Structural damage identification method and system based on multi-population intelligent collaborative algorithm

Abstract

The invention discloses a structural damage identification method and system based on a multi-population intelligent collaborative algorithm, and the method comprises the steps: carrying out the structural damage identification of a beam structure, introducing a noise pollution and sparse regularization item, and constructing a beam structure damage identification sparse regularization auxiliary objective function; based on a seagull optimization algorithm and a sine and cosine algorithm, a dynamic multi-role adaptive cooperative intelligent algorithm is constructed in combination with a nonlinear adaptive region contraction strategy; and carrying out iterative optimization updating on the beam structure damage identification sparse regularization auxiliary objective function based on a dynamic multi-role adaptive collaborative intelligent algorithm to obtain an optimal damage factor vector of the beam structure. According to the method, the damage identification result can be kept in a reasonable and reliable interval, the optimal updating strategy can be adaptively selected, roles are dynamically switched, and therefore the identification precision is improved. The structural damage identification method and system based on the multi-population intelligent collaborative algorithm can be widely applied to the technical field of structural damage identification.

Description

Technical Field

[0001] The present invention relates to the technical field of structural damage identification, and particularly to a structural damage identification method and system based on a multi-population intelligent cooperation algorithm. Background Art

[0002] Affected by unforeseen factors such as aging deterioration, fatigue effect, connection looseness, and overloading, in-service infrastructure will inevitably accumulate damage. Therefore, early identification of structural damage is crucial for ensuring structural safety and timely implementation of maintenance measures. Related vibration-based damage identification methods can be classified into time-domain methods and frequency-domain methods according to the types of data used, where the former uses acceleration data and the latter is based on natural frequencies, modal shapes, or other characteristics. From the perspective of the finite element (FE) model, these methods can also be divided into data-driven methods and model-driven methods. Generally, data-driven methods can only judge whether there is damage in the structure, and their applications are limited by scenarios that require a higher identification level. To solve this problem, model-driven methods (such as model updating and surrogate model methods) provide information on the specific location and degree of damage, and thus have been widely studied and applied in structural damage identification (SDI). Among them, the model updating method shows good prospects because it usually formulates SDI as a mathematical optimization problem, without complex theoretical derivations, and can be solved by various computational intelligence algorithms.

[0003] Selecting an appropriate optimization method is the key to ensuring that the model updating method can achieve satisfactory identification accuracy. Such methods can generally be divided into three categories: sensitivity-based methods, computational intelligence algorithms, and Bayesian model updating methods. However, sensitivity methods highly rely on a well-conditioned sensitivity matrix, appropriately selected initial values, and reliable gradient information. In addition, the requirement of matrix inversion operations in these methods is prone to ill-conditioned problems when dealing with uncertainties such as FE modeling errors, measurement noise, and other environmental interferences, thus affecting the reliability of damage identification results. Bayesian model updating aims to probabilistically describe structural parameters and measurement responses, which requires prior determination of appropriate probability distributions of the parameters involved. However, in high-dimensional optimization problems, Bayesian model updating needs to perform high-dimensional integration to calculate marginal probabilities, which greatly increases the computational burden and limits its practicality in actual structural engineering.

[0004] Due to the stochastic search characteristics of swarm intelligence, it has received increasing attention in the field of SDI. This characteristic enables the SDI process to avoid relying on sensitivity analysis, initial guesses, and probability distribution assumptions, thus providing a more flexible solution. Particle Swarm Optimization (PSO), Dragonfly Algorithm (DA), Artificial Bee Colony Algorithm (ABC), and Grasshopper Optimization Algorithm (GOA) are representative methods applied to SDI. However, when a single swarm intelligence algorithm is used for damage identification, due to incomplete measurements and uncertainties (such as noise pollution), it often faces the challenge of falling into local optimal solutions, thereby increasing the difficulty of finding the global optimal solution. In addition, although a single swarm intelligence algorithm can perform independent searches, it lacks sufficient cooperation mechanisms, limiting its exploration ability in relatively complex SDI problems. To achieve cooperation, three improvement strategies can be summarized in related technologies. One is to optimize the iteration formula; the second is the hybridization of different algorithms; the third is to propose new algorithms. For optimizing the iteration formula, a new formula is introduced in the observation bee stage at the present stage, and a tournament selection strategy is adopted to improve the convergence and global search ability of the original ABC algorithm in the damage identification of truss and beam structures. Or, by introducing enhanced Lévy flight, two-way search for the optimal solution, and a greedy retention strategy, the standard dragonfly algorithm is improved, which also effectively enhances the performance of the original algorithm in structural damage identification. For the hybridization of different algorithms, many hybrid algorithms have been extended and applied to SDI, but no single algorithm can solve all optimization problems. For proposing new algorithms, some new swarm intelligence algorithms, such as Ant Lion Optimizer (ALO), Whale Optimization Algorithm (WOA), etc. However, due to their inherent limitations, a single improved swarm intelligence algorithm often weakens one characteristic while strengthening another. For example, enhancing the global search ability may prolong the iteration time, while accelerating the convergence speed may reduce the accuracy. And these mechanisms increase the computational complexity, and poor interaction design may weaken the optimization performance. Summary of the Invention

[0005] To solve the above technical problems, the object of the present invention is to provide a structural damage identification method and system based on a multi-swarm intelligence cooperation algorithm, which can ensure that the damage identification results are maintained within a reasonable and reliable range and can adaptively select the optimal update strategy, dynamically switch roles, thereby improving the identification accuracy.

[0006] The first technical solution adopted by the present invention is: a structural damage identification method based on a multi-swarm intelligence cooperation algorithm, including the following steps:

[0007] Perform structural damage identification on the beam structure, introduce noise pollution and a sparse regularization term, and construct a sparse regularization auxiliary objective function for beam structure damage identification;

[0008] Based on the Seagull Optimization Algorithm and the Sine Cosine Algorithm, combined with the non-linear adaptive region contraction strategy, a dynamic multi-role adaptive collaborative intelligent algorithm is constructed;

[0009] Based on the dynamic multi-role adaptive collaborative intelligent algorithm, the sparse regularization auxiliary objective function for beam structure damage identification is iteratively optimized and updated to obtain the optimal damage factor vector of the beam structure.

[0010] Furthermore, the step of performing structural damage identification on the beam structure, introducing noise pollution and the sparse regularization term, and constructing the sparse regularization auxiliary objective function for beam structure damage identification specifically includes:

[0011] The beam structure is successively divided into elements and its structural damage is identified, and the first n natural frequencies and the modal vibration modes of the beam structure are extracted;

[0012] Based on the first n natural frequencies and the modal vibration modes of the beam structure, noise pollution is introduced to construct the first n natural frequencies of the beam structure with noise and the modal vibration modes of the beam structure with noise;

[0013] Based on the first n natural frequencies of the beam structure with noise and the modal vibration modes of the beam structure with noise, an additional penalty term based on prior knowledge is introduced to construct the sparse regularization auxiliary objective function for beam structure damage identification.

[0014] Furthermore, the expression of the sparse regularization auxiliary objective function for beam structure damage identification is specifically as follows:

[0015]

[0016] In the above formula, J(α) represents the sparse regularization auxiliary objective function for beam structure damage identification, α represents the damage factor vector, i represents the i-th order, FCR i represents the modal frequency change rate, FAC i represents the modal flexibility confidence criterion, ||α||1 represents the L1 norm, λ represents the regularization parameter, ω represents the weight coefficient, and n represents the first n modes.

[0017] Furthermore, the step of iteratively optimizing and updating the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm to obtain the optimal damage factor vector of the beam structure specifically includes:

[0018] Based on the sparse regularization auxiliary objective function for beam structure damage identification, the non-linear adaptive region contraction strategy is introduced, and the positions of individuals are updated through the migration stage of the Seagull Optimization Algorithm to obtain the initially updated positions of the seagull individuals;

[0019] In the predation stage of the seagull optimization algorithm, seagulls attack migrating birds through spiral trajectory behavior, and the sine-cosine algorithm is introduced to update the positions of the initially updated seagull individuals, and the updated positions of the seagull individuals are output;

[0020] The loop iteratively optimizes and updates the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm until the number of iterations meets the preset threshold, and the optimal damage factor vector of the beam structure is output.

[0021] Furthermore, the position update of the individuals in the migration stage of the seagull optimization algorithm satisfies the following conditions:

[0022] Avoid collisions between individuals, where a non-linear adaptive region contraction strategy is introduced to non-linearly adjust the scaling factor in the collision avoidance positions of individuals, and the collision avoidance position update conditions are constructed;

[0023] Move in the direction of the best neighbor, and construct the best individual guidance update conditions;

[0024] Maintain a distance close to the best search individual, and determine the initially updated positions of the seagull individuals by combining the collision avoidance position update conditions and the best individual guidance update conditions.

[0025] Furthermore, the expression of the non-linear adaptive region contraction strategy is specifically as follows:

[0026]

[0027] In the above formula, A NL (k) represents the non-linear adaptive region contraction strategy, f c represents the variable, k represents the number of iterations, and k max represents the maximum threshold of the number of iterations.

[0028] Furthermore, the expression of the individual position update of the spiral trajectory behavior is specifically as follows:

[0029]

[0030] In the above formula, x, y, and z respectively represent the behaviors of the individual in three planes, and r(θ), θ represent random vectors.

[0031] Furthermore, the individual position update expression of the sine-cosine algorithm is specifically as follows:

[0032]

[0033] In the above formula, x, y, and z respectively represent the behaviors of the individual in three planes, and X i(k) represents the position of the individual after update, r1 represents the adaptive variable, r2 represents the random vector, r4 represents the random parameter, D i (k) represents the position of the updated individual in the k-th iteration, X Best (k) represents the position of the best individual in the k-th iteration.

[0034] The second technical solution adopted by the present invention is: a structural damage identification system based on a multi-population intelligent cooperation algorithm, including:

[0035] The first module is used to perform structural damage identification on the beam structure, introduce noise pollution and sparse regularization terms, and construct a sparse regularization auxiliary objective function for beam structure damage identification;

[0036] The second module is used to construct a dynamic multi-role adaptive cooperation intelligent algorithm based on the seagull optimization algorithm and the sine-cosine algorithm, combined with the non-linear adaptive region contraction strategy;

[0037] The third module is used to iteratively optimize and update the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive cooperation intelligent algorithm to obtain the optimal damage factor vector of the beam structure.

[0038] The beneficial effects of the method and system of the present invention are: through the present invention, by performing structural damage identification on the beam structure, introducing noise pollution and sparse regularization terms, and constructing a sparse regularization auxiliary objective function for beam structure damage identification, by incorporating additional penalty terms based on prior knowledge into the traditional objective function, these methods can ensure that the damage identification results are kept within a reasonable and reliable range, can effectively handle identification problems involving uncertainties, and then based on the seagull optimization algorithm and the sine-cosine algorithm, combined with the non-linear adaptive region contraction strategy, construct a dynamic multi-role adaptive cooperation intelligent algorithm for iterative optimization and update, so that the agents can exchange roles without increasing additional computational overhead through iteration. In addition, the scale factor of the seagull optimization algorithm is non-linearly adjusted, so as to enhance the global search ability in the initial stage and accelerate convergence in the later stage, improve adaptability without additional fitness evaluation, and by integrating different iterative formulas, enable the individuals in the algorithm population to adaptively select the optimal update strategy, dynamically switch roles, and adapt to the requirements of different identification scenarios, thus significantly improving the identification accuracy. Description of the Drawings

[0039] Figure 1 is the flowchart of the steps of a method for structural damage identification based on a multi-population intelligent cooperation algorithm of the present invention;

[0040] Figure 2 is the structural block diagram of a structural damage identification system based on a multi-population intelligent cooperation algorithm of the present invention;

[0041] Figure 3 It is a schematic diagram for comparing linear and non - linear scale factors provided by a specific embodiment of the present invention;

[0042] Figure 4 It is a schematic diagram of a 20 - element simply - supported beam FE model provided by a specific embodiment of the present invention;

[0043] Figure 5 It is a schematic diagram of MSE results with different λ values provided by a specific embodiment of the present invention;

[0044] Figure 6 It is a schematic diagram of the identification result under the condition of no noise pollution provided by a specific embodiment of the present invention;

[0045] Figure 7 It is a schematic diagram of the identification result under the condition of containing noise provided by a specific embodiment of the present invention;

[0046] Figure 8 It is a schematic diagram of a 36 - element truss FE model provided by a specific embodiment of the present invention;

[0047] Figure 9 It is a schematic diagram of the identification result of a single - damage condition of a planar truss provided by a specific embodiment of the present invention;

[0048] Figure 10 It is a schematic diagram of an experimental beam model, equipment and crack conditions provided by a specific embodiment of the present invention;

[0049] Figure 11 It is a schematic diagram of the identification result of an experimental condition provided by a specific embodiment of the present invention. Detailed implementation manners

[0050] The following further elaborates on the present invention in detail in conjunction with the accompanying drawings and specific embodiments. For the step numbers in the following embodiments, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0051] Referring to Figure 1 , the present invention provides a structural damage identification method based on a multi - swarm intelligence collaborative algorithm, and the method includes the following steps:

[0052] S100. Conduct structural damage identification on the beam structure, introduce noise pollution and a sparse regularization term, and construct a sparse regularization auxiliary objective function for beam structure damage identification;

[0053] S110. Conduct element division and structural damage identification on the beam structure in sequence, and extract the first n natural frequencies and modal vibration modes of the beam structure;

[0054] S120. Based on the first n natural frequencies and modal shapes of the beam structure, noise pollution is introduced to construct the first n natural frequencies of the beam structure with noise and the modal shapes of the beam structure with noise.

[0055] Specifically, to quantify structural damage, an embodiment of the present invention constructs a model, represents damage as a linear reduction of the stiffness of each element, and represents it through the damage factor vector α = [α1, α2, … α nele . Specifically, if the damage index of a certain element is equal to 0.1, it indicates that the stiffness of the element has been reduced by 10%. The goal of SDI based on vibration characteristics is to determine the optimal damage factor vector α through changes in the structural vibration characteristics.

[0056] Furthermore, noise pollution is introduced and added to the natural frequencies and modal shapes. The specific formula for the noise pollution modal parameter update formula is as follows:

[0057]

[0058] In the above formula, r n represents the modal parameter with noise, r cal represents the modal parameter without noise, E p represents the noise level, N oise represents a random vector, represents element-wise multiplication.

[0059] S130. Based on the first n natural frequencies of the beam structure with noise and the modal shapes of the beam structure with noise, an additional penalty term based on prior knowledge is introduced to construct a sparse regularization auxiliary objective function for beam structure damage identification.

[0060] Specifically, the objective function is a key component in the FE model updating framework. It needs to be highly sensitive to structural damage while showing low sensitivity to other interference factors such as noise. However, traditional objective functions often present ill-conditioned problems as they mainly focus on minimizing the difference between the simulation model and the target model in measurements or features, especially when there is uncertainty, which easily leads to unreliable results. To solve this problem and achieve more stable and accurate damage identification, regularization techniques become a practical option. By incorporating an additional penalty term based on prior knowledge into the traditional objective function, these methods can ensure that the damage identification results are kept within a reasonable and reliable range. In practical engineering, structural damage often occurs in a few local areas, especially in the early stage of damage. Therefore, the damage factor vector should be a sparse vector, with most elements being zero. Based on this, the L1 regularization technique can effectively handle identification problems involving uncertainty. In this study, a sparse regularization damage identification objective function is defined, and its form is:

[0061]

[0062] In the above formula, J(α) represents the sparse regularization auxiliary objective function for beam structure damage identification, α represents the damage factor vector, i represents the i-th order, FCR i represents the modal frequency change rate, and FAC i represents the modal flexibility confidence criterion, ||α||1 represents the L1 norm, λ represents the regularization parameter, ω represents the weight coefficient, and n represents the first n modes.

[0063] Among them, and represent the modal frequency change rate and the modal flexibility confidence criterion respectively. In the above expression, f i and f i (α) are the measured frequency and the calculated frequency of the i-th order respectively, while F i and F i (α) are the diagonal elements of the measured modal flexibility matrix and the calculated modal flexibility matrix at the i-th order respectively. The L1 norm ||α||1 is defined as ||α||1 = |α1| + |α2| + … + |α nele |. The regularization parameter λ > 0 ensures a balance between overfitting and model fitness.

[0064] S200. Based on the seagull optimization algorithm and the sine-cosine algorithm, combined with the non-linear adaptive region contraction strategy, a dynamic multi-role adaptive collaborative intelligent algorithm is constructed;

[0065] Specifically, due to the lack of uniqueness and flexibility in the update method, the swarm intelligence algorithm based on a single population cannot well solve all optimization problems. In addition, the model-based SDI belongs to a typical NP-hard problem, especially when the available vibration data is limited. To achieve a satisfactory damage identification effect, an efficient and adaptive search mechanism needs to be designed and integrated into the swarm intelligence algorithm. Therefore, in the embodiment of the present invention, a new type of dynamic multi-role adaptive collaborative intelligent algorithm (SCSOA) is developed, which introduces two different population update mechanisms based on the seagull optimization algorithm (SOA) and the sine-cosine algorithm (SCA). In the SOA algorithm, a large number of random numbers are introduced into the iteration formula, which endows it with excellent global search ability, but at the same time results in a slow convergence speed. On the contrary, the update mechanism in SCA enhances the convergence of the algorithm, but compromises in the global search efficiency. Therefore, SOA and SCA can be regarded as two types of populations with different focuses. By dynamically adjusting between these two types of populations, the algorithm can effectively adapt to the dynamic changes of the search space and its requirements. This dynamic adjustment combined with the ever-changing adaptive search space can efficiently balance the exploration stage and the exploitation stage of the algorithm, thus showing high efficiency and effectiveness in the optimization performance.

[0066] S300. Iteratively optimize and update the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm to obtain the optimal damage factor vector of the beam structure.

[0067] S310. Based on the sparse regularization auxiliary objective function for beam structure damage identification, introduce a non-linear adaptive region contraction strategy, and update the position of each individual through the migration stage of the seagull optimization algorithm to obtain the preliminary updated position of the seagull individuals.

[0068] It should be noted that the position update of each individual in the migration stage of the seagull optimization algorithm satisfies the following conditions:

[0069] 1) Avoid collisions between individuals. Among them, introduce a non-linear adaptive region contraction strategy to non-linearly adjust the scaling factor in the collision avoidance position of each individual, and construct the collision avoidance position update condition.

[0070] 2) Move in the direction of the best neighbor, and construct the best individual guidance update condition.

[0071] 3) Keep close to the distance of the best search individual, and determine the preliminary updated position of the seagull individuals by combining the collision avoidance position update condition and the best individual guidance update condition.

[0072] Specifically, SOA is a group of intelligent algorithms inspired by the observation of seagull migration and predation behaviors, which respectively correspond to the exploration and exploitation processes. In SOA, the position of each seagull represents a candidate solution, and its update mechanism is based on the mathematical modeling of the above two behaviors, which is specifically described as follows:

[0073] In the migration stage, the position update of each individual needs to satisfy the following three conditions: one is to avoid collisions between individuals, the second is to move in the direction of the best neighbor, and the third is to keep close to the distance of the best search individual. These conditions ensure that the algorithm can search for the optimal solution in the entire potential solution space. To simulate the first condition, that is, to avoid collisions, the collision avoidance position update formula C of the i-th individual i can be expressed as:

[0074] C i (k) = A L (k) · X i (k)

[0075] where X i (k) represents the position of the i-th individual at the k-th iteration. A L (k) is a scaling factor that changes with the increase of the number of iterations, and its calculation formula is: where f c is a variable, which takes the value of 2 in the embodiments of the present invention, and kmax Indicates the maximum number of iterations.

[0076] Furthermore, it should also be noted that, under the condition of avoiding collisions, the scaling factor in SOA linearly decreases from f c to 0, which achieves a balance between exploration and exploitation. However, damage identification involves the mapping between complex damage factors and extracted features. Therefore, the exploration ability of the algorithm should be enhanced during the early search process to ensure that the global optimal solution can be captured. Thus, this study introduces a non-linear adaptive region contraction strategy, which makes the factor decrease in a non-linear manner. The formula for the non-linear adaptive contraction factor is as follows:

[0077]

[0078] As Figure 3 shown, it demonstrates the situation of A L and A NL changing with the number of iterations. Obviously, at the initial stage of iteration, A NL is much higher than A L , and the decreasing speed is slower, which effectively expands the search range; while in the later stage, the decreasing speed of A NL accelerates, thus ensuring a high convergence efficiency.

[0079] The second condition involves the position of the best individual in the k-th iteration, denoted as X Best (k), which controls the process of other individuals moving towards it. The best individual-guided update formula, its mathematical expression is:

[0080] M i (k) = B(k) · (X Best (k) - X i (k))

[0081] where, M i represents the movement amount of the i-th individual towards X Best (k), and B(k) is a random vector used to balance global search and local development. The calculation formula is B(k) = 2 · A(k) 2 · r and , where r and is a random vector with the same dimension as the individual, and each element is uniformly distributed in the interval from 0 to 1.

[0082] The third condition updates the position of X i (k) based on the above two calculation results. The updated position is denoted as D i , and the position update synthesis formula is:

[0083] D i (k) = |C s,i (k) + Ms,i (k)|

[0084] In the above formula, D i represents the updated position.

[0085] S320. In the predation stage based on the seagull optimization algorithm, seagulls attack migrating birds through spiral trajectory behavior, and the sine-cosine algorithm is introduced to update the positions of the initially updated seagull individuals, and the updated positions of the seagull individuals are output;

[0086] Specifically, in the predation stage, seagulls attack other migrating birds through spiral trajectories. In this stage, the update formula for the position of the i-th seagull individual is:

[0087]

[0088] where x, y, and z respectively represent the behaviors of the individual in three planes, and the update formula for the spiral trajectory behavior is as follows:

[0089]

[0090] where θ and r(θ) are random vectors with the same dimension as the individual. Each element of θ is uniformly distributed in the interval from 0 to 2π, and r(θ) is defined as r(θ) = c1·exp(θ·c2). c1 and c2 are constants, both taking the value of 1 in the embodiments of the present invention. The symbol ⊕ represents an element-wise multiplication operation.

[0091] Furthermore, it should be noted that the sine-cosine algorithm (SCA) is a population-based optimization technique, and its solution update mechanism is derived from the mathematical models of the sine and cosine functions. The periodic characteristics of these functions allow the solution to reposition around the current global optimal solution during the search process. In addition, most population-based optimization techniques rely on random search mechanisms, and SCA also introduces several random variables to increase the probability of finding the global optimal solution. Therefore, the combination of these functions and the random mechanism defines the position update formula of SCA, and its mathematical expression is as follows:

[0092]

[0093] where r1 is an adaptive variable, and the calculation formula is r1 = 2 - 2·k / k max, it gradually decreases as the number of iterations increases; r2 and r3 are random vectors, the elements of r2 are uniformly distributed in the interval from 0 to 1, the elements of r3 are uniformly distributed in the interval from 0 to 2, r4 is a random parameter, uniformly distributed in the interval from 0 to 1, and is used to switch between the sine and cosine components. The value ranges of r1·sin(·) and r1·cos(·) are from -2 to 2. When the absolute value is greater than 1, the algorithm tends to explore different regions in the search space; when the absolute value is less than 1, it tends to develop potential optimal solution regions, thus achieving an effective balance between exploration and development. At the same time, the gradual decay of r1 enables the algorithm to finally converge to the global optimal solution.

[0094] To promote information transmission between different seagull individuals and further improve the performance of SOA in recognition problems, the sine-cosine operator is introduced into the position iteration formula, as shown in the position update formula of the i-th seagull individual. During the iteration process, the sine or cosine operation is selected with a certain probability, and its improved sine-cosine improved position update formula is as follows:

[0095]

[0096] In the above formula, x, y, and z respectively represent the behaviors of the individual in three planes, X i (k) represents the position of the individual after update, r1 represents the adaptive variable, r2 represents the random vector, r4 represents the random parameter, D i (k) represents the position of the updated individual in the k-th iteration, X Best (k) represents the position of the best individual in the k-th iteration.

[0097] S330. The loop iteratively optimizes and updates the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm until the number of iterations meets the preset threshold, and outputs the optimal damage factor vector of the beam structure.

[0098] In summary, the proposed computational framework consists of three main parts. First, a more uncertainty-sensitive and robust objective function is introduced based on sparse regularization. Subsequently, the population update mechanisms of SOA and SCA are integrated, allowing agents to dynamically switch roles within a single iteration to adapt to complex damage scenarios involving uncertainty. Finally, a non-linear adaptive region contraction strategy is adopted to balance global exploration and convergence throughout the iteration process. The effectiveness and superiority of the proposed SCSOA in damage identification are verified through numerical and experimental examples. The combination of the population update mechanism and the adaptive region contraction strategy ensures the balance between exploration and convergence, thus achieving reliable and accurate damage assessment.

[0099] The pseudo-code of the recognition algorithm based on SCSOA proposed in the embodiment of the present invention is specifically as follows:

[0100] 1) Define an objective function assisted by sparse regularization according to the formula of the sparse regularization damage identification objective function; empirically adjust the value of λ;

[0101] 2) Initialize the population within the feasible solution region; set k = 1; set the k max ; termination condition;

[0102] If (the termination condition is not met) then;

[0103] 3) Repeat;

[0104] 4) Evaluate the fitness value of each agent according to the formula of the sparse regularization damage identification objective function and determine X Best (k);

[0105] 5) Apply the non - linear adaptive region contraction strategy and determine A according to the non - linear adaptive contraction factor formula NL ;

[0106] 6) Update the population position through the position update synthesis formula from the collision - avoidance position update formula;

[0107] 7) Use the SCA population update mechanism based on the improved position update formula of sine - cosine to generate the position of the new agent;

[0108] 8) Set k = k + 1;

[0109] 9) Until k reaches max ;

[0110] 10) End If.

[0111] Furthermore, a numerical study is carried out on the embodiments of the present invention. As Figure 4 shown, the FE model of a 20 - element simply - supported beam is presented. The structure is composed of 21 nodes connected by 20 beam elements, with a total length of 3 meters and an element length of 0.15 meters. A beam element with 2 nodes and 4 degrees of freedom is used for modeling. The structure is made of steel and has the following physical properties: elastic modulus E = 210 GPa, density ρ = 7850 kg / m 3 , moment of inertia Ip = 7.6165e -7 m 4 , cross - sectional area S = 0.001164 m 2 . The damage conditions are shown in Table 1, covering single - damage, two - damage, and multi - damage scenarios. The first five natural frequencies and their modal vibration modes are extracted, and the vertical degrees of freedom at the nodes of each element are mainly analyzed.

[0112] Damage identification based on intelligent algorithms sometimes converges to a local optimal solution in a single calculation. Therefore, repeated calculations are usually required to obtain reliable results. In the embodiments of the present invention, the identification of each damage condition is independently performed 100 times, and finally the mean value is taken as the result. To verify the robustness of the proposed method, the embodiments of the present invention introduce noise pollution and add it to the natural frequencies and mode shapes. The specific formula for updating the modal parameters with noise pollution is as follows:

[0113]

[0114] where r n and r cal are the modal parameters with and without noise, respectively. E p represents the noise level, N oise is a random vector whose elements follow a standard normal distribution. The symbol denotes the entry-wise multiplication.

[0115] Table 1 Simulation of damaged elements

[0116] Working condition Damage type Damage degree @ Damaged element 1 Single damage 10％@E10 2 Single damage 20％@E10 3 Single damage 20％@E18 4 Two damages - Asymmetric 15% @ E3, 15% @ E10 5 Two damages - Symmetric 20% @ E3, 20% @ E18 6 Three damages 20% @ E3, 25% @ E10, 15% @ E18

[0117] Furthermore, the value of λ is determined. To determine the appropriate value of the regularization parameter λ, the mean square error (MSE) between the identification results and the actual damage at different λ values is calculated. A medium noise pollution level of 0.02 is selected. As Figure 5 shown, the MSE values of the six damage conditions reach the minimum when λ = 0.03, and λ = 0.03 is selected as the optimal parameter for subsequent identification in the embodiments of the present invention.

[0118] For the identification results in the noise-free case, as Figure 6 shown and in Table 2, under noise-free conditions, all three algorithms can accurately identify the locations of the actual damaged elements. However, significant damage misjudgments occur near both sides of the actual damaged elements for SCA and SOA. In contrast, the proposed SCSOA algorithm exhibits excellent identification accuracy and almost no misjudgments for non-damaged elements. The maximum misjudgment amplitude is only 0.0014. In addition, SCSOA also demonstrates excellent accuracy and stability in damage quantification. The maximum identification error of the actual damaged elements is only -1.1%, and the maximum standard deviation is as low as 0.0155. These results highlight its significant advantages compared to a single update correction mechanism.

[0119] Table 2 Comparison of identification accuracy and stability

[0120]

[0121] Generally speaking, the proposed SCSOA significantly improves the recognition accuracy and stability of actual damaged elements, while greatly reducing the false positives in non-damaged elements. This highlights its superior performance in recognition, which is more excellent compared with a single population update mechanism.

[0122] Further analyzing the recognition results in the presence of noise, the robustness of SCSOA under noise interference was studied by considering 1.5% and 2.0%. The recognition results of six damage conditions based on SCSOA under noise pollution are as Figure 7 shown.

[0123] The recognition results show obvious sparsity. Only the actual damaged elements show significant amplitudes, while the amplitudes of non-damaged elements are small. The maximum recognized damage is 0.0152 under 1.5% noise and 0.0289 under 2.0% noise. This indicates that introducing sparse regularization effectively reduces false positives. However, as the noise level increases, the accuracy of damage quantification decreases, and smaller damaged elements are more sensitive to noise. In summary, the objective function based on sparse regularization used in the embodiments of the present invention enhances the sparsity of the recognition results, which helps to clearly identify the main damaged elements. Although the proposed method shows a certain degree of robustness to noise to some extent, it still needs further improvement.

[0124] To verify the effectiveness of the proposed method in dealing with more complex structures, a truss FE model with 36 elements was introduced. The FE model Figure 8 is shown. The structure is composed of 16 nodes connected by 36 connecting elements, and each element has four degrees of freedom. The material is steel, with an elastic modulus E = 210 GPa, a density ρ = 7850 kg / m 3 , and a moment of inertia I = 8.3333e -10 m 4 , and a cross-sectional area S = 0.0001 m 2 . The truss element is a two-dimensional connecting element with four degrees of freedom. The damage conditions include single damage, two-damage, and multi-damage scenarios, as shown in Table 3. The recognition analysis uses the first five natural frequencies and modal shapes of the structure, and only the vertical degrees of freedom at the nodes of each element are extracted for the modal shapes.

[0125] Table 3 Damage conditions of the truss

[0126] Working condition Damage type Damage degree @ Damaged element 1 Single damage 20％@E5 2 Single damage 20％@E20 3 Double damage 20% @ E6, 20% @ E31 4 Three damages 20% @ E12, 30% @ E20, 25% @ E22

[0127] In the case of no noise pollution, the recognition results of four conditions of the truss based on three algorithms are as Figure 9 shown, and the detailed values are shown in Table 4, where and They represent the highest recognition value in the undamaged elements, the maximum relative error in the actual damaged elements, and the maximum standard deviation in the actual damaged elements, respectively. The introduction of sparse regularization ensures that each algorithm produces sparser results, with significant amplitudes only at the actual damaged elements and the undamaged elements remaining close to zero. However, as the optimization parameter increases, the accuracy of all three algorithms decreases. But the SCSOA algorithm maintains the absolute error within 10%. In addition, the increase in the optimization parameter also leads to an increase in volatility in multiple calculations. The SCA shows the most significant fluctuations, while the SCSOA only shows a slight increase in fluctuations and maintains the highest overall stability.

[0128] It can be seen that the SCSOA is proven to be able to effectively handle structures with more elements and achieve accurate damage location identification through the assistance of sparse regularization. In terms of damage quantification, it is superior to the single-population update algorithm in both accuracy and stability.

[0129] Table 4 Comparison of identification accuracy and stability in the truss damage conditions

[0130]

[0131]

[0132] The main identification results under noise pollution are shown in Table 5, where represents the identified damage factor of the actual damaged element, and RE represents the relative error. The results of the single damage condition show relatively high accuracy, with the RE value not exceeding 1% and no false positives in the undamaged area. However, as the number of damaged elements and the noise level increase, the accuracy decreases. The maximum RE reaches -36.17%. In addition, still remains within 0.02, indicating that the method can accurately identify the damage location on the premise of high reliability. This shows that the proposed method demonstrates a certain degree of robustness even in complex structures.

[0133] Table 5 Identification results under noise conditions

[0134]

[0135] To verify the adaptability of the proposed method in actual structures, a vibration experiment was conducted on a simply supported beam structure in the laboratory. The experimental model and related equipment are as Figure 10 shown. The structure is 3 meters long, with a rectangular cross-section, 0.06 meters high, 0.14 meters wide, and a wall thickness of 0.003 meters. The initial material properties include an elastic modulus of 210 GPa and a density of 7800 kg / m 3. Two cylindrical steel rods are welded to both ends of the steel beam and fixed to the lower support through hinged bearings. A total of 21 acceleration sensors (PCB: ICP333B30) are installed evenly distributed on the beam to capture the acceleration response. The total weight of the sensors is 0.2604 kg, which has a negligible impact on the dynamic characteristics of the beam compared to the total structure weight of 27.2376 kg. The exciter (HEV - 200) is installed 1.65 m from the left support. The first three natural frequencies and modal shapes of the structure are extracted through the built - in algorithm of the LMSSADAS modal data acquisition system. To simulate structural damage, notches are cut in the height direction of the steel beam.

[0136] Initial FE model modification. The initial FE model of this structure consists of 20 beam elements of equal length. To minimize the deviation between the FE model and the actual structure, four parameters are selected for modification, including the linear density ρ A , the flexural stiffness EI, the vertical stiffness k of the support v and the rotational stiffness k of the support θ . The modified parameter values are shown in Table 6. In addition, the frequencies obtained from the modified model are highly consistent with the frequencies measured in the experiment (as shown in Table 7), confirming the effectiveness and accuracy of the modified model in subsequent damage identification.

[0137] Table 6 Parameters before and after modification

[0138] Correction parameter Unit Initial value Corrected value Change rate <![CDATA[ρ A > kg / m 9.0792 7.9325 -12.63％ EI N·m2 159950 140560 -12.12％ <![CDATA[k v > N / m ∞ 5.330e+08 - <![CDATA[k θ > N / rad 0 3.785e+06 -

[0139] Table 7 Frequencies before and after modification

[0140]

[0141] In the damage condition, the measured frequencies of the first three orders are shown in Table 8. With the increase in the number of damaged elements and the degree of damage, the decrease in the measured frequencies indicates the effectiveness of the measurement results. The obtained results are as Figure 11 , and more detailed data are shown in Table 8.

[0142] Table 8 Four damage conditions and the corresponding measured frequencies

[0143]

[0144]

[0145] As Figure 11 shown, the results using sparse regularization show higher sparsity, and significant amplitudes only appear at the actual damage locations. And in all four damage modes, the maximum false positive is only 0.0864.

[0146] Table 9 Comparison of recognition accuracy

[0147]

[0148] As shown in Table 9, except for the relatively large identification error of the 15th unit in working condition 3, the identification error using sparse regularization remains within a range close to -10%. On the contrary, when sparse regularization is not used, the REs of the actual damaged units mostly exceed -10%. When comparing the average REs of the two methods, the error using sparse regularization is -12.7%, which is lower than -14.14% without using sparse regularization. Overall, the experimental verification results show that the proposed method realizes spatial sparsity, accurately locates the damage, and improves the damage quantification accuracy by combining collaborative intelligence and sparse regularization.

[0149] In summary, the embodiment of the present invention proposes a novel SCSOA framework, which is specifically aimed at the structural damage identification problem involving uncertainties, and improves the accuracy and robustness of identification. This framework combines the population update mechanisms of SCA and SOA, enabling individuals in the population to dynamically switch roles to adapt to different identification requirements. At the same time, SOA introduces a non-linear adaptive region contraction strategy to replace the original linear strategy, thus ensuring the balance between the global search ability and the convergence speed. In addition, sparse regularization further enhances the algorithm's ability to handle uncertainties, especially noise pollution, by adding an L1 penalty term to the objective function.

[0150] Therefore, the embodiment of the present invention has the following differences compared with the prior art:

[0151] 1) The collaborative intelligence combining the population update mechanisms of SCA and SOA enables agents to dynamically switch roles to adapt to different identification requirements, and shows advantages over algorithms with a single population update mechanism.

[0152] 2) The introduced adaptive region contraction strategy ensures the balance between the global search ability and the convergence speed. Compared with the original SOA, the identification results are more accurate and stable without additional iterations.

[0153] 3) It shows higher accuracy when identifying the damage conditions of different structures. And it is worth noting that the proposed algorithm shows good robustness in terms of anti-noise ability, and the damage can be inverted with satisfactory accuracy under the condition of noise pollution.

[0154] 4) The proposed SCSOA and adaptive region contraction strategy framework has good versatility, and the embedded agents can be any swarm intelligence algorithm. That is, in future work, the proposed SDI framework can be extended to solve more complex situations, such as identifying FRP debonding in composite material structures.

[0155] Refer to Figure 2, a structural damage identification system based on a multi-swarm intelligence collaborative algorithm, comprising:

[0156] The first module 201 is used to perform structural damage identification on the beam structure, introduce noise pollution and a sparse regularization term, and construct a sparse regularization auxiliary objective function for beam structure damage identification;

[0157] The second module 202 is used to construct a dynamic multi-role adaptive collaborative intelligent algorithm based on the seagull optimization algorithm and the sine-cosine algorithm, combined with a non-linear adaptive region contraction strategy;

[0158] The third module 203 is used to iteratively optimize and update the sparse regularization auxiliary objective function for beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm to obtain the optimal damage factor vector of the beam structure.

[0159] The content in the above method embodiments is applicable to the embodiments of this system. The functions specifically implemented by the embodiments of this system are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those of the above method embodiments.

[0160] The above is a specific description of the preferred embodiments of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art can make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A structural damage identification method based on a multi-swarm intelligent collaborative algorithm, characterized in that: The following steps are involved: Structural damage identification is performed on beam structures, and noise pollution and sparse regularization terms are introduced to construct sparse regularization auxiliary objective function for beam structure damage identification. Based on the Seagull optimization algorithm and the sine-cosine algorithm, combined with the nonlinear adaptive region shrinkage strategy, a dynamic multi-role adaptive collaborative intelligent algorithm is constructed; Based on the dynamic multi-role adaptive collaborative intelligent algorithm, the sparse regularized auxiliary objective function of beam structure damage identification is iteratively optimized and updated to obtain the optimal damage factor vector of the beam structure.

2. According to claim 1, a structural damage identification method based on a multi-swarm intelligent collaborative algorithm is characterized in that: The step of identifying structural damage of the beam structure, introducing noise pollution and sparse regularization terms, and constructing a sparse regularization auxiliary objective function for beam structure damage identification specifically includes: Perform unit division and structural damage identification on the beam structure in turn, and extract the first n-order natural frequencies and modal vibration shapes of the beam structure; Based on the first n-order natural frequencies and modal vibration shapes of the beam structure, noise pollution is introduced to construct the first n-order natural frequencies and modal vibration shapes of the beam structure with noise; Based on the first n-order natural frequencies and modal vibration shapes of the beam structure with noise, an additional penalty term based on prior knowledge is introduced to construct a sparse regularized auxiliary objective function for damage identification of beam structures.

3. According to claim 2, a structural damage identification method based on a multi-swarm intelligent collaborative algorithm is characterized in that: The expression of the sparse regularization auxiliary objective function for beam structure damage identification is specifically as follows: In the above formula, J(α) represents the sparse regularization auxiliary objective function of beam structure damage identification, α represents the damage factor vector, i represents the i-th order, and FCR i Indicates the modal frequency change rate, FAC i represents the modal flexibility confidence criterion, ||α||1 represents the L1 norm, λ represents the regularization parameter, ω represents the weight coefficient, and n represents the first n-order modes.

4. According to claim 3, a structural damage identification method based on a multi-swarm intelligent collaborative algorithm is characterized in that: The step of iteratively optimizing and updating the sparse regularized auxiliary objective function of beam structure damage identification based on the dynamic multi-role adaptive collaborative intelligent algorithm to obtain the optimal damage factor vector of the beam structure specifically includes: Based on the sparse regularization auxiliary objective function of beam structure damage identification, a nonlinear adaptive region shrinkage strategy is introduced, and the individual positions are updated through the migration phase of the seagull optimization algorithm to obtain the preliminary updated individual positions of the seagulls. In the predation phase based on the seagull optimization algorithm, seagulls attack migrating birds through spiral trajectory behavior, and introduce the sine-cosine algorithm to update the initial updated individual positions of seagulls, and output the updated individual positions of seagulls; The sparse regularization auxiliary objective function of beam structure damage identification is iteratively optimized and updated based on the dynamic multi-role adaptive collaborative intelligent algorithm until the number of iterations meets the preset threshold, and the optimal damage factor vector of the beam structure is output.

5. According to claim 4, a structural damage identification method based on multi-swarm intelligent collaborative algorithm is characterized in that: The position update of individuals in the migration phase of the seagull optimization algorithm meets the following conditions: Avoid collisions between individuals, in which a nonlinear adaptive region shrinkage strategy is introduced to nonlinearly adjust the scaling factor in the individual's collision avoidance position, and to construct a collision avoidance position update condition; Move in the direction of the best neighbor and construct the best individual guided update condition; Keeping a distance close to the best search individual, the initial updated seagull individual position is determined by combining the collision avoidance position update condition with the best individual guidance update condition.

6. According to claim 5, a structural damage identification method based on multi-swarm intelligent collaborative algorithm is characterized in that: The expression of the nonlinear adaptive region shrinkage strategy is specifically as follows: In the above formula, A NL (k) represents the nonlinear adaptive region shrinkage strategy, f c represents the variable, k represents the number of iterations, max Indicates the maximum threshold for the number of iterations.

7. The structural damage identification method based on multi-swarm intelligent collaborative algorithm according to claim 6 is characterized in that: The expression of individual position update of the spiral trajectory behavior is specifically as follows: x=r(θ)⊕cos(2π·θ) y=r(θ)⊕sin(2π·θ) z=r(θ)⊕θ In the above formula, x, y, and z represent the behaviors of individuals in three planes, and r(θ) and θ represent random vectors.

8. According to claim 7, a structural damage identification method based on multi-swarm intelligent collaborative algorithm is characterized in that: The individual position update expression of the sine-cosine algorithm is specifically expressed as follows: In the above formula, x, y, and z represent the behavior of the individual in three planes, respectively. i (k) represents the updated position of the individual, r1 represents the adaptive variable, r2 represents the random vector, r4 represents the random parameter, D i (k) represents the updated position of the individual in the kth iteration, X Best (k) represents the position of the best individual in the kth iteration.

9. A structural damage identification system based on multi-swarm intelligent collaborative algorithm, characterized in that: Includes the following modules: The first module is used to identify structural damage of beam structures, introduce noise pollution and sparse regularization terms, and construct a sparse regularization auxiliary objective function for beam structure damage identification; The second module is used to build a dynamic multi-role adaptive collaborative intelligent algorithm based on the Seagull optimization algorithm and the sine-cosine algorithm, combined with a nonlinear adaptive region shrinkage strategy; The third module is used to iteratively optimize and update the sparse regularization auxiliary objective function of beam structure damage identification based on a dynamic multi-role adaptive collaborative intelligent algorithm to obtain the optimal damage factor vector of the beam structure.

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