MEMS-Based Vibration Acquisition for Modal Parameter Identification of Substation Frame

Abstract

As a critical component of substations, the substation frames are characterized by significant height and span, which presents substantial challenges and risks in conducting dynamic response tests using traditional sensors. To simplify these difficulties, this paper introduces an experimental method utilizing MEMS sensor-based vibration acquisition. In this approach, smartphones equipped with MEMS sensors are deployed on the target structure to collect vibration data under environmental excitation. This method was applied in a dynamic field test of a novel composite substation frame. During the test, the proposed MEMS-based vibration acquisition method was conducted in parallel with traditional ultra-low-frequency vibration acquisition methods to validate the accuracy of the MEMS data. The results demonstrated that the MEMS sensors not only simplified the testing process but also provided reliable data, offering greater advantages in testing convenience compared with traditional contact methods. The modal parameters of the substation frame, including modal frequencies, damping ratios, and mode shapes, were subsequently identified using the covariance-driven stochastic subspace identification method. The experimental methodology and findings presented in this paper offer valuable insights for structural dynamic response testing and the wind-resistant design of substation frames.

1. Introduction

Substation frames are spatial truss structures, characterized by their significant height and large spans, typically arranged in rows within power substations. In engineering practice, it is crucial for substation frames in operation to maintain stable dynamic characteristics, often represented by modal parameters. However, due to the cumulative effects of various environmental factors, such as rain, snow, strong winds, and earthquakes, these structures are susceptible to fatigue, potentially altering their dynamic characteristics [1,2,3,4]. The collapse of a single-row substation frame can initiate a chain reaction, posing a serious threat to the normal operation of the substation. Therefore, conducting dynamic characteristic tests on newly constructed substation frames is essential to ascertain the modal parameters and ensure their reliability in service.

From a structural dynamic perspective, field testing is the most reliable method for obtaining the dynamic response of a structure [5,6,7]. However, collecting dynamic responses from substation frames entails significant risks. Traditional methods of acquiring dynamic responses primarily involve deploying contact-type vibration sensors on the target structure. For instance, the 941b ultra-low-frequency vibration pickups are capable of accurately capturing structural vibrations under various load conditions [8]. Despite their accuracy, these sensors may not perform optimally for certain structures, such as tall steel frames. The need to connect vibration pickups to data acquisition devices via shielded cables introduces challenges, particularly when measurement points are located at considerable heights. Under lateral loads, such as wind, the shielded wire may swing, occasionally causing the solder joint between the shielded wire and the sensor to disconnect. As a result, it is necessary to explore a new experimental method to simplify the testing process.

To address the aforementioned issues, computer vision-based vibration measurement technology has become increasingly popular [9,10,11,12]. This method primarily relies on high-precision visual equipment to capture video footage of the target structure, and then employs computer vision processing techniques to extract the vibration response at specific points. However, this approach is not without challenges. Firstly, as a non-contact measurement method, it introduces the potential for errors due to vibrations from the acquisition equipment itself. Secondly, the method requires calibration at fixed positions on the structure, which may not significantly reduce the experimental complexity. Furthermore, the equipment involved is expensive, and the analysis of vibration responses is heavily dependent on the performance of the computing hardware. Consequently, for certain specialized structures, particularly those where height complicates vibration monitoring, there is a clear need for the development of a more user-friendly and cost-effective vibration acquisition method to advance structural dynamic response research [13,14,15,16,17].

At the same time, the development of micro-electromechanical systems (MEMS) technology offers a new option for vibration monitoring [18]. Firstly, MEMS technology has made it possible to miniaturize traditional sensors into tiny semiconductor components, such as MEMS sensors [19,20]. By simulating the structure of traditional sensors, MEMS can achieve acceleration acquisition. Secondly, the development of MEMS technology has significantly reduced the cost of semiconductor components. These two factors enable the application of MEMS sensors in structural vibration monitoring, although the use of MEMS sensors still requires a carrier. Today, most mobile devices are equipped with built-in MEMS sensors, providing a good means to capture structural acceleration responses using MEMS sensors. Moreover, there are examples where MEMS sensors have been utilized to assess structural and seismic behavior, with the aim of detecting and localizing damage [21,22].

Although the simplicity of tests is an advantage, the limitations of MEMS sensors in application should not be overlooked [23]. Firstly, MEMS are not suitable for long-term monitoring of structures. This is because MEMS sensors require specific carriers, such as portable devices and smartphones, and using such carriers for long-term vibration acquisition is impractical. Secondly, MEMS sensors, being micro semiconductor components, differ from specialized acquisition equipment in that they lack robust durability, which may result in time-history data containing background noise. Therefore, when using MEMS sensor data for parameter identification and analysis, it is advisable to choose identification algorithms with better robustness.

Once the structural dynamic response is obtained, the modal parameters identification approach can be employed to determine the modal parameters of the structure, including modal frequencies, damping ratios, and mode shapes [24,25,26]. These parameters collectively reflect the structure’s vibration characteristics, energy dissipation capacity, and modal deformation patterns [27,28,29,30,31,32]. These parameters also play a significant role in structural engineering, such as in the calibration of numerical models, allowing the physical response of numerical models to better approximate the actual structures, thereby further extending research into damage identification under extreme conditions [33]. In power systems, these parameters are primarily used for wind-resistant design of structures [2,24]. On the other hand, the common methods for structural modal parameter analysis include time-domain and frequency-domain approaches [34,35,36,37,38]. Time-domain methods directly utilize the experimental time-domain responses to identify modal parameters, with techniques such as the AutoRegressive Moving Average Model [39], the Random Decrement Technique [40,41], the Covariance-Driven Stochastic Subspace Identification (SSI-Cov) method [42,43,44], and the Data-Driven Stochastic Subspace Identification method [45,46,47]. In contrast, frequency-domain methods transform the time-domain responses into the frequency domain using Fourier Transform for parameter analysis. Notable examples include the Peak Picking method [48] and Frequency-Domain Decomposition (FDD) [49,50].

Amongst these methods, the SSI-Cov approach offers a robust algorithm. It is based on stochastic theory and is particularly effective for modal parameter identification. It constructs a Toeplitz matrix using the covariance matrix of the structural response signals and then extracts modal parameters through singular value decomposition [51,52]. This method is efficient in processing time-domain response data under ambient excitation, and its parameter identification process is minimally affected by noise. The SSI-Cov method has been widely applied to identify the dynamic characteristics of various civil engineering structures, including bridges, high-rise buildings, and some critical civil infrastructures [44,53,54,55]. Therefore, this study employed the SSI-Cov method to identify the modal parameters from the dynamic response time histories of the substation frame.

In summary, this paper proposes an experimental method for obtaining the dynamic response of substation frames under ambient excitation using MEMS sensors for vibration data acquisition. The method involves the deployment of smartphones equipped with MEMS sensors on the target structure to capture vibration responses. Based on this data, the SSI-Cov method is employed to identify the modal parameters of the structure. The second section of this study introduces the field test using MEMS-based vibration acquisition devices, covering an overview of the structure, the principles of MEMS vibration data acquisition, and the execution of the field test. The third section focuses on analyzing the time–frequency response characteristics of the acquired data, along with wind speed data characteristics, and presents the wind profile results for the structure in both parallel and vertical truss directions. In the fourth section, the SSI-Cov method is used to analyze the vibration responses, identifying the primary modal frequencies, damping ratios, and mode shapes of the structure. The findings from this study offer valuable references for vibration testing of tall steel structures and for the wind-resistant design of substation frames.

2. Field Test of Vibration Data Acquisition with Portable Devices

This section first provides an overview of the new substation frame used in the field vibration test. Given the considerable height and large span of the frame, a novel method utilizing MEMS sensors for vibration response acquisition was proposed to simplify the testing protocol. This method was successfully implemented to acquire the dynamic response of the new substation frame.

2.1. Overview of the Test Substation Frame

The test substation frame is located in Baoji, Shaanxi Province, and represents the first of a new type of hybrid Gas-Insulated Substation. Due to the compact overall dimensions of this substation, conducting a dynamic response study on its substation frame holds significant engineering value, as shown in Figure 1a. Typically, substations consist of multiple rows of substation frames. To ensure the overall rigidity of the frame while maintaining the flexibility of the outgoing lines, the structural designers retained the central column of the first substation frame in the substation. Figure 1b illustrates the main dimensions of the test substation frame, which is a double-layer truss structure with left-right symmetry. The upper layer is the outgoing line truss, and the lower layer is the busbar truss. The length from the outermost column to the central column is 18 m, the height of the busbar truss is 15.7 m, and the height of the outgoing line truss is 26 m. Despite the relatively compact structure of this substation frame, a lightning protection wire has been installed to enhance its lightning resistance.

2.2. Working Principle of MEMS Sensors

A smartphone was used as the vibration acquisition device, with vibration data primarily collected through the MEMS sensors embedded in the phone. Modern smartphones are typically equipped with built-in MEMS sensors, as illustrated in Figure 2a. A MEMS sensor functions as a gyroscopic accelerometer with three mutually orthogonal axes designed to detect acceleration from different directions. The inclusion of a gyroscope allows the smartphone to approximately measure gravitational acceleration regardless of its orientation, whether placed horizontally or vertically, thereby eliminating the need for sensor calibration.

MEMS sensors operate based on Newton’s second law, functioning as a mass-spring-damper system within a three-dimensional silicon structure. As shown in Figure 2b, the sensor’s core consists of a mass block attached to a movable arm, which is connected to a fixed arm through a capacitive structure. When the sensor experiences acceleration, the mass block moves opposite to the direction of motion, changing the capacitance and, in turn, the sensing voltage. This voltage change enables the detection of external acceleration. Key components such as the mass block, springs, and dampers are mechanical elements made from silicon using advanced processing techniques and play crucial roles in the sensor’s operation.

2.3. Field Test

To collect vibration responses using MEMS sensors, the first step is to select an appropriate acquisition device. In this test, an iPhone 8 smartphone was chosen as the vibration acquisition device. This device is equipped with precise MEMS sensors capable of continuously capturing structural vibration responses within the frequency range of 0–100 Hz. It should be noted that the primary natural frequencies of civil engineering structures are often concentrated in the low-frequency range (below 10 Hz), which means that using a smartphone as a vibration acquisition device can fully meet engineering requirements. Traditional vibration testing methods typically involve either artificial excitation or ambient excitation. Ambient excitation, which utilizes environmental factors such as microseisms and wind loads as excitation sources, requires no special excitation equipment and provides broadband excitation conditions for the test. Given these advantages, ambient excitation was selected as the excitation condition for this experiment.

Prior to the test, it was necessary to determine the arrangement of the measurement points. In this test, a total of four measurement points was arranged, with two sensors placed at each point—one aligned with the parallel truss direction and the other aligned with the vertical truss direction. The layout of the measurement points is illustrated in Figure 3, with red dots and numbers denote the measurement points’ location and numbers, respectively. As shown, two accelerometers were placed on the central column to capture overall vibration responses, while the other two points were positioned on either side of the column to collect torsional responses.

Upon the researchers’ arrival at the test site, the vibration acquisition system was assembled, as shown in Figure 4. In addition to setting up the MEMS acquisition system, a complete 941b vibration pickup system was installed at corresponding locations to serve as a comparison with the MEMS system. Anemometers were also installed at the test site to monitor wind speed variations during the experiment. After the system setup was complete, the sampling frequency was set to 100 Hz, and the acceleration response of the structure under ambient excitation was continuously recorded for 1800 s.

3. Analysis of Experimental Data Characteristics

This section analyzes the characteristics of the response data obtained from the experiment, with the aim of comparing the data characteristics acquired through the two different collection methods.

3.1. Time–Frequency Characteristics of MEMS Data

Figure 5a presents the time-domain response data collected by the MEMS sensors at measurement point 1 during the test. It is evident that in the direction of gravitational acceleration, the response signal fluctuates around 9.8 m/s² as sampling time increases, which is approximately consistent with the expected gravitational acceleration. In both the parallel and vertical truss directions, the response signals fluctuate around a mean value of zero as sampling time progresses. Figure 5b displays the root power spectral density plot for measurement point 1. In the parallel truss direction, distinct peaks appear at frequencies such as 2.14 Hz and 3.05 Hz; similarly, in the vertical truss direction, peaks are observed at 2.14 Hz and 2.82 Hz. These frequency points often correspond to the structure’s potential modal frequencies.

3.2. Time–Frequency Characteristics of Responses Collected by the 941b System

Figure 6a shows the time-history response at measurement point 1, obtained by using the 941b system. Since the MEMS acquisition system and the 941b vibration pickup system are two independent systems, the response signals measured cannot be perfectly synchronized. On the other hand, the time-domain response obtained from the MEMS acquisition system shows slightly higher amplitude than that from the 941b system. This may be because the MEMS system captured some noise during data acquisition, resulting in a slightly higher standard deviation of the data compared with the 941b system. However, this does not alter the modal characteristics of the structure, as these characteristics are inherent to the structure itself. Figure 6b presents the root power spectral density plot obtained using the 941b vibration pickup system. It can be seen that the resonance peaks in this plot are generally consistent with the peak regions observed in the MEMS root power spectral density plot, with similar amplitude in the peak regions. The main difference lies in the amplitude of the frequency-domain response in the non-resonant peak regions, where the frequency-domain information is primarily contributed by noise. The comparison indicates that in the resonance peak regions, the modal characteristics identified by both systems exhibit good consistency.

3.3. Wind Speed Time History

During the test, anemometers were installed on the busbar truss, specifically at the second truss level, to monitor variations in wind speed at that location. It should be noted that while the wind direction and speed varied randomly, the wind loads acting on the structure primarily occurred along the parallel truss and vertical truss directions. Therefore, wind speed was monitored specifically in these two directions. Traditionally, anemometers are placed at a height of 10 m, and the average wind speed over a 10-min period at this height is calculated to compare the operational wind speed of the structure with the design wind speed. In this study, the anemometers were positioned at the busbar truss at a height of 15.7 m to monitor wind speed variations at the truss location, as shown in Figure 7. The recorded wind speeds in both directions during the test are below 4 m/s. According to wind speed statistics, the average wind speed is 0.68 m/s in the parallel truss direction and 0.80 m/s in the vertical truss direction. From an experimental perspective, wind loads act as partial excitations during tests. The wind speed fluctuates randomly within a small range, suggesting that the wind load provides the structure with a near-stationary random excitation. Additionally, the recorded wind speed and temperature variations during the tests can serve as valuable references for future finite element analysis of the structure.

After obtaining the average wind speed at the truss, the Davenport wind speed theory can be applied to calculate the equivalent wind speed at different heights, as shown in the following equation:

$$U(z)=U(z_{ref}){({\displaystyle \frac{z}{z_{ref}}})}^{\alpha }$$

(1)

where $U(z)$ is the equivalent wind speed at height $z$, $U(z_{ref})$ is the wind speed at the reference height $z_{ref}$, and $\alpha$ is the surface roughness coefficient, typically ranging from 0.1 to 0.3. In this study, $\alpha$ was set to 0.2.

By calculation, the equivalent wind speeds at different heights of the structure are obtained, as illustrated in the wind profile diagram in Figure 8. It can be seen that, at the same height, the average wind speed in the vertical truss direction is consistently higher than in the parallel truss direction; the average wind speeds at the top of the substation frame are 0.80 m/s and 0.96 m/s, respectively. The calculated wind profile results provide a valuable reference for the wind-resistant design of the substation frame from an operational perspective.

4. Modal Analysis of the Substation Frame

4.1. Covariance-Driven Stochastic Subspace Identification

For vibration testing of structures under ambient excitation, the excitation applied to the structure can be considered as stationary white noise. The core of the SSI-Cov method is to project the experimentally obtained responses into the state space of control theory. According to stochastic subspace theory, the discrete state-space model of an n-degree-of-freedom system under white noise excitation can be expressed as:

$$x_{k+1}=A_d{x}_k+w_k$$

(2)

$$y_k=C_d{x}_k+v_k$$

(3)

where $x_k$ is the discrete-time state vector, $y_k$ is the output vector, $A_d$ and $C_d$ represent the state matrix and discrete output matrix, respectively, and $w_k$ and $v_k$ are zero-mean Gaussian white noise.

By further expressing the response as a Hankel matrix and calculating its Toeplitz matrix, the system matrix, observability matrix, and controllability matrix can be obtained. Eigenvalue decomposition of these matrices, combined with the stabilization diagram method, allows for the extraction of the dynamic characteristics of the structure. Figure 9 presents the flowchart for identifying the dynamic characteristics of a structure using the SSI-Cov method. This method is exclusively employed in this study to identify the modal parameters and achieve accurate analysis results. The mathematical framework of the SSI-Cov method can be referenced in the literature [17].

It should be noted that the SSI-Cov method exhibits strong robustness against noise when identifying dynamic parameters, primarily due to the following reasons: (1) The SSI-Cov method identifies modal parameters by constructing the covariance matrix of the response time series. In this process, the covariance matrix primarily reflects the statistical characteristics of the stable components of the signal, while noise typically manifests as uncorrelated or high-frequency components. As a result, the noise components are naturally attenuated within the covariance matrix. (2) In the SSI-Cov method, the modal information of the system is obtained through the subspace decomposition of the system’s covariance matrix. This process essentially distinguishes the true dynamic behavior of the system from noise by means of projection. (3) The SSI-Cov method is typically used in conjunction with the stabilization diagram method, which is highly effective in eliminating noise modes from the data.

In addition, the SSI-Cov method assumes stationary excitation, which introduces certain limitations in its application. In contrast, when analyzing time-evolving behavior with the goal of identifying health status related to the rapid evolution of dynamic parameters, time–frequency analysis techniques such as the Short-Time Impulse Response Function [56], Curvature Evolution Method [57], Band Variable Filter [58], and Stockwell Transform are more effective [59].

4.2. Modal Parameter Identification of the Substation Frame

The modal parameters of the substation frame include modal frequencies, damping ratios, and mode shapes. For substation frames, which are non-symmetrical structures, various modal orders exist in the parallel truss direction, vertical truss direction, and torsional direction. Therefore, the SSI-Cov method is employed to identify the modal parameters from the response data obtained in both directions.

Due to the unique characteristics of structural modes, the stabilization diagram results are first examined, as shown in Figure 10. It can be seen that stable poles with corresponding high energy peaks appear near the frequencies of 2.14 Hz and 3.05 Hz in both stabilization diagrams. This indicates that the structure exhibits vibrations in both directions at these modal frequencies, leading to their initial identification as torsional modes. Additionally, a high-energy peak with a stable pole is observed at 4.78 Hz in the parallel truss direction, identifying it as the first-order mode in the parallel direction. Similarly, a high-energy peak with a stable pole is observed at 2.81 Hz in the vertical truss direction, identifying it as the first-order mode in the vertical direction.

Table 1. The identified results of frequencies and damping ratios.

Mode	Direction	Frequency (Hz)			Damping Ratio (%)
		MEMS	941b	Discrepancy	MEMS	941b	Discrepancy
1	1st Torsional	2.14	2.15	0.01	0.31	0.23	0.08
2	1st Vertical	2.81	2.79	0.02	1.29	1.17	0.12
3	2nd Torsional	3.05	3.06	0.01	0.46	0.33	0.13
4	1st Parallel	4.78	4.79	0.01	0.15	0.12	0.03

lists the identified frequencies and damping ratios for the first four modes of the substation frame. It can be seen that the maximum frequency identification discrepancy between the two methods is 0.02 Hz, occurring in the first-order vertical truss direction, while the maximum damping ratio discrepancy is 0.13%, occurring in the second-order torsional direction. Additionally, the damping ratio for the first-order vertical truss mode is 1.29%, which is significantly higher than that for the first-order parallel truss mode, indicating that the structure exhibits greater energy dissipation capability in the vertical truss direction at the first-order mode.

Table 2. Comparison of modal identification results from different method.

Mode	Direction	Frequency (Hz)			Damping Ratio (%)
		SSI	FDD	Discrepancy	SSI	FDD	Discrepancy
1	1st Torsional	2.14	2.15	0.01	0.31	0.43	0.12
2	1st Vertical	2.81	2.79	0.02	1.29	0.88	0.41
3	2nd Torsional	3.05	3.05	0	0.46	0.27	0.19
4	1st Parallel	4.78	4.79	0.01	0.15	0.23	0.08

provides a comparison of the identification results using the SSI-Cov method and the FDD method. It can be seen that, using the same data, the two time–frequency domain algorithms still exhibit differences in their interpretation of frequency and damping ratio. The frequency identification results are generally consistent, with a maximum discrepancy of 0.02 Hz. However, the damping ratio identification results show some variability, with the largest difference occurring in the first-order vertical truss direction, at 0.41%. The variability in the identification results for the other modes is also slightly higher than the differences observed between datasets obtained from different test methods, primarily due to the different time–frequency domains used in the modeling of the two algorithms.

Nonetheless, an examination of the FDD method’s identification results shows that the damping ratio for the first-order vertical truss mode remains the highest, at 0.88%, indicating a strong energy dissipation capability for this mode. Since each mode shape has a spatial structure, the identification results of the substation frame’s mode shapes will be discussed separately in the next subsection.

4.3. Mode Shapes

Figure 11a shows the first-order torsional mode shape at 2.14 Hz. In this torsional mode, all measurement points, except point 3, vibrate towards the left in the parallel truss direction, while in the vertical truss direction, measurement point 1 vibrates in the opposite direction to the other points. Figure 11b presents the first-order mode shape at 2.81 Hz in the vertical truss direction. It can be seen that, except for measurement point 4 at the center of the second-level busbar truss, which vibrates towards the rear of the substation frame, all other points vibrate towards the front, exhibiting a unidirectional tilt mode shape at the top of the substation frame.

Figure 11c shows the second-order torsional mode shape at 3.05 Hz. In the parallel truss direction, measurement point 2 vibrates out of phase with the other points, while in the vertical truss direction, all points vibrate in the same direction. Figure 11d presents the first-order mode shape at 4.78 Hz in the parallel truss direction, where all measurement points are observed to vibrate in the same direction.

It should be noted that mode shape decomposition is based on the theory of modal superposition, meaning that under actual service conditions, the structure’s mode shapes represent a coupling of multiple modes. However, mode shape decomposition is beneficial for designers seeking to verify construction quality, understand the service state of the structure, and accumulate data and experience for the design of new structures.

5. Conclusions

This study conducted simultaneous MEMS-based and traditional contact-based vibration acquisition on a new substation frame, capturing the dynamic response time histories. Building on this, the modal parameters of the structure under operational conditions were identified using structural dynamics analysis methods. The key conclusions drawn are as follows:

(1).

A method based on MEMS technology for acquiring the dynamic response time histories of structures is proposed, and its feasibility is demonstrated through comparison with traditional vibration monitoring methods. The study found that the vibration response captured by MEMS exhibited slightly higher amplitude compared with results from traditional monitoring methods, primarily due to the MEMS system capturing more environmental noise, which increased the overall variance of the data. However, in terms of frequency-domain analysis, the differences between the two methods at the peak regions were minimal, with the main discrepancies occurring in non-modal, non-resonant regions, corresponding to amplitude differences in the time-domain response.

(2).

The primary modes of the new substation frame were identified as follows: the first-order torsional mode at 2.14 Hz, the first-order vertical truss mode at 2.81 Hz, the second-order torsional mode at 3.05 Hz, and the first-order parallel truss mode at 4.78 Hz.

(3).

The modal parameter identification results indicate minimal frequency identification differences when using different datasets or identification methods, as the structural frequency is an inherent property of the structure. In contrast, the damping ratio identification results show some variability, which is attributed to differences in the data acquisition systems and the identification theories used. Overall, the identification results are relatively stable.

While using MEMS sensors to collect responses in the field test offers significant convenience, it does not fully mitigate their drawbacks, particularly the unavoidable noise components in the collected data. To address the noise issue, three approaches can be considered. The first approach involves processing the collected digital signals directly, such as filtering technique. However, the choice of filtering method and its settings heavily depends on the operator’s experience, introducing a degree of variability in noise reduction. The second approach involves using techniques such as the SSI-Cov algorithm, which leverage covariance matrices to diminish noise effects. The third approach is to directly model the frequency-domain information within the frequency domain. Comparatively, the latter two approaches do not require direct processing of the raw signals and impose fewer demands on the operator. In future research, these two approaches may be more suitable for handling the responses obtained from MEMS sensors.

On the other hand, the SSI-Cov method assumes that the response is driven by a stationary random excitation process. For non-stationary signals, the SSI-Cov method is not appropriate, particularly when analyzing time-evolving behavior with the aim of identifying health status related to the rapid evolution of dynamic parameters. In these cases, time–frequency analysis techniques, such as the Short-Time Impulse Response Function, Curvature Evolution Method, Band Variable Filter, and Stockwell Transform, prove to be more effective.

Additionally, the modal parameter identification results from this study will help researchers monitor the dynamic characteristics of substation frames throughout their life cycle. This will also better support the calibration of numerical models and the wind-resistant design of structures. These areas of research are valuable and merit further exploration in the future.