Dual-Domain Synergistic Optimization for Dynamic Reliability Enhancement of Towering Structures in Nonstationary Wind Fields

Abstract

We propose a wind spectrum–response surface dual-domain coupling method to study the reliability optimization of tall structures under the action of unsteady wind fields. Unlike traditional research, the dual-domain coupling analysis can quickly and accurately capture structural response defects and optimize size. The first parametric modeling technology establishes a high-precision finite element model of the movable boom structure by establishing a dual-domain coupling framework of pulsating wind and structural optimization. Using MATLAB (instructional R2024b version), the pulsating wind is simulated with uncertainty. The pulsating wind speeds at different heights are converted into wind loads acting on the net-sealed movable boom structure. Secondly, the boom structure’s dynamic response analysis and response surface optimization design were carried out. The final results show that the maximum value of displacement of the optimized net sealer boom is reduced by about 8.06%, the maximum value of stress is reduced by about 11.04%, and the stiffness is improved through the stress monitoring of the existing structure. It showed that the wind-resistant capability of the boom studied by this method is enhanced, improving the study’s efficiency.

1. Introduction

With the continuous growth of people’s demand for electricity, the necessity of developing long-distance, high-capacity, and trans-regional power transportation is increasing, and the construction environment of overhead transmission lines is complicated. The construction of new transmission lines across farmland, valleys, railroads, highways, and in-transit lines is also growing significantly yearly [1,2,3,4,5]. At the same time, laying new transmission lines usually presents problems, such as intersecting with ground lines or crossing people’s work areas. To prevent falling objects from causing injuries to pedestrians or vehicles, it is necessary to build crossing frames in advance on both sides of the crossing and then carry out sealing net protection [6,7,8,9,10]. Overhead transmission lines are built in the sealing network structure across the road, railroad, highway, or other in-transit lines; their primary role is preventing the occurrence of broken line accidents and effectively intercepting falling broken lines to ensure that in-transit line regular operation follows, to ensure that the construction of the line is standard, and also to protect in-transit line regular operation [11,12]. However, the traditional sealing net structure has the disadvantages of a long construction period, high cost, and ample floor space, and it will bring serious safety hazards to workers at height.

Therefore, in recent years, the electric power industry has begun to study structures with a high degree of automation, low cost, and compact occupation. The new crawler-type net sealing machine comprises a lifting boom, a telescopic boom, a top protection net, etc. The boom adopts a nested truss structure, which can complete the net sealing operation with a span of 80 m and a height of 20 m. The net sealer’s boom is a large-span space truss structure, a typical wind-sensitive structure with mechanical characteristics such as large deformation and high node stress; scholars at home and abroad have researched similar structures for these characteristics.

Ren Xu Dong [13] conducted a wind fatigue analysis on the Dong Ting Lake truss suspension bridge using pulsating wind in Yueyang City, Hunan province. Finally, he concluded that the boom’s fatigue is most unfavorable when the wind’s angle of attack is −3° and that the tower on the leeward side is the critical point of fatigue damage. However, he did not give measures to improve fatigue strength, optimization, etc. Zhang Meng [14] studied the dynamic response of wind load on the sealing structure under different spans, wind speeds, and additional diagonal cables and finally suggested mitigating the wind deflections. However, although the effects of various factors on the sealing structure were considered comprehensively, optimization and enhancement have not yet been conducted at the most unfavorable locations of the sealing structure. Li Jing Yang [15] introduced a new type of transmission structure (TC-PTS) suitable for mountainous terrain, established a finite element model, and performed wind fatigue analysis. The results showed that the intrinsic frequency and displacement timescales calculated for this transmission structure were highly accurate and efficient, and the most unfavorable wind angle of 90° was obtained for the TC-PTS. Yan Han [16] proposed an analytical framework for efficiently assessing the fatigue reliability of typical large-span steel truss suspension bridges under random wind loads. The dynamic stress response of the bridge at critical locations was obtained by finite element analysis, which was sensitive to loading at one-quarter of the top and bottom chords of the main trusses. Still, ultimately, no one was given a way to reduce the sensitivity at this location. Da Silva Natalia Pinheiro [17] used a combined EPS and TS wind field simulation method for transmission line dynamic response, gave a comparison between the joint wind field results and the results under the equivalent static load method in the code, and finally gave the conclusion that the technique is helpful for transmission line structural design updates. Alberto Lorenzon [18] proposed a CFD turbulence model to evaluate wind-induced fatigue loads, enhancing the details of this research, such as consideration of the computational cost of the model and improvement of computational efficiency. However, only the summarized theoretical knowledge was presented, and the fluid–structure coupling verification of the actual model was not carried out. Meanwhile, nonlinear dynamic modeling and wind-induced analysis of large-span scalable nested net sealers have rarely been reported. In addition, the stochastic and time-varying nature of random wind loads can cause unknown dynamic responses from the boom structure and even failure in severe cases. Therefore, clarifying the dynamic reaction of the boom structure of the net sealer under random wind loads is crucial for its reliability, and at the same time, optimizing the known resulting deformations, stresses, etc., to find their optimal solution is also necessary.

When the mesh sealing machine unfolds its work, the five sections of telescopic arms in turn extend the required length, and finally, the front support arm falls into place to play a supporting role. The traveling mechanism of the net sealer lifting arm will have counterweights to secure the tie rod end of the net sealer and maintain its stability. At the same time, four retractable round tube supports are landed further to preserve the stability of the rate sealer arm structure and ensure the reliability of this tall truss structure under aerodynamic loads. We have considered the most hazardous working condition of the structure in terms of wind response without the support of the round tube support, while mainly considering the effect of pulsating wind on the boom structure. The tracked net sealer is shown in Figure 1.

The technical route of this paper integrates a systematic framework of numerical simulation and experimental validation for wind fatigue studies of boom structures. Initially, the working wind field data are collected, based on which the random wind speed is simulated by MATLAB and converted into wind load to be applied to the finite element model of the boom for dynamic response, and the corresponding data are obtained. Secondly, the response surface optimization of stress, displacement, and modal frequency is carried out to select the most unfavorable position of the boom size as the input parameter, find the data mainly affecting the structure through sensitivity analysis, divide the parameter range by the derivation of the objective function, use the CCD composite design to obtain the response surfaces of the stress and displacement, screen the response surfaces to find the optimal solution and make the structural prediction, and finally compare the results with the pressure monitoring test. Finally, the results are compared with the pressure monitoring test. The technical route studied in this paper is shown in Figure 2.

We proposed the wind spectrum–response surface two-domain coupling method to solve the reliability optimization problem of towering structures under the unsteady field. The boom structure’s dynamic response analysis and response surface optimization design were carried out by establishing the two-domain coupling analysis framework of pulsating wind and optimized structure. Finally, the stress monitoring of the existing structure was carried out. The results show that the wind spectrum–response surface two-domain coupling method is feasible and combines the wind response of the towering structure and the response surface optimization design more comprehensively, with low cost and improved efficiency, compared with the traditional single study of the wind response of the structure and the optimization of the European structure.

2. Numerical Simulation of Stochastic Wind Field

We have only considered the wind effects and not referred to the more detailed adverse effects (e.g., traffic vibration from vehicles passing by while the net sealer is unfolding its work) [19]. In this section, numerical simulations of the wind field will be carried out for the boom of the unfolded net sealer. To reduce the computational workload of the simulation while guaranteeing accuracy, the boom is divided into four segments. In practical engineering, pulsating wind contains three dimensions of wind direction: downwind, crosswind, and vertical. Crosswind is too small in terms of its effect on the structure, while the value of vertical wind is negligible, so only the effect of downwind on the structure is considered [20]. Each section of the boom is divided into four segments, respectively, and the 3D correlation of the boom is considered due to the substantial distance between the points. Forty-five points are simulated for the boom, and the simulated positions are shown in Figure 3. The parameters of each section of the boom are shown in

Table 1. Design parameters and dimension values of each boom section (mm).

Serial Number	Beam Thickness	Web Thickness	Boom Cross-Section Dimensions	Boom Length
Section 1 Telescopic arm	5	4	2830 × 2000	18,510
Section 2 Telescopic arm	5	4	2490 × 1755	17,820
Section 3 Telescopic arm	4	3	2190 × 1540	17,730
Section 4 Telescopic arm	4	2	1930 × 1925	17,660
Section 5 Telescopic arm	5	1.5	1710 × 1090	17,000
Inner lifting arm	5	4	2375 × 2375	10,590
Outer lifting arm	6	3	2755 × 2375	10,240
Front support arm	5	1.5	1710 × 1090	18,510

.

2.1. Pulsating Wind Characteristics

During machine operation, since wind loads have inherent characteristics and can have an effect on the boom structure, it is necessary to study the response of the boom structure under wind loads, which requires the acquisition of specific information about the external wind field and the wind loads acting on the boom structure. The harmonic superposition method and Davenport spectrum are used to simulate the wind field under the actual wind speed of pulsating wind. Finally, the accuracy of the simulation results is verified [21,22]. The pulsating wind can be regarded as a random dynamic wind, showing the characteristics of randomness and time variability. At the same time, it is known from the observation that the wind speed and direction at various locations on the windward side are often inconsistent when the gust acts on the windy structure. Even though the difference is significant, the spatial correlation must be considered in studying the pulsating wind speed at various nodes on the boom [23,24]. Pass-through receives pulsating wind speed. The simulation parameters of the wind field in which the net sealer is located are shown in

Table 2. Main parameters of wind field simulation.

Name	Key Parameters
Simulation methods	Harmonic superposition method (physics)
Average wind speed model	Exponential law
Ground roughness category	Class B
Roughness coefficient	0.15
Target power spectrum	Davenport spectrum
Total time	600
Time interval of wind speed time history (s)	0.1
Attenuation coefficient	${{\displaystyle C}}_{\mathrm{x}}=8,{{\displaystyle C}}_{\mathrm{y}}=16,{{\displaystyle C}}_{\mathrm{z}}=10$
Frequency point sampling interval (Hz)	0.001–6

.

$$\begin{array}{l}{v}_j\left(t\right)={\displaystyle \sum _{m=1}^j{\displaystyle \sum _{l=1}^N\left|H_{jm}\left({\omega }_l\right)\right|}}\cdot \sqrt{2\Delta \omega }\cdot \cos \left[{\omega }_{l}t+{\psi }_{jm}\left({\omega }_l\right)+{\theta }_{ml}\right]\\ j=1,2,3,\dots ,n\end{array}$$

(1)

where $\Delta \omega =\omega /N$ is the frequency increment; $H_{jm}\left({\omega }_l\right)$ is the modulus of the above lower triangular matrix; the wind spectrum is divided in the frequency range into $N$ of identical parts. ${\psi }_{jm}\left({\omega }_l\right)$ is the phase angle between two different action points; ${\theta }_{ml}$ is a function between 0 and 2π random numbers that are uniformly distributed between them; ${\omega }_l=l\cdot \Delta \omega$ is an increasing variable in the frequency domain.

2.2. Numerical Simulation of Pulsating Wind Speed

We propose that the wind fatigue response of the boom structure of a tracked net sealer is simulated in a region under five pulsating wind speeds. The key parameters of the simulation are shown in Table 2. The pulsating wind speed time course was simulated using MATLAB software, considering a base wind speed of 10 m/s, where the maximum pulsating wind speed was about 14 m/s. Therefore, the pulsating wind speed and wind speed power spectra were obtained. Due to space constraints, only the simulation results for several simulation points are listed, as shown in Figure 4 and Figure 5.

The results in Figure 4 indicate that the pulsating wind speed at each simulation point of the boom system floats up and down around 10 m/s, which realistically simulates the influence of natural wind on the boom of the net sealing machine when it is unfolded for work. Figure 5 compares the simulated pulsating wind speed and the target spectra at each simulated representative point of the net sealer downwind boom structure to verify the stability and accuracy of the pulsating wind speed spectra obtained from the simulation.

The results indicate that in Figure 5, the simulated spectrum floats compared with the target spectrum position, and the two trends are the same and in good agreement. Therefore, the above method of simulating pulsating wind speed is more reliable and closer to the actual situation. It can be used to analyze the wind-driven dynamic response of the following boom structure.

2.3. Wind Load Calculation

After obtaining the pulsating wind speed time range at each loading point of the boom structure using numerical simulation, the total wind speed time range sample can be obtained by superimposing the pulsating wind speed time range with the mean wind speed at the point. Based on the quasi-stationary assumption, the total wind speed time range is converted to the wind pressure time range:

$$\mathrm{P}(\mathrm{t})={\displaystyle \frac{1}{2}}\rho {{\displaystyle V\left(\mathrm{t}\right)}}^2$$

(2)

where $V\left(\mathrm{t}\right)=V+\mathrm{v}\left(\mathrm{t}\right)$; $V$ is the average wind speed; and $\mathrm{v}\left(\mathrm{t}\right)$ is the pulsating wind speed time course.

Based on the above wind pressure timescale, the total wind pressure timescale is transformed into the wind load timescale required for the wind response of the boom structure.

$$F(\mathrm{t})={{\displaystyle C}}_{\mathrm{d}}V(\mathrm{t})\mathrm{A}$$

(3)

where ${{\displaystyle C}}_{\mathrm{d}}$ is the structural form factor. In this paper, the arm structure of the net sealer is taken as 1.2. $A$ is the windward area of the structure at a particular place, and the values are shown in

Table 3. Windward area of each section of the boom.

Category	Windward Area (m2)
1	14.73
2	13.76
3	32.96
4	17.16

.

Figure 6 shows the boom structure’s wind pressure load time profile at each simulated representative point.

3. Wind Vibration Response Analysis

3.1. Transient Analysis

A pulsating wind simulation of the boom structure was conducted in a 90° downwind direction. Firstly, the point-line diagram of the beam unit was created in ANSYS Workbench (instructional 2024 version) to simulate the supporting columns, beam rods, and web rods of each section of the boom structure, and the point-line diagram was also given a cross-section treatment. The auxiliary side plates and small weld structures were ignored when building the boom model, and the rods’ wall thickness errors were not considered. Considering the articulated relationship between the front support arm, the end spanning arm, the spanning arm, and the lifting arm, only rotational degrees of freedom were retained in these two positions. The pulley realizes the telescoping process of the traversing arm, and due to the slight friction of the pulley, the sliding contact was set up at this joint for simulation.

The boom material was T700 high-strength steel. Since the rod unit only withstands axial force and torque, it was suitable for simulating the structure of the net frame, rope, etc. It can accurately simulate the axial load and provide accurate stress and strain information, so it adopts the rod unit to mimic the structure of the tensile rope. The material property was set as a constant value. In the finite element model, the number of beam cells was 18,698, and the number of rod cells was 8. The local mesh enlargement of the boom is shown in Figure 7.

The boom and tension cable structure sections were fixedly supported using binding contact to the outer lifting arm, the front support arm, and the end of the support frame (serial numbers 1, 8, and 15 in Figure 3). The arm frame needs to meet the corresponding strength and stiffness requirements; that is, the maximum stress and the maximum deformation shall not exceed the permissible value of the material, and the Mises stress and the maximum deformation of the arm frame are analyzed as the object of study for its strength and stiffness. Selecting 19, 39, 45, and 54 as representative points in the unfolded view of the net sealer boom, the simulated downwind displacement timescales are shown in Figure 8, and the downwind stress timescales are shown in Figure 9.

The stress cloud and displacement cloud of the boom structure are shown in Figure 10 and Figure 11.

The results indicate that under the random wind load excitation at a 90° wind angle, the most significant displacement and stress response are at the representative point 39 across the height of the boom. The maximum displacement is at the fourth and fifth sections of the boom connection, with 94.963 mm at the fourth and fifth boom section joints, and the maximum stress is 389.62 MPa. At the same time, the tension cable structure (analog point 54) and the foremost part of the boom (analog point 45) showed significant stresses. The results show that the boom structure meets the strength and stiffness requirements of the material, is within the safe range, and has some margin, so the response of displacement and stress can be further optimized.

3.2. Modal Analysis

When the machine is under construction, its boom structure is subjected to wind load, which makes it vibrate and deform to different degrees, so it is necessary to carry out pre-stress modal analysis on the boom, which can truly reflect its vibration characteristics and modal parameters. The first six orders of the modal vibration pattern of the net sealing machine boom are shown in Figure 12, and the intrinsic frequency and vibration pattern are shown in

Table 4. Overall frequency and vibration pattern of the net sealer arm modes.

Modal Order	Intrinsic Frequency/(Hz)	Oscillatory Trend
1-order	0.42539	Vibration in the 135° direction along the YZ axis
2-order	0.4271	Vibration in the 45° direction along the YZ axis
3-order	0.43159	Vibration in the 135° direction along the YZ axis
4-order	0.43273	Vibration in the 45° direction along the YZ axis
5-order	0.86283	Horizontal vibration along the Z-axis
6-order	0.99733	Horizontal vibration along the Z-axis

.

The results of the modal analysis show that the boom structure is affected by the pulsating wind. The tension cable structure above the boom is the first to vibrate, followed by the overall boom vibration. The low intrinsic frequency means that the structure responds significantly to low-frequency excitation. The first four orders of vibration of the structure are led by the tie rod structure along the YZ axis, which may be due to the decreasing width of the overall structure of the boom and the weak width and stiffness of the front support arm, resulting in the center of mass and the center of stiffness of the overall structure not overlapping. The bending vibration triggers the moment of inertia, which leads to additional torsional displacement and makes it vibrate around the YZ axis. Under the influence of wind load, the 5th–6th order modal vibration energy is transferred to the boom as a whole, which is concentrated along the Z-axis at the connection of the third and fourth sections of the boom.

4. Boom Structure Response Surface Optimization

4.1. Boom Modal Parameterization

Response surface optimization selects an appropriate experimental design solution, generates a design table, and calculates the associated values based on the design parameters and response objectives. Fitting methods are utilized to establish the relationship between the design variables and the response objectives and, finally, to find the optimal value among the known feasible solutions [25,26,27,28,29].

Optimization is a multi-loop solution process that begins with parameterizing the net sealer boom structure. According to the wind response analysis results, the most dangerous position occurs at the connection of the fourth and fifth sections of the boom. In the fundamental dynamic characteristic analysis, the buckling analysis method is used to study the telescopic boom; the bottom of the lifting arm is fixed, the front support arm is retracted, and the load is gradually applied to the front end of the fifth section of the telescopic boom. The result shows that the instability occurs at this position first. Therefore, the following boom width and length are selected for optimization.

Its design variables are the width and total length of the fourth and fifth sections of the boom, respectively. Figure 13 shows the parameterization of the net sealer’s boom’s structural dimensions. L1 is the width of the fourth section of the telescopic boom; L2 is the width of the fifth section of the boom; L3 is the length of the fifth section of the telescopic boom.

Table 5. Optimized design variable ranges.

Input Variable	Initial Value/mm	Variation Range/mm
L1	1650	(1555, 1650)
L2	1330	(1200, 1350)
L3	17,000	(16,000, 17,500)

shows the initial values and optimization ranges of the design variables for each optimization.

Optimizing the boom structure ensures its design requirements, such as strength and stiffness. The structural stresses and displacements are used as optimization limiting parameters. The maximum value of the boom’s stress is 389.62 MPa, and the maximum deformation value is 94.963 mm.

4.2. Sensitivity Analysis

Sensitivity is the rate at which an objective function or a constraint changes when a design variable is changed, i.e., the objective function or constraint is derived [30,31,32].

$${\delta }_{sen}\left({\displaystyle \frac{y_i}{x_j}}\right)={\displaystyle \frac{\partial y_i}{\partial x_j}}={\displaystyle \frac{y_i\left(X+\Delta x_j\cdot e\right)-y_i\left(X\right)}{\Delta x_j}}$$

(4)

where ${\delta }_{sen}$ is the sensitivity; $e$ and $X$ variables of the same dimension; $y_i$ is the objective function; $x_j$ are the design variables; $\Delta x_j$ is the amount of change in the design variable.

The design tests determine the degree of influence of these three factors on the overall maximum time deformation, maximum time stress, and 1st order intrinsic frequency of the structure. Figure 14 indicates that the structure’s stress and deformation are most seriously affected by L1 and L3, and its 1st-order intrinsic frequency is also mainly affected by these two parameters simultaneously. The results indicate from the 1st-order modal cloud diagram that the structure’s tie structure is the first to vibrate, but the factors that affect its frequency are mainly L3 and L1.

4.3. Optimization Process and Result Analysis

We adopted the Central Composite Design (CCD) experimental type and designed 15 groups of design variables. The response surfaces of the maximum time stress and maximum time deformation of the boom structure and its two design variables, with the most substantial influencing factors, were simulated by the genetic aggregation type of response surface, as shown in Figure 15 and Figure 16.

From Figure 15 and Figure 16, the results indicate that the maximum value of temporal stress in the structural boom increases with L₃ decreasing first and then growing with the rise in L1. The effects show first an increase and then a decrease. The maximum value of the boom structural temporal deformation also increases with L₃ decreasing and then increases with L₁. The changes are slow.

Through the MOGA (Multi-objective Genetic Algorithm) screening preference method, after 8670 evaluations and the convergence and selection of three candidate points, and after many iterations of calculation, the optimization course curves of the maximum value of time stress, as well as the maximum value of time deformation of the arm structure, were derived, as shown in Figure 17 and Figure 18. The final design point parameter solving was performed to arrive at the optimized design point values and results, as shown in

Table 6. Optimized design point values and results.

L1	L2	L3	Deformation	Stress
1568.7 mm	1211.5 mm	16,478 mm	87.302 mm	346.59 MPa

. A comparison of the first six orders of intrinsic frequencies and modal shapes before and after optimization is shown in

Table 7. Comparison before and after natural frequency optimization.

Modal Order	Natural Frequency
	Pre-Optimization/Hz	Post-Optimization/Hz	Amount of Growth/Hz
1-order	0.42539	0.84277	0.41738
2-order	0.4271	0.8616	0.4345
3-order	0.43159	0.85505	0.42346
4-order	0.43273	0.85731	0.42548
5-order	0.86283	1.7094	0.84657
6-order	0.99733	1.9759	0.97857

. Compared with the first six orders of modal frequencies before optimization, all the inherent frequencies increase afterward.

The optimization results show that the maximum value of temporal structural deformation is reduced by about 8.06%, and the maximum value of temporal stress is decreased by about 11.04%. The values of stress and deformation do not exceed the limit of permissible stress and maximum deformation, which indicates that the structure’s design is within a reasonable range and that the whole meets the design requirements of the structural arm.

After optimization, it can be seen that the intrinsic frequency is increased, and the stiffness of the structure is improved, but the vibration energy is not transferred to the overall structure of the boom; the tie rods at the windward side are mainly affected by the wind load, considering that the width of the truss of the structure presents a step-by-step decrease, which leads to vulnerability compared with the tie rods of the distal end, so it is necessary to pay attention to the structural tie rods of the boom when it is carrying out the work. For this towering and long truss structure, the modes are strongly coupled, and the optimization may trigger the coupling of the modal frequencies, resulting in the overall modal frequencies remaining compact. After structural optimization, the first-order mode shapes gradually migrate from the middle vulnerable region of the tie rods to the two ends. Meanwhile, the fourth and fifth section boom joints are still weak after optimization, but their fragility is significantly reduced compared with before optimization. Therefore, focusing on these two positions is essential when working on the net sealer.

5. Stress Monitoring Test

The telescopic arm of the mesh sealing machine was deployed to enter the working state, and the stress test of the metal structure was carried out at the positions. Working condition: Loads are arranged at the two ends of the telescopic boom in sections 1, 3, and 5; 960 kg in the left front and rear wings; 960 kg in the right front and rear wings at 3/4; 450 kg in the middle of the two ends of the telescopic boom in section 3. The fourth section under the telescopic arm was selected as the test point. Sandpaper was used to polish its surface, and the strain gauges were fixed for stress monitoring. The actual diagram of the net sealing machine is shown in Figure 19. The number 1 in the figure is the connection point of the fourth and fifth boom sections, and stress monitoring is conducted at this position. Specific data are shown in

Table 8. Stress monitoring parameters of the net sealing machine boom structure.

Stress Monitoring Parameters
Instrument model	ZY-B3	Strain gauge type	BX120-10AA
Weather conditions	Fine day	Wind speed	7.2 m/s
Temperature	10 °C	Humidity	47% RH
Measurement point	1	Stress	277.85 MPa
Simulation result	346.59 MPa	Inaccuracies	24.74%

.

By comparing the measured results with the optimized results, the error is about 24.74%. Considering the wind speed and the actual support structure will appropriately increase the error in the simulation results. Still, side by side, it proves that the method can reduce the value of the stress to achieve the purpose of optimization.

6. Conclusions

We proposed a wind-induced vibration control strategy based on the two-domain coupling and cooperative optimization of wind spectrum and response surface, focused on solving the optimization problem of the dynamic reliability of tall boom structures under the action of unsteady wind fields, and drew the following conclusions:

(1)

We establish a dual-domain coupled analysis framework for turbulent pulsation and structural optimization, which integrates fluid–structure coupling and response surface optimization design, breaking through the limitations of traditional single-domain analysis (e.g., only wind study of the structure or independent optimization design). The results show that the maximum displacement is reduced by 8.06%, the maximum stress is reduced by 11.04%, and the structural stiffness is improved. Meanwhile, the actual stress monitoring proves the feasibility of this method, which provides a new research idea for the wind response and structural optimization of scalable towering structures.

(2)

Under the action of random wind loads, the traditional optimization method of the structure requires hundreds of iterations (each iteration requires a complete CFD analysis). The dual-domain coupled optimization only needs selection of the external dimensions according to the most unfavorable location of the structure. A few sample points can construct the response surface of structural dimensions. The response surface dimensions can be screened to find the best-fitting dimensions of the structure to cope with the wind response, which simplifies the process of structural wind response and optimization and improves the efficiency of the study.

(3)

Since this paper only investigates the horizontal extension mechanism toward the ground, potential problems such as chaotic structural response and damage misreporting need further investigation. Considering the limitations of this paper, the wind spectrum–response surface two-domain coupling can be generalized to similar towering structures, and in the future, we will further explore the mechanism of forming a certain angle with the ground and make an in-depth exploration, such as aerial work trucks, cranes, crawler cranes, and other scalable machinery, to make them meet the unfolded working range length and reduce the stress and deformation values to minimize the structural damage misreporting, thus reducing the probability of accidents. This ensures applicability to a broader range of structures and guides cross-scale wind studies of high-altitude retractable devices.

(4)

In the future, multimodal sensors and threshold alarm systems can be integrated into the machines. The main study is in the critical area of the fourth and fifth sections of the jib joints, which can more accurately improve the monitoring accuracy, real-time response, and prevention. Still, we should pay attention to the economy of the large-scale deployment of sensors and the long-term maintenance costs. At the same time, delay in the data processing may lead to problems such as lagging response. Uncertainty factors, such as noise, can be introduced by adding other uncertainty factors, such as the turbulent noise term of the wind field, through stochastic equations when building a pulsating wind field, which can significantly improve the practical value of wind response analysis.