) is the optimal solution found by the whole population in the K-th iteration.
Then, each particle after updating is screened by adopting an improved roulette method, namely, the fitness function maximum value FtmaxSubtracting the fitness function value F corresponding to each particle in the populationtAnd screening all particles in the population by a first probability, wherein a calculation formula of the first probability is as follows:
Figure BDA0002435402540000042
then, the particles obtained by screening are crossed and mutated, namely a certain number of particles are selected from the particles obtained by screening and are put into a hybridization pool, the particles in the hybridization pool are randomly crossed to obtain filial particles after cross mutation, the filial particles after cross mutation are selected according to a second probability, and a new population is constructed together with the father particles which do not enter the hybridization pool, wherein the calculation formula of the second probability is as follows:
Figure BDA0002435402540000043
where, dE ═ f '-f, f' is the value of fitness corresponding to the cross-mutated particle, dE is the difference between the fitness value after cross-mutation and the fitness value corresponding to the previous generation particle, and p is the second probability of selecting the cross-mutated child particle.
And screening out global optimal particles from the updated population, and determining all solutions in a solution space corresponding to the global optimal particles as optimal measuring point parameters of the I-beam structure.
And (3) setting parameters of the optimal solution number of the model according to different target measuring point number requirements, and performing superiority comparison experiments of the algorithm by using a fast descent method and a standard particle swarm algorithm. The standard particle swarm algorithm flowchart is shown in fig. 1. The fast descent method adopts a method recorded in a thesis of a recognition method for loads of complex sections of long and thin structures. And comparing and analyzing the combination mode of the measuring points, the recognition percentage error of the stress state and the time required by training based on the training results of different algorithms.
The results when the number of selected mesh points for training was 2 were analyzed, and the results are shown in table 1. The fast descent method, the standard particle swarm algorithm and the improved particle swarm algorithm can find out two proper measuring point combinations, the identification percentage error of the stress state of the improved particle swarm algorithm is the minimum, the identification percentage error of the stress state of the standard particle swarm algorithm is the second, the identification percentage error of the stress state of the fast descent method is the maximum, and the time difference required by program operation is not much.
The results when the number of selected mesh points for training was 3 were analyzed, and the results are shown in table 2. The fast descent method, the standard particle swarm algorithm and the improved particle swarm algorithm can find the combination of three proper measuring points, the identification percentage error of the stress state of the improved particle swarm algorithm is the minimum, the identification percentage error of the stress state of the standard particle swarm algorithm is the second, the identification percentage error of the stress state of the fast descent method is the maximum, and the efficiency advantage of the improved particle swarm algorithm is obvious compared with the condition that the time required by program operation and the number of the measuring points are 2.
Table 1 three methods for identifying results when the number of axial force identification geodesic points is 2
Figure BDA0002435402540000051
Table 2 three methods for identifying results when the number of axial force identification geodesic points is 3
Figure BDA0002435402540000052
The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

Claims (4)

1. A beam structure measuring point optimizing method based on an improved particle swarm algorithm is characterized by comprising the following steps:
s1, a measuring point optimizing model of an I-beam structure is constructed in advance, and the measuring point optimizing model comprises an objective function and constraint conditions;
s2, randomly generating N populations according to the constraint conditions; each of the N populations comprises M particles, each particle forms a solution space of the mathematical model, and both N and M are positive integers;
s3, performing iteration updating on each current population for S times respectively to obtain N updated populations, wherein S is a positive integer;
s4, screening out global optimal particles from the updated N populations, and determining all solutions in a solution space corresponding to the global optimal particles as optimal measuring point parameters of the I-beam structure;
wherein, in the process of performing iteration update for each current population for S times, each iteration in the iteration for S times includes:
s31: calculating the fitness value and the temperature of the population according to the simulated annealing idea;
s32: updating the speed and position of each particle in the population, screening each particle by adopting an improved roulette method according to a genetic algorithm, and then crossing and mutating the screened particles;
wherein, adopt an improved roulette method to carry out the screening, specifically do:
using fitness function maximum FtmaxSubtracting the fitness function value F corresponding to each particle in the populationtAnd screening all particles in the population by a first probability, wherein a calculation formula of the first probability is as follows:
Figure FDA0002435402530000011
wherein, Ft′=Ftmax-Ft,FtIs the vector of fitness in the current population, t represents the current population algebra, FtmaxIs the maximum value of fitness in the current population, PiIs the first probability that the ith particle is screened.
2. The method for optimizing a measuring point of a beam structure according to claim 1, wherein in step S32, the step of crossing and mutating the screened particles comprises the following steps:
selecting a certain number of particles from the particles obtained by screening, placing the particles into a hybridization pool, randomly performing cross operation on the particles in the hybridization pool to obtain cross-mutated daughter particles, selecting the cross-mutated daughter particles according to a second probability, and constructing a new population together with parent particles which do not enter the hybridization pool, wherein the second probability has the following calculation formula:
Figure FDA0002435402530000012
where, dE ═ f '-f, f' is the value of fitness corresponding to the cross-mutated particle, dE is the difference between the fitness value after cross-mutation and the fitness value corresponding to the previous generation particle, and p is the second probability of selecting the cross-mutated child particle.
3. The method for optimizing a measuring point of a beam structure according to claim 1, wherein in step S32, the speed and the position of each particle in the population are updated according to the following formula:
Vi(k+1)=ωVi(k)+c1rand(pbesti(k)-Vi(k))+c2rand(gbest(k)-Xi(k)),
Xi(k+1)=Xi(k)+Vi(k+1),
wherein, Xi(k +1) is the position vector of the i-th generation iteration particle of k +1, Vi(k +1) is the velocity vector of the iterative particle i of the (k +1) th generation, and omega isInertial weight, c1And c2As a learning factor, pbesti(k) For the optimal solution found by the k-th iteration particle i itself, gbest (k) is the optimal solution found by the whole population in the k-th iteration.
4. The method for optimizing the measuring points of the beam structure according to claim 1, wherein the objective function is determined according to the magnitude and the position of the strain of each measuring point, and the constraint condition is determined according to the variation range of the strain and the position of each measuring point.
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