Landscape tower wind-induced vibration control method based on tuned mass-damping-inertia device

Abstract

The invention discloses a landscape tower wind-induced vibration control method based on a tuned mass-damping-inertia device. The landscape tower wind-induced vibration control method comprises the following steps: step 1, establishing an LTs-TMDI system; step 2, establishing a motion equation of the LTs-TMDI system, converting the motion equation of the LTs-TMDI system into an algebraic equation by using Laplacian transformation, and performing algebraic solution on the motion equation through a Laplacian domain to obtain a control response transfer function of the LTs-TMDI system; 3, deducing a closed solution of a wind vibration control ratio of the LTs-TMDI system according to an uncontrolled response transfer function before the TMDI is installed and a controlled response transfer function after the TMDI is installed; 4, performing parameter optimization on the wind vibration control ratio of the LTs-TMDI system by adopting an artificial bee colony ABC algorithm or a particle swarm optimization PSO algorithm to obtain an optimal parameter range of the wind vibration control ratio; and step 5, in the optimal parameter range, carrying out optimal wind vibration control on the LTs-TMDI system. The method has the effects that the peak acceleration of the twisted column and the spiral beam landscape tower LTs can be remarkably reduced, and the requirement for the comfort of pedestrians is met.

Description

Technical Field

[0001] The present invention relates to the technical field of wind-induced vibration control, and in particular to a wind-induced vibration control method for a landscape tower based on a tuned mass-damper-inertia device. Background Art

[0002] With the development of tourism, landscape towers (LTs) with curved and twisted columns and spiral beams are becoming increasingly popular among the public due to their high height, diverse shapes and complex forms. However, due to their slender and lightweight characteristics, coupled with low damping ratio, accurate determination of design wind loads is crucial for evaluating the impact of wind on landscape towers. The complex aerodynamic shape of landscape towers may lead to complex vortex shedding under wind loads, which may increase the drag coefficient. In addition, the closely arranged and staggered components may be affected by aerodynamic interference and instabilities, such as wake-induced vibration. Therefore, compared with structures with traditional aerodynamic shapes, landscape towers exhibit more significant vibrations under wind loads. Excessive accelerations at the platforms of these structures may cause discomfort to pedestrians. Therefore, mitigating the response of high-rise structures such as landscape towers to wind excitation has become a focus of recent research.

[0003] To address wind-induced vibrations in high-rise buildings and the resulting discomfort for pedestrians, researchers are increasingly focusing on vibration damping devices. Large active control devices can exacerbate the vibrations of low-profile (LT) lattice structures, making simpler passive control a more practical solution. The tuned mass damper (TMD) is one of the most classic and widely used damping devices. A TMD primarily consists of an inertial mass, stiffness elements, and damping elements. By adjusting the mass and stiffness of the TMD, its natural frequency can be matched to the resonant frequency of the structure, effectively absorbing energy and damping the vibration of the structure. It has been proven to be effective in reducing structural vibrations caused by wind loads, earthquakes, and other external forces. However, due to the limited space available for the damper and the difficulty of installation, the tuned mass damper (TMD) is not suitable for LTs. Therefore, selecting the right damper is crucial.

[0004] Disadvantages of existing technologies: Wind loads may cause structural damage and reduced pedestrian comfort in landscape towers (LTs) with twisted columns and spiral beams. Currently, there is little research on wind-induced vibration reduction for pedestrian comfort in LTs, and mature theories are still being developed. Summary of the Invention

[0005] The present invention provides a method for controlling wind-induced vibration of landscape towers based on tuned mass-damper-inertia, which can significantly reduce the peak acceleration of twisted column and spiral beam landscape towers LTs to meet pedestrian comfort requirements.

[0006] To achieve the above-mentioned object, the present invention provides a method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertia device, the key of which is to include the following steps:

[0007] Step 1: Establishing an LTs-TMDI system, wherein the LTs-TMDI system is provided with a twisted column and spiral beam landscape tower LTs, and a tuned mass-damper-inertial device TMDI is installed on the platform of the twisted column and spiral beam landscape tower LTs;

[0008] Step 2: Establish the motion equation of the LTs-TMDI system, transform the motion equation of the LTs-TMDI system into an algebraic equation using Laplace transform, and solve the motion equation algebraically in the Laplace domain to obtain the control response transfer function of the LTs-TMDI system;

[0009] Step 3: Based on the uncontrolled response transfer function of the tuned mass-damper-inertial device (TMDI) before installation and the controlled response transfer function after installation, derive the closed-form solution of the wind-induced vibration control ratio of the LTs-TMDI system.

[0010] Step 4: Use the artificial bee colony ABC algorithm or the particle swarm optimization PSO algorithm to optimize the parameters of the wind-induced vibration control ratio of the LTs-TMDI system, and compare the optimization results to obtain the optimal parameter range of the wind-induced vibration control ratio of the LTs-TMDI system;

[0011] Step 5: Within the optimal parameter range, a new tuned mass-damper-inertial device (TMDI) is designed based on the actual parameters of the twisted column and spiral beam landscape towers. The new tuned mass-damper-inertial device (TMDI) is installed on the platforms of the twisted column and spiral beam landscape towers to achieve optimal wind-induced vibration control of the LTs-TMDI system.

[0012] Through the above design, the frequency response transfer function of LTs equipped with a TMDI was first derived from the mechanical impedance. Subsequently, a closed-form solution for the wind-induced vibration control ratio was derived to quantitatively evaluate the TMDI's control performance. Finally, the optimal design parameters of the TMDI were determined using artificial bee colony (ABC) and particle swarm optimization (PSO) algorithms, and their computational performance was compared. A critical mass ratio exists in the optimal design of TMDI vibration control in LTs. When the mass ratio exceeds or falls below its critical value, increasing the damping ratio may promote or inhibit the damping effect. By analyzing the sensitivity of the TMDI system to parameter changes, recommended ranges for the mass ratio, damping ratio, frequency ratio, and apparent mass ratio were determined. Within the recommended parameter range, the peak acceleration of the LTs was significantly reduced, meeting pedestrian comfort requirements.

[0013] Preferably, in step 2, the motion equation of the LTs-TMDI system is converted into an algebraic equation using Laplace transform, which is expressed as follows:

[0014]

[0015] Where M is the generalized mass; C is the generalized damping; k is the stiffness coefficient; X(s) is the Laplace transform of the displacement response x(t), and x(t) is the generalized displacement of LTs. is the first mode function, q(t) is the generalized modal coordinate of LTs; Y(s) is the Laplace transform of the displacement response y(t), y(t) is the displacement of the TMDI mass block relative to LTs; F(s) is the generalized wind load f(t) provided by TMDI; F T (s) is the control force provided by TMDI; Z(s) is the normalized mechanical impedance of TMDI; ζ is the damping ratio; μ is the mass ratio; β is the ratio of the inertia coefficient of TMDI to the mass block, that is, the apparent mass ratio; λ is the frequency ratio; b is the inertia coefficient; c is the damping coefficient; m is the mass coefficient; the subscript TMDI denotes tuned mass-damper-inertia device; the subscript LTs denotes the twisted column and spiral beam landscape tower.

[0016] Preferably, in step 2, the control response transfer function expression of the LTs-TMDI system is as follows:

[0017]

[0018] As a preference, the expressions of the generalized mass M, generalized damping C, and generalized stiffness K of the LTs-TMDI system are as follows:

[0019]

[0020] Where m(z) represents the distributed mass; EI(z) represents the bending stiffness; z represents the generalized coordinate, z∈[0,H], H is the total height of LTs; ω LTs represents the natural frequency of LTs.

[0021] Preferably, in step 3, the calculation expression of the wind vibration control ratio of the LTs-TMDI system is as follows:

[0022]

[0023] Among them, S f (ω) is the power spectrum density function of the generalized wind load; H U (iω) is the uncontrolled response transfer function, H U (s)=ω LTs 2 / (s 2 +2ζLTs ω LTs s+ω LTs 2 ), i represents the imaginary unit; ω represents the frequency; s is the algebra of iω; H T (iω) is the control response transfer function; σ T is the standard deviation of displacement amplitude after TMDI installation, σ u is the standard deviation of the displacement amplitude before TMDI installation; J is the wind-induced vibration control ratio, which is defined as the ratio of the standard deviation of the displacement amplitude at the platform before and after TMDI installation. The smaller the value of the wind-induced vibration control ratio, the better the wind-induced vibration control performance of the system;

[0024] Substituting s=iω into formula (6) and expanding the resulting complex expression, we obtain the response transfer function formula:

[0025]

[0026] A=-ω LTs 2 (1+β+λ 2 +λ 2 μ+4λζ TMDI ζ LTs ) (9)

[0028] B=-2ω 3 ω LTs (λζ TMDI (1+μ)+(1+β)ζ LTs )+2ωλω LTs 3 (ζ TMDI +λζ LTs ) (10)

[0029] For ease of calculation, the integral is tabulated for the specific simple form of H(iω), and the response transfer function formulas (7) and (8) are as follows:

[0030]

[0031] The integral of the response transfer function is approximated as follows

[0032]

[0033]

[0034] The values of the parameters in the formula are as follows:

[0035]

[0036] C1=0,C0=ω LTs2 ,D2=1,D1=2ζ LTs ω LTs ,D0=ω LTs 2 (17)

[0037] On this basis, the expression of wind-induced vibration control ratio is obtained as follows:

[0038]

[0039] Preferably, in step 4, the wind vibration control ratio parameters of the LTs-TMDI system include mass ratio, damping ratio, frequency ratio and apparent mass ratio.

[0040] As an example, the optimal parameter range is: mass ratio μ = [0.00, 0.03], damping ratio ζ TMDI =[0.1,0.3], frequency ratio λ =[0.85,1.1], apparent mass ratio β =[0.1,0.5].

[0041] The beneficial effects of the present invention are as follows: the peak acceleration of the twisted column and spiral beam landscape tower LTs can be significantly reduced, so that the peak acceleration can meet the pedestrian comfort requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of the present invention;

[0043] Figure 2 Schematic diagram of the structure of the twisted column and spiral beam landscape tower LTs in the embodiment;

[0044] Figure 3 This is a diagram defining the wind deflection angle in the wind tunnel test of the aeroelastic model in the embodiment;

[0045] Figure 4 : is a graph showing the peak acceleration of the prototype platform at different wind angles in the embodiment;

[0046] Figure 5 Schematic diagram of a tuned mass-damper-inertial device (TMDI) in an embodiment;

[0047] Figure 6 The relative error and time reduction rate comparison chart of ABC and PSO in the embodiment;

[0048] Figure 7 Graph showing the iterative process and time reduction rate of the nonlinear inertia weight method in an embodiment;

[0049] Figure 8 A comparison diagram of the effects of parameter changes on the wind-induced vibration control ratio in the embodiment;

[0050] Figure 9This is a comparison chart of the effects of different parameters on the wind-induced vibration control ratio in the embodiment;

[0051] Figure 10 This is a diagram showing the TMDI vibration reduction effect in the embodiment. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0053] The prototype of this embodiment represents a landscape tower with a total height of 63.76 meters, which has a curved and twisted column and spiral beam located in a western city. The tower is divided into two main parts: the tower body and the belt structure, such as Figure 2 The tower structure utilizes curved box girders and counterclockwise twisted steel box columns, while the strip structure is constructed using a lattice system consisting of two box girders and an intermediate connecting box girder. The aeroelastic model was designed according to the fundamental proportionality law, as shown in Table 1. The model was tested in the TK-400 DC wind tunnel at the Tianjin Water Transport Engineering Research Institute. The wind tunnel test section measures 15 meters long, 4.4 meters wide, and 2.5 meters high, with a maximum wind speed of 30 meters per second and a minimum wind speed of 0 meters per second.

[0054] Table 1. Similarity ratio of scaled LT models

[0055]

[0056] Given its function as a scenic tower, pedestrian comfort is a primary concern and its evaluation criteria are based on peak acceleration at the platform. The acceleration time history at the platform must be measured. Figure 3 The wind angle setting is explained. The acceleration response of the aeroelastic model is converted into a prototype using dimensional analysis, such as Figure 4 shown.

[0057] like Figure 4 As shown, at a wind direction of 90°, the acceleration at the LTs platform reaches a peak value of 0.205 m / s 2 , exceeding the acceleration limit of 0.200m / s specified for the platform 2 This excess can lead to poor pedestrian comfort. Located in Chongqing, China, the landscape tower is a built-in LTs as a landmark building, attracting countless visitors every day. To enhance the visitor experience, it is necessary to implement wind-induced vibration reduction measures.

[0058] like Figure 1 A method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device is shown, comprising the following steps:

[0059] Step 1: Establishing an LTs-TMDI system, wherein the LTs-TMDI system is provided with a twisted column and spiral beam landscape tower LTs, and a tuned mass-damper-inertial device TMDI is installed on the platform of the twisted column and spiral beam landscape tower LTs;

[0060] Step 2: Establish the motion equation of the LTs-TMDI system, transform the motion equation of the LTs-TMDI system into an algebraic equation using Laplace transform, and solve the motion equation algebraically in the Laplace domain to obtain the control response transfer function of the LTs-TMDI system;

[0061] Step 3: Based on the uncontrolled response transfer function of the tuned mass-damper-inertial device (TMDI) before installation and the controlled response transfer function after installation, derive the closed-form solution of the wind-induced vibration control ratio of the LTs-TMDI system.

[0062] Step 4: Use the artificial bee colony ABC algorithm or the particle swarm optimization PSO algorithm to optimize the parameters of the wind-induced vibration control ratio of the LTs-TMDI system, and compare the optimization results to obtain the optimal parameter range of the wind-induced vibration control ratio of the LTs-TMDI system;

[0063] Step 5: Within the optimal parameter range, a new tuned mass-damper-inertial device (TMDI) is designed based on the actual parameters of the twisted column and spiral beam landscape towers. The new tuned mass-damper-inertial device (TMDI) is installed on the platforms of the twisted column and spiral beam landscape towers to achieve optimal wind-induced vibration control of the LTs-TMDI system.

[0064] The tuned mass-damper-inertial device (TMDI) is mounted on the platform of the structure, such as Figure 5 The mass coefficient and stiffness coefficient of the main tuned system are denoted as m and k respectively. In the second tuned system, the damping coefficient and inertia coefficient are denoted as c and b respectively.

[0065] In step 2, the Laplace transform is used to transform the motion equation of the LTs-TMDI system into an algebraic equation, which is expressed as follows:

[0066]

[0067] Where M is the generalized mass; C is the generalized damping; k is the stiffness coefficient; X(s) is the Laplace transform of the displacement response x(t), and x(t) is the generalized displacement of LTs. is the first mode function, q(t) is the generalized modal coordinate of LTs; Y(s) is the Laplace transform of the displacement response y(t), y(t) is the displacement of the TMDI mass block relative to LTs; F(s) is the generalized wind load f(t) provided by TMDI; F T(s) is the control force provided by TMDI; Z(s) is the normalized mechanical impedance of TMDI; ζ is the damping ratio; μ is the mass ratio; β is the ratio of the inertia coefficient of TMDI to the mass block, that is, the apparent mass ratio; λ is the frequency ratio; b is the inertia coefficient; c is the damping coefficient; m is the mass coefficient; the subscript TMDI denotes tuned mass-damper-inertia device; the subscript LTs denotes the twisted column and spiral beam landscape tower.

[0068] In step 2, the control response transfer function expression of the LTs-TMDI system is as follows:

[0069]

[0070] The expressions of the generalized mass M, generalized damping C, and generalized stiffness K of the LTs-TMDI system are as follows:

[0071]

[0072] Where m(z) represents the distributed mass; EI(z) represents the bending stiffness; z represents the generalized coordinate, z∈[0,H], H is the total height of LTs; ω LTs represents the natural frequency of LTs.

[0073] In step 3, the calculation expression of the wind-induced vibration control ratio of the LTs-TMDI system is as follows:

[0074]

[0075] Among them, S f (ω) is the power spectrum density function of the generalized wind load; H U (iω) is the uncontrolled response transfer function, H U (s)=ω LTs 2 / (s 2 +2ζ LTs ω LTs s+ω LTs 2 ), i represents the imaginary unit; ω represents the frequency; s is the algebra of iω, s=iω; H T (iω) is the control response transfer function; σ T is the standard deviation of displacement amplitude after TMDI installation, σ u is the standard deviation of the displacement amplitude before TMDI installation; J is the wind vibration control ratio, which is defined as the ratio of the standard deviation of the displacement amplitude at the platform before and after TMDI installation;

[0076] Substituting s=iω into formula (6) and expanding the resulting complex expression, we obtain the response transfer function formula:

[0077]

[0078] A=-ω LTs 2 (1+β+λ 2 +λ 2 μ+4λζ TMDI ζ LTs ) (9)

[0080] B=-2ω 3 ω LTs (λζ TMDI (1+μ)+(1+β)ζ LTs )+2ωλω LTs 3 (ζ TMDI +λζ LTs ) (10)

[0081] For ease of calculation, the integral is tabulated for the specific simple form of H(iω), and the response transfer function formulas (7) and (8) are as follows:

[0082]

[0083] The detailed derivation conditions and key operation steps of formula (11) are as follows:

[0084] The objective integral expression formula is:

[0085]

[0086] Coefficient A i (i=0,1,..,4) and B j (j=0,1,..,3) have been systematically redefined to facilitate notational consistency:

[0087]

[0088] Substituting formula (A.2) into formula (A.1) yields:

[0089]

[0090] To generalize the formula, the polynomial function Y n (ω) and Z n (ω) is defined as:

[0091]

[0092] When n=4, the polynomial function is expressed as:

[0093]

[0094] Introduce function X n (ω) and define its expression as:

[0095]

[0096] Assumptions When n=4, we have:

[0097]

[0098] Let x1, x2, ..., x n are the roots of Z(ω), and assuming they are not equal. The sum of the residuals in the upper half plane, denoted by T, yields the following result:

[0099]

[0100] where Z′(ω k ) is Z(ω k ) with respect to ω.

[0101] By the factor theorem, we have:

[0102]

[0103] Therefore, Z(-ω k ) is obtained by the following function:

[0104]

[0105] Least common multiple of factors ω k +ω i is the product of the sums of all paired roots Formula (A.8) can be rewritten as:

[0106]

[0107] To facilitate the solution, Q k (ω) is introduced and its expression is defined as:

[0108]

[0109] In formula (A.11), The solution formula is:

[0110]

[0111] When n=4, Q k (ω) is:

[0112]

[0113] therefore, The solution of formula (A.11) is:

[0114]

[0115] Use a0ω k u +a1ω k u-1 +...+a u Replace P u (u=0,1,...,3). Therefore, formula (A.15) can be written as:

[0116]

[0117] In this case, it is clear that the determinant has become ω k Here we will denote it as f(ω k ). Therefore, formula (A.11) can be written as:

[0118]

[0119] Substitution and To formula (A.17) and further simplify and organize:

[0120]

[0121] Since Y(ω k )f(ω k ) is also the result of ω k A polynomial function, so any term of the polynomial can be calculated independently, that is, solving It can be transformed into solving the following equation:

[0122]

[0123] The solution of formula (A.19) is the function The sum of all remainders can be solved using the following equation:

[0124]

[0125] According to formula (A.20):

[0126]

[0127] Here Γ n (n=0,1,...,4) can be calculated using the following formula:

[0128]

[0129] Substituting formula (A.21) into formula (A.18) yields:

[0130]

[0131] Simplifying each term in formula (A.23), we get the following results:

[0132]

[0133] Finally, substituting equation (A.2) into (A.24) yields:

[0134]

[0135] At this point, the derivation is completed.

[0136] The integral of the response transfer function is approximated as follows:

[0137]

[0138] The values of the parameters in the formula are as follows:

[0139]

[0140] On this basis, the expression of wind-induced vibration control ratio is obtained as follows:

[0141]

[0142] In step 4, the wind vibration control ratio parameters of the LTs-TMDI system include mass ratio, damping ratio, frequency ratio and apparent mass ratio.

[0143] Both ABC and PSO are global optimization algorithms based on swarm intelligence. The PSO algorithm relies on information sharing and collaboration among particles and has a memory characteristic. This helps particles explore the TMDI parameter space of the landscape tower more effectively and avoid falling into local optimality. The method is simple, easy to implement, requires few parameters, and can achieve rapid modeling of multi-parameter TMDI optimization. When the ABC algorithm, inspired by bee colony foraging, is applied to the wind vibration control of the landscape tower, it can efficiently find the optimal TMDI parameter combination in a large parameter space. It is simpler than the genetic algorithm, has fewer control parameters, and converges faster than the ant colony algorithm in similar problems, making it suitable for TMDI parameter optimization. The goal is to minimize the dimensionless acceleration index J, as shown in Equation (18). It is affected by the damping ratio, frequency ratio, mass ratio, and apparent mass ratio of the TMDI. By defining a suitable parameter range, the optimization of J aims to achieve the most effective control of the TMDI response to acceleration. In order to solve the problem of the algorithm falling into local optimality and incomplete convergence, and to ensure a balance between computational efficiency and result accuracy, the population size of the PSO and ABC algorithms was ultimately set to 200, and the number of iterations was fixed to 1000. The expression of the threshold L in MATLAB is shown in formula (20).

[0144] The ABC and PSO algorithms use the wind-induced vibration control ratio calculation expression (18) as the control target equation to search for the optimal parameter solution (a total of four parameters: frequency ratio, mass ratio, apparent mass ratio, and damping ratio). First, the target equation (18) is input and iteratively solved within the given parameter (four parameters) interval to find the optimal wind-induced vibration control ratio J.

[0145] Since both ABC and PSO are probabilistic optimization algorithms, the optimization results are averaged after ten runs.

[0146] L = round(0.5×n var ×N) (20)

[0147] Where: round is the function that rounds the threshold L; n var is the number of unknown parameters.

[0148] In MATLAB vector representation, the range of preselected values is as follows:

[0149] μ=[0.01:0.01:0.3] β=[0:0.01:1] (21)

[0150] On this basis, the dimensionless index control ratio J is used as the objective function, and λ, ζ TMDI is the design variable. In MATLAB vector notation, the tuning value range is as follows:

[0151] λ=[0.6:0.1:3]ζTMDI =[0.01:0.01:0.30] (22)

[0152] To validate the results and compare the performance of the two algorithms under the same conditions, this section provides a comparative analysis of the ABC and PSO algorithms across two operating conditions. MATLAB was used to obtain the computational results and the time required to reach stability for both algorithms. These results were then compared and analyzed. The optimal solution for the vibration control ratio J in this study was determined. Since both ABC and PSO are probabilistic optimization algorithms, the results are averaged over 10 runs to account for variability.

[0153] Figure 6 The relative error between the two algorithms and the time reduction rate of ABC compared to PSO are shown. Figure 6 As shown in the figure, when the apparent mass ratio is in the range of [0-1], the relative error of the two algorithms ranges from 0.18% to 0.6%, verifying the effectiveness of the optimal solution. Moreover, the optimal solution obtained using ABC is more accurate. Compared with PSO, ABC reduces the time required to reach a stable result by 79-90%, significantly improving computational efficiency. Therefore, for complex calculations and situations requiring high-precision results, ABC is superior to PSO. Figure 6 As shown in the figure, when the inertia change of TMDI increases the complexity of its interaction with the landscape tower, this complexity leads to the complication of the system's motion equations, intensifies the coupling between parameters, increases the calculation error, and reduces the time reduction rate.

[0154] The limited communication between individual particles in PSO requires time and inertia to update their states, complicating parameter selection. In contrast, the simplicity of the swarm size and search range in the ABC algorithm makes it easier to implement. Furthermore, during the ABC algorithm's search process, each bee operates independently, enabling simple parallel computation and improving computational efficiency. In contrast, implementing parallel computation in the PSO algorithm is more challenging.

[0155] The inertia weight w reflects the speed of the current particle and is affected by the previous generations of particles. A larger inertia weight w indicates a stronger global search capability but a weaker local search capability. On the contrary, a small w means a weak global optimization capability but a strong local optimization capability. Compared with a fixed value, a dynamic w tends to produce better optimization results. Currently, the linear decreasing weight (LDW) strategy is widely adopted. In this study, a nonlinear decreasing inertia weight is proposed based on the linear method. It is expressed as follows:

[0156]

[0157] where l max The maximum number of iterations of the algorithm, generally considered ws =0.9,w e When =0.4, the algorithm performs best.

[0158] Figure 7 The changes of linear decreasing inertia weight and nonlinear decreasing inertia weight as well as the time reduction rate of nonlinear decreasing inertia weight relative to linear decreasing inertia weight are explained. Figure 7 As shown in (a), the ABC algorithm converges to this value more quickly, reducing computation time and improving optimization efficiency. Compared to the linear decreasing inertia weighting method, the nonlinear decreasing inertia weighting proposed in this paper results in a larger w value in the early stages of the search, enhancing the particles' global search capabilities, and a smaller w value in the later stages of the search, improving the particles' local optimization capabilities, thereby obtaining a more optimal solution. Calculations show that compared to the linear decreasing inertia weighting method, the nonlinear method reduces the time required to achieve the same result by 28.4-76.7%, significantly improving computational efficiency. This method can be extended to more complex optimization problems.

[0159] like Figure 7 As shown in (b), the time reduction rate is minimized when the TMDI damping ratio is 0.15. This is likely because 0.15 is closer to the optimal damping ratio for TMDI within the damping ratio range, and the algorithm may use it as a reference point for the optimization process. When the damping ratio approaches its optimal value, the gradient changes in the parameter space tend to be relatively gentle. Therefore, the impact of the difference between linear and nonlinear decreasing inertia weights on the algorithm's convergence speed is weakened. In this case, regardless of the inertia weight strategy used, the particles converge to the optimal solution more quickly, resulting in a smaller time reduction rate.

[0160] In this section, the approximate ranges of the control parameters, namely μ, β, λ and ζ TMDI , was roughly determined in J and analyzed using both the ABC and PSO optimization algorithms. The results of the two algorithms were then compared, focusing on their relative errors and computational time. The errors in the results of both algorithms did not exceed 0.7%, demonstrating their reliability. However, the PSO algorithm exhibited a relatively long computational time. To address this issue, improvements were made to the PSO algorithm to improve its efficiency. The improved PSO algorithm significantly reduced computational time without sacrificing accuracy. In subsequent work, the optimal range of LTs control parameters will be further investigated based on these two optimization algorithms.

[0161] In order to study the control effect of TMDI on the wind-induced vibration response of LTs, the ABC algorithm is used to optimize the parameters of the LTs-TMDI system, such as Figure 8 The present invention investigates the influence of various parameters such as frequency ratio λ, mass ratio μ, and apparent mass ratio β on the vibration reduction effect of TMDI.

[0162] The changing trend of LTs wind vibration control ratio is as follows Figure 8 (a)-(c) As shown. As the damping ratio increases, the vibration control effect of TMDI improves. When the frequency ratio is closer to 1, the vibration reduction occurs more quickly and effectively, indicating that the TMDI system resonates with the vibration of LTs and absorbs its vibration energy, thereby achieving effective vibration reduction. Figure 8 As shown in (b)-(e), increasing the mass ratio also enhances the vibration reduction capability of TMDI. In the range of [0.01-0.1], the vibration control ratio decreases most rapidly and the vibration reduction effect is the best. However, when the mass ratio exceeds 0.1, the vibration reduction effect becomes less obvious. When ζ TMDI The vibration control ratio decreases rapidly for μ = [0.17-0.22] and μ = [0.001-0.01]. For damping ratios in the range [0.01-0.22], the vibration control ratio decreases by 53.94% for μ = 0.1, and by 49.73% for μ = 0.03. In contrast, the mass ratio decreases by 70%, while the damping ratio decreases by only 4.21%. This demonstrates that the mass ratio in TMDI designs can be kept below 0.1, saving installation space and reducing complexity while still providing effective vibration reduction.

[0163] Figure 8 (c)-(d) show that when the parameter ζ TMDI , μ and λ are considered as constants, increasing β enhances the damping effect compared to TMDI (β=0), but the improvement of the damping rate is not significant. TMDI When μ reaches 0.22, the value range of J is [0.4626, 0.4843]. When μ reaches 0.1, the value range of J is [0.6037, 0.6588]. This shows that the wind vibration control ability of TMDI is more dependent on the parameter damping ratio. In terms of vibration reduction efficiency, TMDI is more sensitive to changes in the damping ratio. Figure 8 (f) It can be concluded that the vibration reduction effect of TMDI is more strongly affected by the damping ratio and frequency ratio than by the mass ratio and apparent mass ratio.

[0164] like Figure 9 As shown in (a)-(i), the 3D surface presents a long and narrow shape, indicating that the parameter changes in the parameters significantly affect the vibration control. Figure 9 As shown in Figures (a) to (c), the introduction of the inertia chamber changes the damper's natural frequency, preventing the TMDI from effectively resonating with the main structure. Consequently, the damping rate decreases from 47.1% to 39.7% as the apparent mass ratio increases. Figure 9(d)-(f) illustrate the effect of frequency ratio and mass ratio on vibration reduction effect under different damping ratios. As the damping ratio increases, the damping efficiency increases from 44.9% to 58.1%. As the damping ratio increases, the inclination angle of the "groove" gradually becomes steeper. When the damping ratio is 0.3, the groove inclination angle is the largest, and the vibration reduction efficiency increases from 11.3% to 58.1%. When the damping ratio is 0.06, the vibration reduction rate increases from 20.7% to 44.9%; when the damping ratio is 0.1, the vibration reduction rate increases from 18.7% to 52.4%. This shows that the larger the damping ratio and the smaller the mass ratio, the worse the vibration reduction effect of TMDI. Figure 9 As shown in (g)-(i), as the damping ratio increases, the damping rate decreases from 27.9% to 17.2%. At this time, as the mass ratio increases, the damping rate gradually increases. The results show that the mass ratio has a significant impact on the contribution of the damping ratio to the damping effect.

[0165] Figure 9 (j) shows the effect of apparent mass ratio and mass ratio on vibration reduction under different damping ratios. In general, as the mass ratio increases, the damping rate gradually decreases. It is worth noting that as the apparent mass ratio increases, the vibration reduction first increases and then decreases. The position of the maximum point indicates an approximately linear relationship between the mass ratio and the apparent mass ratio, and this linear relationship remains consistent regardless of how the damping ratio changes. In addition, as Figure 9 (j) As shown in the upper left corner, it is also verified that when the damping ratio is high, the small mass ratio suppresses the vibration reduction effect of TMDI. Figure 9 As shown in (k) and (l), when the damping ratio exceeds 0.1, the TMDI damping rate gradually decreases. Figure 9 (l) and Figure 9 From the dark region observed in (k), it is clear that the best damping effect occurs when the apparent mass ratio is between 0.1 and 0.5, given the known frequency ratio and considering the economic performance.

[0166] Based on the above analysis, a more detailed optimization is carried out within the above parameter range to achieve effective vibration reduction while taking into account the economy and safety of actual construction. The recommended interval for each parameter is: μ = [0.005, 0.03], ζ TMDI =[0.1,0.3],λ=[0.85,1.1]. When other parameters are constant, the apparent mass ratio has the least impact on the vibration reduction effect. Considering the economic factors of actual projects, the recommended range of the apparent mass ratio is [0.1-0.5].

[0167] Since the platform acceleration obtained through the test in this study reaches a peak at a wind yaw angle of 90° and exceeds the standard value, damping measures are taken for the LTs at this angle. Figure 10 As shown. Figure 10It can be clearly seen that within the recommended range, the peak acceleration at a 90° wind yaw angle is significantly reduced, thus meeting the pedestrian comfort requirements. When λ is close to 1, as μ increases, the peak acceleration decreases from 0.199 m / s to 2 Reduced to 0.166m / s 2 For ζ TMDI In the interval [0.1, 0.3], the trend and value of the peak acceleration are similar, which is determined by the value of λ. Specifically, when ζ TMDI =0.10, the peak acceleration is 0.192m / s 2 Reduced to 0.154m / s 2 , and when TMDI =0.30, which is 0.193m / s 2 Reduced to 0.156m / s 2 When the damping ratio is 0.1, the peak acceleration is low, indicating that the damping effect is optimal at this damping ratio. The research results verify the rationality of the recommended TMDI design range, significantly improving the vibration reduction capacity of LTs and enhancing pedestrian comfort.

[0168] In this embodiment, in order to improve the wind resistance of landscape towers (LTs) with torsional columns and spiral beams, wind tunnel tests were conducted to measure the peak acceleration at different wind deflection angles. Based on the mechanical impedance method, a frequency response transfer function was established under controlled conditions. Considering the first-order mode of the LTs, a closed-form solution for the wind-induced vibration control ratio was derived. To obtain the optimal design parameters of the TMDI, the artificial bee colony (ABC) and particle swarm optimization (PSO) algorithms were used. The PSO algorithm was further improved using the nonlinear decreasing inertia weight method. Subsequently, the impact of parameter changes on the vibration reduction performance of the TMDI was analyzed. Finally, the value ranges of the design parameters were recommended. The main conclusions of this invention are as follows:

[0169] (1) The peak acceleration of the LTs in the downwind direction at different wind angles from 0° to 345° was obtained through wind tunnel tests. The test results show that the peak acceleration of the platform at a wind angle of 90° reaches 0.205m / s 2 , exceeding the acceleration limits specified in European and Chinese standards.

[0170] (2) The ABC algorithm has high computational accuracy. Compared with the PSO algorithm, the time required for the ABC algorithm to reach a stable result is reduced by about 85%. Compared with the linear decreasing inertia weight method, the improved PSO reduces the time required to reach a similar result by about 50%.

[0171] (3) In the vibration control optimization design of TMDI for LTs, there is a critical mass ratio. When the mass ratio is greater than or less than this critical value, an increase in the damping ratio can promote or inhibit the vibration reduction effect, respectively. In addition, when the frequency ratio is close to 1, there is an optimal apparent mass ratio, which results in the best vibration reduction effect. At this point, the mass ratio and the apparent mass ratio show an approximately linear relationship, and this relationship remains consistent despite changes in the damping ratio.

[0172] (4) The vibration reduction effect of LTs mainly depends on the parameters of TMDI: frequency ratio and damping ratio. For the LTs proposed in this embodiment, the optimal parameter range is mass ratio μ = [0.00, 0.03], damping ratio ζ TMDI =[0.1,0.3], frequency ratio λ=[0.85,1.1], apparent mass ratio β=[0.1,0.5]. Within the recommended range, the peak acceleration is significantly reduced, meeting pedestrian comfort requirements.

[0173] (5) The parameter optimization design of the TMDI in this invention meets the comfort requirements of pedestrians for LTs. To achieve an effective TMDI design, it is crucial to accurately analyze the changes in the main structural stiffness and external loads. Minimizing the deviation between the actual frequency and the design frequency is also crucial because it is the main goal of vibration reduction.

[0174] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertia device, characterized in that: The following steps are involved: Step 1: Establishing an LTs-TMDI system, wherein the LTs-TMDI system is provided with a twisted column and spiral beam landscape tower LTs, and a tuned mass-damper-inertial device TMDI is installed on the platform of the twisted column and spiral beam landscape tower LTs; Step 2: Establish the motion equation of the LTs-TMDI system, transform the motion equation of the LTs-TMDI system into an algebraic equation using Laplace transform, and solve the motion equation algebraically in the Laplace domain to obtain the control response transfer function of the LTs-TMDI system; Step 3: Based on the uncontrolled response transfer function of the tuned mass-damper-inertial device (TMDI) before installation and the controlled response transfer function after installation, derive the closed-form solution of the wind-induced vibration control ratio of the LTs-TMDI system. Step 4: Use the artificial bee colony ABC algorithm or the particle swarm optimization PSO algorithm to optimize the parameters of the wind-induced vibration control ratio of the LTs-TMDI system, and compare the optimization results to obtain the optimal parameter range of the wind-induced vibration control ratio of the LTs-TMDI system; Step 5: Within the optimal parameter range, a new tuned mass-damper-inertial device (TMDI) is designed based on the actual parameters of the twisted column and spiral beam landscape towers. The new tuned mass-damper-inertial device (TMDI) is installed on the platforms of the twisted column and spiral beam landscape towers to achieve optimal wind-induced vibration control of the LTs-TMDI system.

2. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 1 is characterized in that: In step 2, the Laplace transform is used to transform the motion equation of the LTs-TMDI system into an algebraic equation, which is expressed as follows: (Ms 2 +Cs+k)X(s)=F(s)+F T (s) ms 2 [X(s)+Y(s)]+F T (s)=0 Where M is the generalized mass; K is the generalized stiffness; C is the generalized damping; k is the stiffness coefficient; X(s) is the Laplace transform of the displacement response x(t), and x(t) is the generalized displacement of LTs. is the first mode function, q(t) is the generalized modal coordinate of LTs; Y(s) is the Laplace transform of the displacement response y(t), y(t) is the displacement of the TMDI mass block relative to LTs; F(s) is the generalized wind load f(t) provided by TMDI; F T (s) is the control force provided by TMDI; Z(s) is the normalized mechanical impedance of TMDI; ζ is the damping ratio; μ is the mass ratio; β is the ratio of the inertia coefficient of TMDI to the mass block, that is, the apparent mass ratio; λ is the frequency ratio; b is the inertia coefficient; c is the damping coefficient; m is the mass coefficient; the subscript TMDI denotes tuned mass-damper-inertia device; the subscript LTs denotes the twisted column and spiral beam landscape tower.

3. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 2, characterized in that: In step 2, the control response transfer function expression of the LTs-TMDI system is as follows:

4. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 1, characterized in that: The expressions of the generalized mass M, generalized damping C, and generalized stiffness K of the LTs-TMDI system are as follows: Where m(z) represents the distributed mass; EI(z) represents the bending stiffness; z represents the generalized coordinate, z∈[0,H], H is the total height of LTs; ω LTs represents the natural frequency of LTs.

5. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 1 is characterized in that: In step 3, the calculation expression of the wind-induced vibration control ratio of the LTs-TMDI system is as follows: Among them, S f (ω) is the power spectrum density function of the generalized wind load; H U (iω) is the uncontrolled response transfer function, H U (s)=ω LTs 2 / (s 2 +2ζ LTs ω LTs s+ω LTs 2 ), i represents the imaginary unit; ω represents the frequency; s is the algebra of iω; H T (iω) is the control response transfer function; σ T is the standard deviation of displacement amplitude after TMDI installation, σ u is the standard deviation of the displacement amplitude before TMDI installation; J is the wind vibration control ratio, which is defined as the ratio of the standard deviation of the displacement amplitude at the platform before and after TMDI installation; Substituting s=iω into formula (6) and expanding the resulting complex expression, we obtain the response transfer function formula: A=-ω LTs 2 (1+β+λ 2 +λ 2 m+4lz TMDI g LTs ) (9) B=-2ω 3 oh LTs (lz) TMDI (1+μ)+(1+β)ζ LTs )+2oh LTs 3 (g) TMDI +lz LTs ) (10) For ease of calculation, the integral is tabulated for the specific simple form of H(iω), and the response transfer function formulas (7) and (8) are as follows: The integral of the response transfer function is approximated as follows: The values of the parameters in the formula are as follows: C1=0,C0=ω LTs 2 ,D2=1,D1=2ζ LTs oh LTs ,D0=ω LTs 2 (17) On this basis, the expression of wind-induced vibration control ratio is obtained as follows: E1=2E3(1+β+λ 2 (1+m)+4lz TMDI g LTs ) E2=-2λ(1+β+βμ)(ζ TMDI +lz LTs ) E3=λ(1+μ)ζ TMDI +(1+b)g LTs (19)。 6. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 1, characterized in that: In step 4, the wind vibration control ratio parameters of the LTs-TMDI system include mass ratio, damping ratio, frequency ratio and apparent mass ratio.

7. The method for controlling wind-induced vibration of a landscape tower based on a tuned mass-damper-inertial device according to claim 6, characterized in that: The optimal parameter range is: mass ratio μ = [0.00, 0.03], damping ratio ζ TMDI =[0.1,0.3], frequency ratio λ =[0.85,1.1], apparent mass ratio β =[0.1,0.5].

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