NSCRO-SL-based double-cable model collaborative vibration reduction multi-objective optimization method

Abstract

The invention discloses an NSCRO-SL-based double-cable model collaborative vibration reduction multi-objective optimization method, which mainly comprises the following steps of: carrying out finite element modeling on a double-cable model and a collaborative vibration reduction system based on a vibration reduction system consisting of VD and TMD-CT; mathematical modeling is carried out for a parameter design problem of a double-cable system, two design indexes (a dynamic characteristic index and a vibration reduction performance index) are provided, and then a non-dominated sorting algorithm (NSCRO-SL for short) suitable for multi-objective function optimization is provided on the basis of a CRO-SL algorithm. And finally, performing parameter design solution on a multi-target problem based on two design indexes in the VD and TMD-CT double-cable model parameter design process by using NSCRO-SL. According to the method, the problem of multi-objective optimization in the VD and TMD-CT-based double-cable model parameter design process is effectively solved, the performance of a multi-objective algorithm in optimization and search problems is improved by adopting multiple different matrix layers, and excellent parent parent corals are reserved by adopting an elite algorithm, so that excellent parents in previous iterations are reserved.

Description

Technical Field

[0001] This invention relates to the field of vibration control technology for engineering structures, and specifically to a method for designing and optimizing the collaborative vibration reduction parameters of a dual-cable model based on the multi-objective optimization algorithm NSCRO-SL. Background Technology

[0002] Cable-stayed bridges, as one of the main forms of long-span bridges, are prone to multimodal and high-order vibrations under external excitations such as wind loads, vehicle loads, and earthquakes due to the large slenderness ratio and low inherent damping of their cables. With the continuous increase in bridge span, the length and flexibility of the cables increase significantly, leading to more complex vibration characteristics. Traditional single-point damping systems (such as single viscous dampers (VDs) or tuned mass dampers (TMDs)) are insufficient to effectively suppress the multimodal vibrations of long cables. Engineering practice on numerous cable-stayed bridges both domestically and internationally shows that even with dampers installed, high-order vortex-induced vibrations can still occur in the cables, indicating significant limitations of existing vibration reduction technologies in controlling the vibration of long cables. Currently, vibration control measures for cable-stayed bridges mainly include aerodynamic measures, auxiliary cable structure measures, and external damper measures. Among these, external damper measures (such as VDs and TMDs) are widely used due to their wide applicability and flexible installation. However, when using a single damper to control multimodal vibration of long cables, there are technical problems such as unclear coupling effects between dampers, insufficient adaptability of traditional optimization algorithms, and limited vibration reduction performance.

[0003] To address the aforementioned issues, existing research has attempted to employ combined vibration reduction measures, such as combining cross-tie (CT) auxiliary cables with dampers to form a TMD-CT structure. While this method can suppress vibrations within a specific frequency range to some extent, its control over local vibration modes remains unsatisfactory. Furthermore, the introduction of auxiliary cables in a dual-cable system leads to changes in modal frequencies and mode shapes, rendering traditional damper parameter design methods inapplicable. Therefore, a multi-objective optimization algorithm that can balance global optimization capabilities with solution set diversity is urgently needed.

[0004] In view of the above, this invention proposes a multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL, in order to solve the above problems. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, this invention proposes a multi-objective optimization method for synergistic vibration reduction of a dual-cable model based on NSCRO-SL. This method aims to solve the problems of unclear damper synergistic effect, low parameter optimization efficiency, and insufficient vibration reduction performance in the prior art, and provides a new technical solution for the effective control of multimodal vibration of cable-stayed cables.

[0006] A multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL, characterized by the following steps:

[0007] S1: Based on the vibration reduction system composed of VD and TMD-CT, finite element modeling is performed on the dual-cable model and the synergistic vibration reduction system. Mathematical modeling is performed on the parameter design problem of the dual-cable system and two design indicators are proposed.

[0008] S2: Based on the CRO-SL algorithm, a non-dominated sorting algorithm (NSCRO-SL) suitable for multi-objective function optimization is proposed.

[0009] S3: Use the NSCRO-SL to solve the multi-objective problem of the two design indices in the parameter design process of the VD and TMD-CT dual-cable model.

[0010] The beneficial effects of the above technical solution are as follows:

[0011] (1) This invention provides a multi-objective optimization method for coordinated vibration reduction of a dual-cable model based on NSCRO-SL. It uses VD and TMD-CT to perform coordinated vibration reduction on a dual-cable system. In the process of designing the parameters of the coordinated vibration reduction system, two design indices and multiple parameters are considered simultaneously, which effectively solves the problem of multi-objective optimization in the parameter design process of a dual-cable model based on VD and TMD-CT.

[0012] (2) In the NSCRO-SL algorithm of this invention, non-dominated sorting and crowding distance are introduced into the traditional CRO algorithm, which solves the problem of evaluating the merits of multi-objective functions and maintaining population diversity. At the same time, the use of a variety of different matrix layers improves the performance of multi-objective algorithms in optimization and search problems.

[0013] (3) In the NSCRO-SL algorithm of this invention, the elite algorithm is used to retain the excellent parent corals and let them occupy the coral reef, so as to avoid the accumulation of voids and solve the problem of void accumulation due to the limited number of attempts by larvae and the influence of coral predation factors. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the process for optimizing the parameters of a dual-cable hybrid system based on the NSCRO-SL method according to the present invention;

[0015] Figure 2 This is a schematic diagram of the NSCRO-SL optimization algorithm proposed in this invention;

[0016] Figure 3 This is a schematic diagram illustrating the generation of offspring using NSCRO-SL in the multi-matrix layer of this invention;

[0017] Figure 4 A schematic diagram showing the arrangement of the dual-cable rigid auxiliary cable and damper system used;

[0018] Figure 5 This is a schematic diagram comparing the Pareto fronts of the optimization results of NSCRO-SL and NSGA-Ⅱ in this invention.

[0019] Figure 6 This is a schematic diagram comparing the iterative convergence of the optimization calculation results of NSGA-Ⅱ and NSCRO-SL in this invention;

[0020] Figure 7 This is a schematic diagram showing the changes in modal frequencies before and after optimization in this invention;

[0021] Figure 8 This is a schematic diagram showing the optimized parameters and fitness function values ​​of the auxiliary cable and damper in a specific implementation. Detailed Implementation

[0022] The foregoing and other technical contents, features and effects of the present invention will be clearly presented in the following detailed description of the embodiments with reference to the accompanying drawings. All contents mentioned in the following embodiments are based on the accompanying drawings.

[0023] Example 1, such as Figure 1 , Figure 4 As shown, this invention employs a vibration reduction system composed of VD and TMD-CT to reduce vibration in a dual-cable system. Therefore, this invention proposes two design specifications: the first design specification... The first is the energy-based PBDI index, which measures the multimodal vibration level of the stay cable. A decreasing PBDI indicates that the multimodal vibration of the stay cable is under control. The second design index... It is the negative value of the average value of the first m modal frequencies of the cable-stayed bridge. The smaller the value, the higher the overall frequency of the first m orders of the stay cable, meaning the dynamic characteristics of the stay cable are improved, causing the natural frequency of the stay cable to move away from the frequency of common wind-induced vibrations (the first 3 Hz). These are the influencing factors, i.e., the independent variables, in the dual-cable hybrid system. The calculation of the first two design indices is given in formula (1), and the minimum value of both objective functions is calculated:

[0024] (1)

[0025] In the formula: It is the i-th variable in the dual-cable hybrid system. This represents the lower bound of the i-th variable. This represents the upper limit of the i-th variable; To calculate the integral of the objective function with respect to time, The i-th modal frequency of the cable-stayed bridge, The size should make the front The frequency range of first-order modal vibration can cover up to 3Hz;

[0026] Let be the state vector of the cable-stayed bridge, defined as: ,in These are the modal coordinates of the stay cables. Its derivative;

[0027] The initial value is set to , The initial force applied is expressed in Newtons (N). The size does not affect the final result, only the PBDI value; without applying external excitation, the stay cable... The system decays freely to a steady state within a given time period, and its PBDI value is calculated simultaneously, where time... It must be large enough to reach a stable state, i.e., the state vector. Matrix Q is a 2n×2n positive definite matrix, and its values ​​are as follows:

[0028] (2)

[0029] In the formula: These are the weighting coefficients for the k-th order mode. They can be weighted according to the importance of different order modes to better match the structural vibration reduction requirements. It is the first Angular frequencies of the first mode; It is the maximum value of the k-th eigenvector, where k is a natural number from 1 to n. express arrive The k-th mode between.

[0030] Example 2, as Figure 2 , Figure 3 As shown, the CRO (Coral Reefs Optimization) algorithm is a heuristic algorithm based on the behavioral processes occurring in coral reefs. The basic single-objective optimization algorithm of CRO mainly includes the following:

[0031] (1) Initialize the reef: Let R be a grid of size R1×R2, and let R represent the reef. Each grid cell can be assigned one coral. Each coral in the reef is a candidate solution for the vibration reduction system parameters. Then determine the initial filling ratio P0 of the reef. The initial number of corals in the reef is R×P0. Reef cavities without coral settlement will accommodate new corals later in the algorithm.

[0032] (2) Generation of new corals: CRO generates new corals in each iteration. Coral generation occurs through two methods: broadcast spawning and incubation.

[0033] a) External sexual reproduction or broadcast spawning: Before new corals are produced, the probability P of broadcast spawning needs to be determined. b To produce new larvae, two broadcast ovipositors will be selected and a crossover operator or other measures will be applied. It is important to note that the two broadcast ovipositors selected as parents will not be selected for reproduction in the next iteration.

[0034] b) Internal sexual reproduction or brooding: Hermaphroditic corals primarily reproduce through brooding. The probability of a selected coral brooding is 1-P. b This reproduction is simulated through any mutation mechanism. The mutation type used in this invention is randomly selected within a parameter range.

[0035] (3) Coral Placement: Each newly created coral will attempt to settle at a random location on the reef. When the chosen location is a hole, the coral will settle directly at that location. When a coral is already settled at the chosen location, the newly created coral and the existing corals will be compared using a fitness function; corals with lower fitness will be replaced by corals with higher fitness. Furthermore, the CRO algorithm defines the maximum number of attempts a coral can make in each iteration. .

[0036] (4) Predation: Corals may die during reef formation. After each reproductive iteration, a small number of corals in the reef become preyed upon, thus making room for the next generation. The preyed corals are the least adapted corals in the reef. The probability of a coral being preyed upon is P. d The number of corals preyed upon each time is N. d .

[0037] (5) Final coral population: The final number of iterations N needs to be determined before proceeding with the iteration. iterations The coral reef will continue to iterate as long as the current number of iterations is less than the final number of iterations.

[0038] CRO-SL builds upon CRO by introducing matrix layers from real coral reef ecosystems, impacting the broadcast spawning process. Each matrix layer in a coral reef represents a different broadcast spawning process (different models, operators, parameters, constraints, repair functions, etc.). These matrix layers significantly improve performance in optimization and search problems.

[0039] Based on the fundamental CRO and CRO-SL optimization algorithms, this invention proposes a non-dominated sorting (NSS) NSCRO-SL algorithm suitable for multi-objective function optimization. This algorithm extends single-objective CRO-SL optimization to multi-objective scenarios, improving upon the original algorithms while retaining their advantages. NSCRO-SL addresses the issues of evaluating the merits of multi-objective functions and maintaining population diversity by introducing non-dominated sorting and crowding distance. Furthermore, the algorithm retains strategies from CRO such as broadcast spawning, incubation to generate new corals, and coral predation, ensuring its ability to search for optimal solutions, and utilizes the matrix layer to enhance the population's competitive co-evolutionary capabilities.

[0040] In extending traditional CRO-SL to multi-objective optimization, it was found that when the number of larval attempts was small, the generated superior larvae were not effectively preserved; simultaneously, due to coral predation mechanisms, poorly adapted corals were preyed upon during iterations. These two factors combined resulted in holes never being occupied by new corals. As the number of iterations increased, the number of empty holes continued to rise, leading to problems such as decreased convergence, loss of diversity, getting trapped in local optima, reduced computational efficiency, and decreased decision quality. Therefore, this invention employs an elite algorithm to retain superior parent corals and allow them to occupy the reef, avoiding the accumulation of empty holes and thus preserving superior parent corals from each iteration. The optimization process of NSCRO-SL is as follows: Figure 2 As shown. It should be noted that this algorithm can only guarantee an approximate optimal solution, not an absolute optimal one.

[0041] like Figure 3 As shown, the matrix layers in this invention employ the following five types: harmonic search mutation, multi-point crossover, simulated binary crossover, hybrid crossover, and differential evolution mutation. Each of the five matrix layers has an equal probability of being selected, i.e., a 20% probability of selection. A schematic diagram of the five matrix layers is shown below. Figure 1 As shown. The five matrix layers are described below:

[0042] (1) Harmony Search Mutation (HS): This operator originates from the harmony search algorithm. The harmony search algorithm is a population-based metaheuristic algorithm that mimics the improvisational performance of an orchestra when composing melodies. Harmony search mutation controls the generation of new larvae in one of the following ways:

[0043] i. Harmonious Memory Rate (HMCR) is a component of a new larva whose value is randomly selected from other larvae within a probability range of [0,1].

[0044] ii. The pitch adjustment rate (PAR) is finely adjusted within the probability range of [0,1] for the current larva, replacing it with any adjacent value (with the same probability). In the parameter optimization calculation of this invention, the harmonic memory rate (HMCR) is set to 0.8, and the pitch adjustment rate (PAR) is set to 0.2.

[0045] (2) Multipoint crossover (MPX): Multipoint crossover, also known as generalized crossover, refers to randomly setting k crossover points in an individual's chromosomes, and then using a binary template at these k crossover points to determine whether parts of the individual need to be swapped. Two parent larvae are selected as the larva undergoing multipoint crossover and another randomly selected larva from the parent family. The two resulting new larvae undergo non-dominated sorting; the larva with the lower sorting rank is selected as the new larva, and the other is eliminated. When... When, it is a single-point intersection, when When two points intersect, k is a random integer ranging from 2 to the number of variables in the parameter optimization calculation of this invention.

[0046] (3) Simulated Binary Crossover (SBX): This operator is a crossover operator that simulates single-point binary crossover, mainly used in multi-objective evolutionary algorithms with real-code encoding. Two new larvae cross over using the formula: Generate, among which It is a new larva. It considers the parent larvae. It is determined by the distribution factor The value is determined dynamically and randomly according to formula (3). Here, u is a random number between 0 and 1, indicating that both formulas in formula (3) have a 50% probability of being selected for calculation. It is a custom parameter. The larger the value, the greater the probability that the offspring will closely resemble the parent. In the parameter optimization calculations of this invention... :

[0047] (3)

[0048] (4) Mixed crossing (BLX-δ): New larvae In the interval Uniformly distributed within, among which , , , It is a constant. In the parameter optimization calculation of this invention .

[0049] (5) Differential Evolutionary Mutation (DE): This operator originates from the differential mutation operator in the differential evolution algorithm, which possesses powerful global search capabilities. DE introduces a different mechanism to explore the search space. Therefore, it utilizes individual differences to disrupt the larval population, thereby generating new larvae by applying each encoded parameter of the larvae. This introduces a perturbation, where F is an evolutionary factor weighted by the perturbation amplitude. The invention also introduces CR, which is the probability that each code is perturbed. In the parameter optimization calculations of this invention… , .

[0050] The NSCRO-SL parameters used in this invention are shown in Table 1. Figure 4 As shown, this invention proposes using VD and TMD to control the multimodal vibration of a stay cable, wherein the TMD is installed on the rigid auxiliary cable (CT), forming a TMD-CT. The two stay cables, VD, and TMD-CT together constitute a dual-cable hybrid system. The dual-cable hybrid system proposed in this invention is as follows: Figure 4 As shown. Figure 4 The image shows a dual-cable hybrid system with three rigid auxiliary cables, three TMDs, and two viscous dampers installed simultaneously.

[0051]

[0052] In the simulation analysis of this invention, two cables from a cable-stayed bridge in Lanzhou are used as the main cables. The physical parameters of the two cables are shown in Table 2. The auxiliary cable is a rigid auxiliary cable and needs to provide support for the TMD (Transport Damping Device). Therefore, a steel bar with an elastic modulus of 195.0 GPa is used as the rigid auxiliary cable in this experiment.

[0053]

[0054] Both stay cables were modeled in ANSYS using finite element models based on the relevant parameters of the target cable. The cable force was corrected using formula (4) to ensure that the natural frequency of the cable was consistent with that of the actual cable.

[0055] (4)

[0056] In the formula: Let be the frequency of the i-th mode in the finite element model. These are the measured modal frequencies of the structure. represents the weighting coefficients for each mode of the structure, and n represents the number of modes considered.

[0057] The VD is fixed at position 0.04L (Note: L represents the total length of the stay cable, and 0.04L represents the installation position of the VD at 0.04 of the total length), and the mass of the mass block in the TMD is 50 kg. Two stay cables are connected to both ends of the rigid auxiliary cable, and no pretension is applied to the auxiliary cable. The objective function and parameter range of this invention in this embodiment are shown in formula (5):

[0058]

[0059] like Figure 4 As shown in the formula, , , These are the installation locations of the three TMD-CTs. , , , , , , , , These are the angular frequencies of the three TMDs. Damping ratio , , These are the damping coefficients of the viscous dampers installed on C1 and C2, respectively. , , This refers to the length of the lower cable-stayed cable 2. The optimization process for the parameters of the dual-cable hybrid system based on the NSCRO-SL method is as follows: Figure 1 As shown, firstly, finite element modeling is performed on the dual-cable model and the synergistic vibration reduction system. Secondly, mathematical modeling is performed on the parameter design problem of the dual-cable system, and two new design indices (dynamic characteristic index and vibration reduction performance index) are proposed. Then, the NSCRO-SL multi-objective optimization algorithm is used to solve the multi-objective problem of the two parameter design indices in the parameter design process based on the VD and TMD-CT dual-cable models.

[0060] At the same time, in order to determine The invention considers the number of the first m low-frequency modes. First, the larval population is initialized, and an unoptimized larva is selected. Modal analysis is performed on the dual-cable hybrid system under the parameters of this larva to obtain its first 20 modal frequencies, as shown in Table 3. Table 3 shows that the first 7 frequencies of the stay cable are below 3 Hz. The presence of densely packed modes below 3 Hz in the dual-cable system is extremely detrimental to the vibration control of the cable. When the frequency of the external excitation is within this range, multiple different modes of the system may be excited. Furthermore, the frequency range below 3 Hz is also the frequency range where wind and rain vibrations frequently occur. Therefore, to improve the modal frequencies of the system within the 3 Hz range, the invention... The average value of the first 7 frequencies is selected as the optimization target, i.e., m=7.

[0061]

[0062] When using NSGA-II to optimize parameters, the population size is 160 and the number of iterations is 50, which is consistent with the use of NSCRO-SL.

[0063] In this invention, the Coverage and Spread metrics are used to evaluate NSGA-II and NSCRO-SL. The Coverage metric measures the proportion of a solution set (A) that covers another solution set (B). Specifically, it calculates how many solutions in solution set A are dominated by at least one solution in solution set B. A larger C(A,B) value indicates a stronger coverage of solution set A by solution set B, and is used to assess the quality of the solution set. The Spread metric measures the uniformity of the distribution of solution sets in the Pareto front. A smaller Spread value indicates a more uniform distribution of solution sets, and is used to assess the diversity of solution sets. The calculation formulas for the Coverage and Spread metrics are shown in formulas (6) and (7):

[0064] (6)

[0065] In the formula: a is a solution in solution set A, b is a solution in solution set B, and |A| is the total number of solutions in solution set A. Let be the number of solutions in solution set A that are dominated by at least one solution in solution set B. Where solution b is weakly dominated by solution a if and only if b is no worse than a in all objectives.

[0066] (7)

[0067] In the formula: The distance between the first and second solutions in the solution set. To find the distance between the penultimate and penultimate solutions in the solution set, The distance between the i-th solution and the (i+1)-th solution in the solution set. For all The average value of n is the total number of solutions in the solution set.

[0068] The auxiliary cable and cable end damper were simultaneously optimized using NSGA-Ⅱ and NSCRO-SL, and the optimization results were obtained after 50 iterations. Figure 5As shown, the Pareto front results and calculated coverage and distribution indices for NSGA-II and NSCRO-SL after 50 iterations are presented. The coverage index for NSGA-II is 0.623, while that for NSCRO-SL is 0.250. This indicates that the optimization results of NSCRO-SL are more weakly dominated by those of NSGA-II, suggesting that the quality of the NSCRO-SL solution set is higher. The distribution index for NSGA-II is 1.269, while that for NSCRO-SL is 1.100. This indicates that NSCRO-SL has better uniformity and richer solution set diversity than NSGA-II. Figure 5 The distribution of optimization results data points also shows that NSGA-II has 69 sets of optimization results, but most of them are highly clustered, while NSCRO-SL's optimization results are more evenly distributed, and NSCRO-SL's optimization results are no weaker than NSGA-II's. Therefore, this invention selects the results optimized by NSCRO-SL, and fills the 24 sets of results with a ranking level of 1 obtained after NSCRO-SL optimization into the following... Figure 8 Table 4. Optimization parameters and fitness function values ​​for auxiliary cables and dampers are shown in Table 4. Figure 8 As shown in Table 4.

[0069] like Figure 6 The figure shows the curves of the optimal and average values ​​of the two fitness functions of the NSGA-Ⅱ and NSCRO-SL populations during 50 iterations. From... Figure 6 (a) The optimal convergence curves show that in the early stages of iteration, NSGA-II and NSCRO-SL converge at almost the same rate. By the 10th iteration, NSCRO-SL converges to around 3, which is faster than NSGA-II. By the 18th iteration, the convergence results of NSGA-II and NSCRO-SL are almost identical. However, in subsequent iterations, the convergence of NSGA-II almost stagnates, while NSCRO-SL's convergence slows down to the 27th iteration. It converged again, even in the 50th generation. Convergence still occurred, and the convergence result at generation 50 was 0.133 smaller than that of NSGS-II. The average convergence curves show that after convergence to generation 18, the average convergence curve of NSGA-II remained relatively stable, while the average convergence curve of NSCRO-SL still exhibited significant fluctuations after generation 18. This indicates that compared to NSGA-II, NSCRO-SL has a more pronounced mutation capacity and can still improve population quality and stability in later iterations. Furthermore, the smaller average convergence curve of NSGA-II compared to NSCRO-SL suggests that the convergence result of NSGA-II is stuck in a narrowing pattern. The local solution set is relatively small, while the NSCRO-SL convergence results are more average and the solution set diversity is richer, which is consistent with the Pareto front results.

[0070] from Figure 6 (b) The optimal convergence curves show that in the early stages of iteration, NSGA-II and NSCRO-SL showed no difference in convergence results. However, by the 9th generation, NSGA-II converged faster, quickly reaching approximately -2.36 Hz. From the 8th generation onwards, however, convergence almost stagnated. In contrast, NSCRO-SL's convergence curve converged more slowly by the 8th generation, but then converged rapidly again by the 27th generation, with the convergence result differing from NSGA-II by only 0.005 Hz – a very small difference. The average convergence curves also show that NSGA-II's average convergence curve fluctuated less after the 8th generation, while NSCRO-SL's average convergence curve exhibited significant fluctuations both before and after the second convergence in the 27th generation. This indicates that NSCRO-SL possesses a more prominent global search capability compared to NSGA-II. Meanwhile, the convergence curve of the NSGA-II average value is larger than that of the NSCRO-SL average value, indicating that the convergence result of NSGA-II is stuck in a certain state. The local solution set is relatively large, while the NSCRO-SL convergence results are relatively average and the solution set diversity is relatively rich, which is consistent with the Pareto front results.

[0071] from Figure 8 Table 4 shows that some optimization results have fitness functions biased towards higher frequencies, while others have biased towards lower PBDI values. In this invention, to prevent the results from being biased towards either objective function, the eleventh set of optimization parameters, which can balance the two objective functions, is selected for further analysis.

[0072] The results of the eleventh group of larvae optimized by NSCRO-SL were compared with those of the first generation of larvae selected in the first iteration. The comparison results of the first 20 modal frequencies are as follows: Figure 7 As shown. From Figure 7 The results show that the frequencies of the first seven modes are significantly improved after optimization, with the fifth vibration mode being very close to 3 Hz, and the sixth and seventh vibration modes exceeding 3 Hz. The frequencies of the 10th to 16th vibration modes are also significantly improved compared to before optimization, proving that the NSCRO-SL optimization algorithm proposed in this invention can effectively improve the system modal frequencies under multimodal vibration conditions.

[0073] The above description is only for illustrating the present invention and should be understood as not being limited to the above embodiments. Various modifications that conform to the spirit of the present invention are within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL, characterized in that, Includes the following steps: S1: Based on the vibration reduction system composed of VD and TMD-CT, finite element modeling is performed on the dual-cable model and the synergistic vibration reduction system. Mathematical modeling is performed on the parameter design problem of the dual-cable system and two design indicators are proposed. S2: Based on the CRO-SL algorithm, a non-dominated sorting algorithm (NSCRO-SL) suitable for multi-objective function optimization is proposed. S3: Use the NSCRO-SL to solve the multi-objective problem of the two design indices in the parameter design process of the VD and TMD-CT dual-cable model.

2. The multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL according to claim 1, characterized in that, The two design specifications include: Dynamic performance indicators, vibration reduction performance indicators; The expressions for the two design indices are shown in formula (1): (1) In the formula, It is an energy-based vibration reduction performance index; the smaller the value, the higher the degree to which the multimodal vibration of the cable-stayed cable is controlled. It is the negative value of the average value of the first m modal frequencies of the cable-stayed bridge, representing a dynamic characteristic index. The smaller the value, the higher the overall increase in the first m modal frequencies of the cable-stayed bridge. The i-th modal frequency of the cable-stayed bridge, It is the i-th variable in the dual-cable hybrid system. This represents the lower bound of the i-th variable. This represents the upper limit of the i-th variable. The size should make the front The frequency range of first-order modal vibration can cover up to 3Hz; Let be the state vector of the cable-stayed bridge, defined as: ,in These are the modal coordinates of the stay cables. Its derivative; The initial value is set to , The initial force applied is expressed in Newtons (N). Size does not affect the final result, only Value size; Let be the time it takes for the stay cable to freely decay to a steady state without applying external excitation, and It must be large enough to reach a stable state, i.e., the state vector. ; Matrix Q is a 2n×2n positive definite matrix, and its values ​​are shown in formula (2): (2) In the formula, These are the weighting coefficients for the k-th mode. They can be weighted according to the importance of different modes to better suit the structural vibration reduction requirements. It is the first Angular frequencies of the first mode; It is the maximum value of the k-th eigenvector, where k is a natural number from 1 to n. express arrive The k-th mode between.

3. The multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL according to claim 1, characterized in that, Step S2 includes: The single-objective CRO-SL optimization is extended to multi-objective scenarios. By introducing non-dominated ranking and crowding distance strategies, the problems of evaluating the merits of multi-objective functions and maintaining population diversity are solved. The broadcast spawning, hatching and new coral generation, and coral predation strategies in CRO are retained to ensure its ability to search for optimal solutions; Employing various matrix layers improves the performance of multi-objective algorithms in optimization and search problems, and enhances the competitive and cooperative evolutionary ability of the population; An elite algorithm is used to preserve superior parent corals and allow them to occupy the coral reef, thus avoiding the accumulation of cavities and preserving superior parent corals from each iteration.

4. The multi-objective optimization method for collaborative vibration reduction based on a dual-cable model using NSCRO-SL according to claim 3, characterized in that, The various matrix layers include: The following five methods are used: harmony search mutation, multipoint crossover, simulated binary crossover, hybrid crossover, and differential evolution mutation, and the probability of each matrix layer being selected is equal, that is, the probability of each matrix layer being selected is 20%. Other mutation strategies besides the five mentioned above can also be used to replace the matrix layer, and different probabilities of the matrix layer being selected can be set to improve the co-evolutionary ability of the population.

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