CN117195746B - Beam structure damage identification method based on multivariate strategy dragonfly algorithm - Google Patents
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Abstract
The invention discloses a beam structure damage identification method based on a multi-strategy dragonfly algorithm, which comprises the following steps: acquiring the front n-order natural frequency and the mode shape of the beam structure with noise interference; constructing a beam structure damage identification objective function based on the front n-order natural frequency and the mode shape of the beam structure with noise interference; based on a dragonfly algorithm, a fusion enhanced Laiwei flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy are carried out, and a multi-strategy dragonfly algorithm is constructed; and carrying out iterative optimization on the beam structure damage identification objective function based on a multivariate strategy dragonfly algorithm until the iterative termination condition is met, so as to obtain an optimal damage factor vector of the beam structure. The invention can effectively improve the beam structure damage recognition precision through the multi-strategy dragonfly algorithm integrating the three optimization strategies. The beam structure damage identification method based on the multi-strategy dragonfly algorithm can be widely applied to the technical field of structure damage identification.
Description
Technical Field
The invention relates to the technical field of structural damage identification, in particular to a beam structural damage identification method based on a multi-strategy dragonfly algorithm.
Background
Bridge structure damage identification is a final target of bridge structure health monitoring, and relates to comparison between two system states, and as science and technology are continuously advanced, the construction aspect of super high-rise buildings and large-span bridges is more and more complex, however, the bridge structure damage is comprehensively influenced by subjective artificial factors and objective natural reasons, and the structure damage is continuously accumulated in the forms of crack expansion, material performance degradation and the like;
Structural damage identification is a typical inverse problem, and based on structural monitoring data, the collected response is subjected to deep analysis, and the main contents of structural modeling, damage parameterization, response multiple analysis, inversion identification algorithm design and the like are involved. Structural damage can lead to changes in structural dynamics which can be analyzed to locate and even quantify the damage. In practical research, structural damage recognition can be classified into a model-based recognition method and a model-free recognition method according to the use or non-use of a finite element model. No model usually only can judge whether the structure is damaged or not, and a model identification rule can locate and even quantify the damage. Therefore, the model identification method is more commonly used in the structural damage identification research. Among them, model modification is a typical representative of model methods. The method converts the structural damage identification into a mathematical optimization problem, and the parameterized evaluation of the actual structural state is realized by iteratively optimizing selected parameters to minimize the error between model calculation and actual measurement. The method has the advantages that a large number of iterations of the model correction process can be realized through a sensitivity analysis method and a group intelligent algorithm, and matrix inverse operation and complex probability inference are not involved, so that the method is convenient and effective to apply, has the advantage of solving the NP-hard problem, and is widely studied in the field of structural damage identification. At present, particle swarm algorithm, ant-lion algorithm, fish swarm algorithm, whale algorithm and the like are successfully applied to the field of structural damage identification. However, most algorithms still have problems of insufficient recognition accuracy and noise robustness to be improved.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide the beam structure damage identification method based on the multi-strategy dragonfly algorithm, and the accuracy of beam structure damage identification can be effectively improved through the multi-strategy dragonfly algorithm fused with three optimization strategies.
The first technical scheme adopted by the invention is as follows: a beam structure damage identification method based on a multivariate strategy dragonfly algorithm comprises the following steps:
dividing the beam structure, carrying out structural damage identification research on the divided beam structure by a finite element method, and extracting the front n-order natural frequency and the mode shape of the beam structure;
Adding noise to the front n-order natural frequency and the mode shape of the beam structure to obtain the front n-order natural frequency and the mode shape of the beam structure with noise interference by considering the influence of noise on the mode shape;
Constructing a beam structure damage identification objective function based on the front n-order natural frequency and the mode shape of the beam structure with noise interference;
Based on a dragonfly algorithm, a fusion enhanced Laiwei flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy are carried out, and a multi-strategy dragonfly algorithm is constructed;
and carrying out iterative optimization on the beam structure damage identification objective function based on a multivariate strategy dragonfly algorithm until the iterative termination condition is met, so as to obtain an optimal damage factor vector of the beam structure.
Further, the expression for adding noise to the front n-order natural frequency and the mode shape of the beam structure is specifically as follows:
rnoi＝rcal(1+EpNoise)
In the above equation, r noi、rcal represents the added noise and the noise-free mode shape, F p represents the noise level, and N oise represents the gaussian distributed random number compliant with N (0, 1), respectively.
Further, the expression of the beam structure damage recognition objective function is specifically as follows:
In the above formula, J (alpha) represents a beam structure damage recognition objective function, alpha represents a beam structure damage factor vector, FCR i (alpha) represents an absolute value of an i-th order frequency relative change rate, F i (alpha) represents the ith order measurement and calculation frequency, respectively, MACFLEX i (alpha) represents the modal compliance confidence,/>F i (α) represents the diagonal elements of the i-th order measurement and calculation mode compliance, respectively,/>F i (α) represents a transpose of the i-th order measurement and diagonal elements of the computation mode compliance, w 1、w2 represents a weight coefficient, M represents a matrix, |m (α) | * represents a trace norm, i.e., a sum of singular values of the computation matrix M, N M represents a mode order, and λ represents a regularization coefficient.
Further, the step of constructing a multi-strategy dragonfly algorithm based on the dragonfly algorithm by fusing the enhanced Laiwei flight strategy, the optimal solution bidirectional search strategy and the greedy retention strategy specifically comprises the following steps:
And based on a dragonfly algorithm, fusing an enhanced Laiyiton flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy to construct a multi-strategy dragonfly algorithm, wherein the enhanced Laiyiton flight strategy is used for improving the global search capability of dragonfly individuals in the multi-strategy dragonfly algorithm, the optimal solution bidirectional search strategy is used for improving the search efficiency of the dragonfly individuals in the multi-strategy dragonfly algorithm, and the greedy retention strategy is used for improving the search precision of the dragonfly individuals in the multi-strategy dragonfly algorithm.
Further, the step of iteratively optimizing the beam structure damage identification objective function based on the multivariate strategy dragonfly algorithm until the iteration termination condition is satisfied to obtain an optimal damage factor vector of the beam structure specifically comprises the following steps:
Initializing parameters of a multi-strategy dragonfly algorithm, wherein the parameters of the multi-strategy dragonfly algorithm comprise initial population quantity, maximum iteration times, position information of dragonfly individuals, speed information of the dragonfly individuals and the field of the dragonfly individuals;
Updating motion parameters of speed information of an individual dragonfly and field information of the individual dragonfly, wherein the motion parameters of the speed information of the individual dragonfly comprise separation motion, alignment motion, gathering motion, food attraction motion and natural enemy avoidance motion;
judging whether other dragonfly individuals exist in the field information of the dragonfly individuals or not;
If the algorithm exists, performing dimension-by-dimension updating through an individual position updating formula of a multi-strategy dragonfly algorithm, and reserving evolution dimensions through a greedy reservation strategy until the updating times reach the maximum iteration times, and outputting an optimal damage factor vector of the beam structure;
and if the damage factor vector does not exist, carrying out the Layvern flight on the dragonfly individual based on the reinforced Layvern flight strategy, and outputting the optimal damage factor vector of the beam structure.
Further, the expression of the individual position updating formula of the multi-strategy dragonfly algorithm is specifically shown as follows:
In the above-mentioned method, the step of, And/>Respectively representing the position and the speed of the ith individual at the (k+1) th iteration,/>Representing the position of the ith individual at the kth iteration,/>Representing the global optimal position of the current iteration number, r represents a random number subject to U (0, 1).
Further, the expression of the enhanced lewy flight is specifically as follows:
In the above formula, k represents the current iteration number, levy (·) represents the Levy flight, and β represents the Levy flight control parameter.
The method has the beneficial effects that: according to the method, a multi-element strategy dragonfly algorithm is constructed by fusing a reinforced LayWith flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy, when no other individuals exist in the neighborhood range of the dragonfly algorithm, the dragonfly individual can execute LayWith flight, namely a random walk mode, the global search capability of the dragonfly individual in a search space can be improved, the optimal solution bidirectional search strategy can remarkably improve the search efficiency, the thought of the strategy is to search in two different directions of the individual until the optimal solution is found, the updating information of each dimension is considered for the greedy retention-based dimension-by-dimension updating strategy, whether the dimension is updated is determined according to the fitness value, the multi-element strategy dragonfly algorithm fusing three optimization strategies can effectively improve the structural damage recognition precision of the original dragonfly algorithm, the multi-element strategy dragonfly algorithm can accurately position the structural damage in the multiple recognition process, and the multi-element strategy dragonfly algorithm has good robustness to noise.
Drawings
Fig. 1 is a step flow chart of a beam structure damage identification method based on a multi-element strategy dragonfly algorithm in an embodiment of the invention;
FIG. 2 is a flow chart illustrating steps for identifying beam structure damage in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a numerical simulation model of a simply supported beam in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a structural damage recognition result according to an embodiment of the present invention;
fig. 5 is a schematic diagram of the structure damage recognition result of the multi-strategy dragonfly algorithm with different noise levels according to the embodiment of the present invention;
FIG. 6 is a schematic representation of the front third order mode shape for the lossless state of an embodiment of the present invention;
Fig. 7 is a schematic diagram showing the structure damage recognition result of the experimental structure according to the embodiment of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
The dragonfly algorithm is a novel intelligent optimization algorithm, the main inspiration of the algorithm is derived from static and dynamic clustering behaviors of the dragonfly in the nature, the algorithm has strong optimizing capability, and the algorithm has been successfully applied to the fields of machinery, image recognition, structure optimization and the like in recent years. Although the application of the dragonfly algorithm in other fields has achieved a certain result, the application effect in the field of structural damage identification is not clear, so the invention aims to introduce the basic principle of the dragonfly algorithm, define an objective function by combining structural modal parameters and research the application effect of the dragonfly algorithm in structural damage identification. In addition, aiming at the problem of insufficient precision of the original dragonfly algorithm in structural damage recognition, the invention provides a multi-strategy dragonfly algorithm by fusing reinforced Laiwei flight, optimal solution bidirectional search and greedy reservation so as to improve the precision of structural damage recognition solution.
Referring to fig. 1 and 2, the invention provides a beam structure damage identification method based on a multi-strategy dragonfly algorithm, which comprises the following steps:
S1, dividing a beam structure, carrying out structural damage identification research on the divided beam structure by a finite element method, and extracting the front n-order natural frequency and the mode shape of the beam structure;
Specifically, as shown in fig. 3, the finite element model is used for performing a bridge SDD study, where the simply supported beam model is divided into 10 equal length units, the unit types are two-node four-degree-of-freedom plane curved beam units, the elastic modulus e=210 GPa, the material density ρ=7580 kg/m 3, the length l=3.0m, the cross section is a rectangular cross section, the area a=1.164E -3m2 and the moment of inertia a= 7.6165E -7m4 are all the same, the population numbers are 100, and the maximum iteration number is 100. Taking the mode order n=7, wherein the mode shape only considers the vertical degree of freedom of each unit node;
In the structural damage identification problem, a unit stiffness reduction model is generally used for damage description. The model ignores the influence of damage on mass distribution, and represents the whole stiffness matrix K d after damage as the linear superposition of the unit stiffness matrix K ui, and has the advantages of simple expression and clear physical meaning, and the mathematical expression is as follows:
In the above formula, alpha i represents the damage factor of the ith unit, which satisfies 0.ltoreq.alpha i <1, 0 represents no damage, 1 represents complete damage, and nel represents the number of units.
S2, considering the influence of noise on the mode shape, adding noise to the front n-order natural frequency and the mode shape of the beam structure to obtain the front n-order natural frequency and the mode shape of the beam structure with noise interference;
Specifically, as shown in the damage condition setting table 1, single damage, two damage and multiple damage conditions are considered respectively, and meanwhile, the influence of noise on the mode shape is considered, namely, the noise is added to the frequency and the mode shape at the same time, and the noise adding formula is as follows:
rn＝rcal(1+EpNoise)
In the above equation, r n、rcal represents the added noise and the noise-free mode shape, E p represents the noise level, and N oise represents the gaussian distributed random number compliant with N (0, 1), respectively.
TABLE 1 damage condition settings
| Working conditions of | Damage degree @ Damage Unit | Noise level (%) |
| 1 | 10％@E5 | 0，1，3 |
| 2 | 20％@E5 | 0，1，3 |
| 3 | 10％@E5，10％@E8 | 0，1，3 |
| 4 | 20％@E5，10％@E8 | 0，1，3 |
| 5 | 10％@E3，20％@E5，10％@E8 | 0，1，3 |
S3, constructing a beam structure damage identification objective function based on the front n-order natural frequency and the mode shape of the beam structure with noise interference;
specifically, the expression of the beam structure damage recognition objective function is specifically as follows:
In the above formula, J (alpha) represents a beam structure damage recognition objective function, alpha represents a beam structure damage factor vector, FCR i (alpha) represents an absolute value of an i-th order frequency relative change rate, F i (alpha) represents the ith order measurement and calculation frequency, respectively, MACFLEX i (alpha) represents the modal compliance confidence,/>F i (α) represents the diagonal elements of the i-th order measurement and calculation mode compliance, respectively,/>F i (α) represents a transpose of the i-th order measurement and diagonal elements of the computation mode compliance, w 1、w2 represents a weight coefficient, M represents a matrix, |m (α) | * represents a trace norm, i.e., a sum of singular values of the computation matrix M, N M represents a mode order, and λ represents a regularization coefficient.
S4, based on a dragonfly algorithm, a fusion enhanced Laiwei flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy are carried out, and a multi-strategy dragonfly algorithm is constructed;
s41, dragonfly algorithm;
Specifically, the dragonfly algorithm is an emerging intelligent optimization algorithm for groups, the inspiration of which is derived from hunting and migration behaviors of the dragonfly in the nature, and in the algorithm, the population behaviors of the dragonfly are simulated into two modes: static and dynamic populations; in the static population mode, the dragonfly population is divided into a plurality of sub-populations, and space searching is carried out to capture prey, which is similar to the exploration process of a swarm intelligent algorithm; in the dynamic population mode, dragonfly populations are highly aggregated, which is similar to the development process of the swarm intelligence algorithm. Mathematically, the dragonfly algorithm abstracts the behavior of dragonfly individuals into five behaviors of separation, alignment, aggregation, food attraction and natural enemies avoidance, and according to these behaviors, the position update formula of dragonfly individuals can be expressed as:
In the above-mentioned method, the step of, And/>Respectively representing the position and the speed of the ith individual in the (k+1) th iteration, S i、Ai、Ci、Fi and E i respectively representing the influence of 5 actions of corresponding separation, alignment, aggregation, food attraction and avoidance on speed update, S, a, c, f, E respectively representing the weight coefficient corresponding to the 5 actions, and w is the previous flying speed/>R k represents the kth iteration to/>A radius range as a center for judging whether two individuals are adjacent;
S411, no speed update of other individuals exists in the field;
In particular, if If no other individuals exist in the field, the speed update adopts the Lewy flight, which is specifically calculated as follows,
Levy(d)＝0.01·r1·σ·|r2|-β
In the above formula, r 1～U(0,1),r2 to U (0, 1); beta is a flight constant, and 1.5 is taken;
further, the expression of σ is:
In the above equation, σ represents a step size coefficient.
S412, updating the speed of other individuals in the field;
In particular, if If other individuals exist in the field, 5 behavior modes are considered for speed update, wherein the speed update comprises separation movement, alignment movement, gathering movement, food attraction and natural enemies avoidance;
S4121, separating movement;
Specifically, the separation motion is used for avoiding collision of individual dragonfly bodies in the search space, and the calculation formula of Si is as follows:
In the above formula, N represents the number of individuals within the range of X i.
S4122, alignment movement;
Specifically, the alignment motion is used for coordinating the speed among individuals in the field of the individual X i, and is expressed by A i, and the calculation formula is as follows:
in the above equation, V j represents the speed of the jth individual.
S4123, aggregating motion;
Specifically, if the aggregate motion represents the aggregate force of the center in the field of X i to the individual X i, the calculation formula of C i is:
In the above formula, C i denotes an aggregation motion.
S4124, food sucking movement;
Specifically, food attraction represents the distance between the individual X i and the food, when the corresponding F i calculation formula is:
Fi＝X+-Xi
In the above equation, X + represents the specified food source location, and in the dragonfly algorithm, the optimal individual for the current iteration is typically taken as X +.
S4125, avoiding natural enemy movements.
Specifically, the avoidance natural enemies reflect the distance between the individual X i and the natural enemies, and the corresponding E i calculation formula is:
Ei＝X-+Xi
In the above formula, X - represents the specified natural enemy position, and in the dragonfly algorithm, the worst individual of the current iteration is generally taken as X -.
S42, a multi-element strategy dragonfly algorithm;
Specifically, when the traditional dragonfly algorithm processes complex optimization problems, local optimization is easy to fall into, so that accuracy of structural damage recognition results is reduced, and meanwhile, when the complex optimization problems are processed, the dragonfly algorithm is required to keep better diversity in the whole solving process so as to improve the recognition probability of the global optimal solution, so that three optimization strategies of reinforcing Laiwei flight, optimal solution bidirectional searching and greedy reservation are fused to provide a multi-strategy dragonfly algorithm;
S421, reinforcing Laiwei flight;
Specifically, during the dragonfly individual position update iteration, when no other individuals exist in the neighborhood, the dragonfly individual performs the Lewy fly, i.e. the random walk mode. The mode can improve the global searching capability of dragonfly individuals in the searching space. However, the updated location of the lewy flight does not guarantee a certain distribution around the optimal solution. Therefore, the Gaussian distribution random number is introduced to restrain the step length of each Laiweier flight, and the line step length scaling factor is added before the Laiweier flight step length, so that the step length of the Laiweier flight is reduced along with the increase of the iteration times. Thus, the formula for enhanced Lewy flight is as follows:
Where r represents a random number subject to U (0, 1) and k represents the current number of iterations.
S422, performing two-way searching on the optimal solution;
specifically, the bidirectional search strategy is a strategy widely used to find the optimal solution problem, which can significantly improve the search efficiency. The idea of this strategy is to search in two different directions of the individual until the optimal solution is found. The advantage of this approach is that the search range can be extended without spending a lot of time, thus making the optimization process of the algorithm more efficient. Therefore, in the multivariate strategy dragonfly algorithm, the individual location update formula is modified as shown in the following formula:
where r is a random number subject to U (0, 1), And the global optimal position of the current iteration number is represented.
S423, greedy reservation strategy;
Specifically, in the iteration process of the original dragonfly algorithm, a full-dimension updating mode is adopted, and then evaluation is carried out. However, this full-dimensional update approach tends to result in mutual collision interference between dimensions, thereby reducing the optimization capability of the algorithm. To solve this problem, the present invention proposes a greedy reservation-based dimension-wise update strategy to consider the update information of each dimension and determine whether to update the dimension according to the fitness value. Specifically, the strategy updates dimension by dimension in the dragonfly individual location updating process. If the updated solution can improve the fitness value of the current solution, the updated result of the dimension is reserved; if not, the previous dimension information is reserved and the next dimension update is entered. Through the greedy reserved dimension-by-dimension updating strategy, the evolution dimension information of dragonfly individuals can be considered more comprehensively, interference of irrelevant solutions is eliminated, mutual interference among different dimension information is effectively restrained, the search precision of a dragonfly algorithm can be improved through the greedy reserved strategy, the algorithm can explore the space of an optimal solution more pertinently, and optimization requirements of high-dimension problems can be met better.
And S5, carrying out iterative optimization on the beam structure damage identification objective function based on a multivariate strategy dragonfly algorithm until the iterative termination condition is met, and obtaining an optimal damage factor vector of the beam structure.
Specifically, initializing parameters of the multi-strategy dragonfly algorithm, wherein the parameters of the multi-strategy dragonfly algorithm comprise initial population quantity, maximum iteration times, position information of dragonfly individuals, speed information of the dragonfly individuals and the fields of the dragonfly individuals; updating motion parameters of speed information of the dragonfly individual and the field of the dragonfly individual, wherein the motion parameters of the dragonfly individual comprise separation motion, alignment motion, gathering motion, food attraction and natural enemies avoidance; judging whether other dragonfly individuals exist in the field of the dragonfly individuals or not; if the number of the updating times reaches the maximum iteration times, the optimal damage factor vector of the beam structure is output; and if the damage factor vector does not exist, carrying out the Layvern flight on the dragonfly individual based on the reinforced Layvern flight strategy, and outputting the optimal damage factor vector of the beam structure.
Firstly, comparing the structural damage recognition effect of a dragonfly algorithm with that of a multi-strategy dragonfly algorithm, and comparing and researching the structural damage recognition performance difference of the original dragonfly algorithm and the multi-strategy dragonfly algorithm, wherein the recognition results of the two algorithms on 5 different working conditions are shown in a figure 4, a histogram is the average value of 100 calculation results, and the accuracy of a unit damage final recognition value is reflected; the scatter diagram shows 100 times of recognition results of the unit damage, the discrete degree reflects the stability of the unit damage value in the multiple recognition process, and as can be seen from fig. 4, the dragonfly algorithm and the multi-element strategy dragonfly algorithm can accurately recognize the main damage of different damage working conditions of the simple beam model, and fewer damage misjudgment exists. The identification accuracy of the single damage working condition is highest, and the unit damage identification accuracy is increased along with the increase of the assumed damage degree. In the working condition 2, the two algorithms have almost no damage misjudgment unit in all 100 times of identification, and the damage identification value of the real damage unit is almost consistent with the assumed value. However, under the working conditions of two injuries and multiple injuries, the identification accuracy of the real injury units of the two algorithms is reduced to a certain extent, and the damage misjudgment of the non-injury units is increased. In contrast, the structural damage recognition mean of the multivariate strategy dragonfly algorithm is closer to the hypothesized unit damage; for example, in the case of the 8# unit in the working condition 4 and the 3# unit in the working condition 5, the recognition result of the multi-strategy dragonfly algorithm is more accurate. The recognition accuracy of the multi-strategy dragonfly algorithm is higher than that of the dragonfly algorithm, in addition, the distribution situation of scattered points can show that the structural damage recognition result based on the multi-strategy dragonfly algorithm is more concentrated, which shows that the structural damage recognition stability of the multi-strategy dragonfly algorithm in multiple recognition is higher in reliability due to the dragonfly algorithm, and therefore, the dragonfly algorithm and the multi-strategy dragonfly algorithm can realize accurate structural damage recognition of a simply supported beam structure. In contrast, the structural damage recognition precision based on the multi-strategy dragonfly algorithm is higher, and the stability of the structural damage recognition is better in multiple times of recognition, so that the multi-strategy dragonfly algorithm can be considered to have better performance in the aspect of structural damage recognition;
Further, in consideration of the influence of the noise, the result of identifying structural damage by the multi-element strategy dragonfly algorithm is shown in fig. 5, and it can be seen from fig. 5 that as the noise level increases, the accuracy of identifying the multi-element strategy dragonfly algorithm tends to decrease. The accuracy of cell identification particularly in real lesions decreases, while damage misjudgment in non-lesions increases. Especially at 3% noise level, the damage misjudgment is the most serious. However, besides the poor recognition accuracy of the No. 3 unit in the working condition 5, the multi-strategy dragonfly algorithm method has high recognition accuracy on the real damage in other working conditions, and can better position and quantify the main damage in the structure. Therefore, the multi-strategy dragonfly algorithm has certain robustness in a noise environment and has application prospects in experimental and engineering structures.
Further, the simulation experiment of the present invention is specifically as follows:
The first step, the experimental object of the invention is a single-span simple beam model made of 6063 aluminum alloy, the length of the model is 1m, the cross section adopts a rectangular cross section, and the size is 0.03mX0.005 m. The Young modulus of the model material is 68.9GPa, the density is 2950kg/m 3, the Poisson ratio is 0.33, and the mode data acquisition system in the experiment consists of DH dragonfly algorithm S dynamic acquisition software, dynamic signal test analysis system DH8302 (16 channels), piezoelectric acceleration sensor 1A102E (charge output) and ICP force hammer LC02 (5 KN). In the experimental process, 9 acceleration sensors are arranged on the structure, and hammering force is applied at a position 0.45m away from the left end support, so that modal information of the structure is obtained;
And secondly, correcting the initial finite element model, wherein in the experimental process, errors necessarily exist between experimental modal data measured under the nondestructive condition and the calculation result of the initial finite element model due to the influences of factors such as deviation between actual material parameters and ideal conditions, deviation between actual geometric dimensions and ideal conditions, non-ideal hinging of a structural support and the like. Therefore, before the structural damage identification is performed, model correction is performed on the initial finite element structure according to experimental modal measurement under the nondestructive condition, so as to obtain a reference model capable of effectively serving the subsequent structural damage identification;
By a modal test on the lossless model, the front third-order mode of vibration of the structure (shown in fig. 6) and the front third-order frequency (shown in table 2) can be obtained. It can be seen that the ratio of measured frequency to fundamental frequency is slightly lower than the theoretical order square, and the larger the order rise deviation. The error calculation in table 2 is performed by the method of (calculated value-actual measured value)/actual measured value×100%, and the result of calculation of the value reflects that the error between the calculated frequency and actual measured frequency of the initial finite element model is large, and it is necessary to perform initial finite element model correction.
Four parameters are considered to be selected for initial finite element model correction, including linear density ρA, bending stiffness EI, vertical spring stiffness kv at the support and torsional spring stiffness kθ. The values of the four parameters before and after correction are shown in table 3, and it can be seen that the change rate is within + -20%, and no particularly large change occurs, which ensures the actual physical meaning of the corrected parameters. In addition, the calculated frequency (shown in table 2) and the measured frequency of the modified finite element model are basically consistent, which indicates that the selected modification parameters are effective, and the modification result is reasonable. The obtained finite element model can serve as a reference model for subsequent structural damage identification after initial model correction;
TABLE 2 actual measurement frequency and model calculation frequency
Table 3 comparison of parameters before and after correction of simply supported beam model
| Model correction parameters | Unit (B) | Initial value | Correction value | Rate of change |
| ρA | kg/m | 0.4425 | 0.4920 | 10.06％ |
| EI | Nm2 | 21.5625 | 17.2569 | -19.96％ |
| kv | N/m | ∞ | 3.7464e4 | - |
| kθ | N/rad | 0 | 6.88560 | - |
Thirdly, the damage simulation and recognition are carried out on the beam in the width direction in a laboratory to simulate the damage, 4 damage working conditions are totally simulated in the experimental process, detailed information is shown in a table 4, the table also shows the structure front third-order measurement frequency under different damage working conditions, it can be seen that the front third-order frequency is reduced to different degrees along with the aggravation of the damage degree of the unit, the third-order frequency is reduced most obviously, as shown in fig. 7, the third-order frequency is consistent with the theory, and the frequency measurement value of the experimental damage working conditions is reasonable and effective;
TABLE 4 Experimental damage condition and corresponding measurement frequency
As can be seen from the damage identification result in FIG. 7, the method provided by the invention can effectively realize the positioning and quantification of structural damage under all four experimental conditions. Especially under the single damage operating mode, the recognition accuracy is the highest. As is clear from the figure, the recognition result of the cell No. 5 is almost identical to the simulation damage. The identification results of the two working conditions only have slight damage misjudgment at the No. 2 unit, the identification accuracy of the multi-damage working condition is reduced to a certain extent, and particularly the trend of precision reduction is more obvious along with the increase of the damage units. It can be seen from the figure that the recognition values of units 3 and 5 in operating mode 4 are significantly larger, with a larger relative error than in operating mode 3. However, comparing the identification results of the damaged unit and the non-damaged unit, it can be found that the identification value of the damaged unit is still more significant, and has a good indication effect. The method has positive guiding significance for damage positioning in actual engineering.
While the preferred embodiment of the present application has been described in detail, the application is not limited to the embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the application, and these equivalent modifications and substitutions are intended to be included in the scope of the present application as defined in the appended claims.
Claims (3)
1. A beam structure damage identification method based on a multivariate strategy dragonfly algorithm is characterized by comprising the following steps:
dividing the beam structure, carrying out structural damage identification research on the divided beam structure by a finite element method, and extracting the front n-order natural frequency and the mode shape of the beam structure;
Adding noise to the front n-order natural frequency and the mode shape of the beam structure to obtain the front n-order natural frequency and the mode shape of the beam structure with noise interference by considering the influence of noise on the mode shape;
Constructing a beam structure damage identification objective function based on the front n-order natural frequency and the mode shape of the beam structure with noise interference;
Based on a dragonfly algorithm, fusing an enhanced Laiwo flight strategy, an optimal solution bidirectional search strategy and a greedy retention strategy to construct a multi-strategy dragonfly algorithm, wherein the enhanced Laiwo flight strategy constrains the step length of each Laiwo flight by introducing Gaussian distribution random numbers, and adds a line step length scaling factor before the Laiwo flight step length for improving the global search capability of dragonfly individuals in the multi-strategy dragonfly algorithm, the optimal solution bidirectional search strategy is used for improving the search efficiency of the dragonfly individuals in the multi-strategy dragonfly algorithm, the greedy retention strategy considers the update information of each dimension, and determines whether to update the dimension according to fitness values for improving the search precision of the dragonfly individuals in the multi-strategy dragonfly algorithm;
the expression of the enhanced Lewy flight is specifically as follows:
；
In the above-mentioned method, the step of, Representing the current iteration number,/>Representing Lewy flight,/>Representing the control parameters of the lewy flight,Represents the/>Individual at/>Location of the next iteration,/>Represents the/>Individual at/>Location of the next iteration,/>Representing compliance/>Random numbers of (a);
Initializing parameters of a multi-strategy dragonfly algorithm, wherein the parameters of the multi-strategy dragonfly algorithm comprise initial population quantity, maximum iteration times, position information of dragonfly individuals, speed information of the dragonfly individuals and the field of the dragonfly individuals;
Updating motion parameters of speed information of an individual dragonfly and field information of the individual dragonfly, wherein the motion parameters of the speed information of the individual dragonfly comprise separation motion, alignment motion, gathering motion, food attraction motion and natural enemy avoidance motion;
judging whether other dragonfly individuals exist in the field information of the dragonfly individuals or not;
If the algorithm exists, performing dimension-by-dimension updating through an individual position updating formula of a multi-strategy dragonfly algorithm, and reserving evolution dimensions through a greedy reservation strategy until the updating times reach the maximum iteration times, and outputting an optimal damage factor vector of the beam structure;
If the damage factor vector does not exist, carrying out the Layvern flight on the dragonfly individual based on the reinforced Layvern flight strategy, and outputting the optimal damage factor vector of the beam structure;
the expression of the beam structure damage identification objective function is specifically as follows:
；
In the above-mentioned method, the step of, Representing beam structure damage recognition objective function,/>Representing the damage factor vector of the beam structure,Represents the/>Absolute value of the relative rate of change of the order frequency,/>Respectively represent the/>Order measurement and calculation frequency,/>Representing modality compliance confidence,/>Respectively represent the/>Order measurement and calculation of diagonal elements of modal compliance,/>Represents the/>Transposition of order measurement and diagonal element of computational modality compliance,/>Representing the weight coefficient,/>Representing matrix,/>Representing trace norms, i.e. computing matrices/>Sum of singular values,/>Representing the modal order,/>Representing regularization coefficients.
2. The beam structure damage identification method based on the multivariate strategy dragonfly algorithm as claimed in claim 1, wherein the expression for adding noise to the front n-order natural frequency and the mode shape of the beam structure is specifically as follows:
；
In the above-mentioned method, the step of, Respectively represent the mode shape of added noise and noiselessRepresenting the level of noise that is present,Representing compliance/>Is a gaussian distribution of random numbers.
3. The beam structure damage identification method based on the multi-element strategy dragonfly algorithm according to claim 2, wherein the expression of the individual position update formula of the multi-element strategy dragonfly algorithm is specifically as follows:
；
In the above-mentioned method, the step of, And/>Respectively represent the/>Individual at/>Position and speed of the next iteration,/>Represents the/>Individual at/>Location of the next iteration,/>Representing the global optimal position of the current iteration number,/>Representing compliance/>Is a random number of (a) in the memory.
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