aResearch Institute of Urbanization and Urban Safety, University of Science and Technology Beijing, Beijing 100083, China
bShenzhen Key Laboratory of Urban Disasters Digital Twin, Shenzhen 518023, China
cKey Laboratory of Civil Engineering Safety and Durability of Ministry of Education of the People's Republic of China, Department of Civil Engineering, Tsinghua University, Beijing 100084, China
dChina State Construction Engineering Corporation Ltd., Beijing 100029, China
Vision-based digital shadowing is a highly efficient way to monitor the health of buildings in use. However, previous studies on digital shadowing have been limited to laboratory experiments. This paper proposes a novel computer-vision-based digital shadow workflow and presents its successful application in a real engineering case. In this case, a 345.8-m supertall building experienced unexpected shaking under normal meteorological conditions. This study established a digital shadow of the building using three-dimensional displacement measurements based on super-resolution monocular vision, revealing the hidden structural dynamics and inherent mechanical reasons for the abnormal shaking. The proposed digital shadowing workflow is a feasible roadmap for developing vision-based digital shadows of real-world structures using low-cost cameras. The abnormal vibration event in the supertall building considered in this study is the first of its type worldwide. The results of this study offer practical strategies and invaluable insights into the prevention and mitigation of this type of global risk, thereby contributing to the lifespan extension of buildings in use worldwide. Furthermore, with the increasing number of general sensing devices, such as surveillance cameras in cities, the proposed method may unleash the immense potential of general sensing devices in achieving the leap from structural health monitoring to city health monitoring.
Donglian Gu, Qingrui Yue, Li Li, Chujin Sun, Xinzheng Lu.
Vision-Based Digital Shadowing to Reveal Hidden Structural Dynamics of a Real Supertall Building.
Engineering, 2024, 43(12): 153-165 DOI:10.1016/j.eng.2024.10.002
Most countries in the world are urbanized. In 2020, global urbanization averaged 56.2% [1], and the urbanization rates of 12 countries (e.g., the United States, Japan, and Australia) were over 80%.
High urbanization rates have made the maintenance of existing buildings increasingly important. Despite the implementation of necessary design methodologies, building structures inevitably deteriorate over time. This deterioration can stem from a multitude of causes, including the adverse effects of environmental factors and aging of construction materials. In addition, structural deterioration can result from infrequent extreme events, such as earthquakes, hurricanes, and floods. Therefore, structural health is affected by operational and environmental factors over a building’s lifetime, and a building’s service life may end before its designed lifespan is reached [2].
Finite element (FE) methods are conventionally employed to study the static or dynamic behaviors of building structures during daily use or disasters [3], [4], [5], [6]. However, design-document-based FE models often fail to consider the effects of environmental changes, aging, repair, and other factors that affect structures during their service lives accurately. Consequently, it is difficult for a design-document-based FE model to predict a building’s structural behavior over its service life accurately [7], [8].
Digital twin (DT) technology [9] has recently gathered pace in engineering applications as it allows for the convergence of a real structure and its digital counterpart throughout its entire life cycle. A DT is a digital replica of a living or non-living physical entity, characterized by cyber-physical interaction, which is typically composed of four parts: ① modeling or simulation of a physical entity as a virtual entity; ② data collection and fusion from the physical entity; ③ interaction and collaboration between the physical and virtual entities; and ④ service provided by the virtual entity [10]. As a digital counterpart to physical systems, DTs need to be re-synchronized with those systems at sufficiently high resolution, but often also in near-real time. However, FE simulations of structures typically take hours, which is often not fast enough for in-process twinning because building components are modeled using hundreds to millions of discrete elements, for which certain physical properties are calculated in relation to their neighbors [11]. To address this challenge, the digital shadow (DS) concept has been widely used as an approximation of DT [11]. The most significant difference between a DT and a DS is that a DT integrates the virtual and physical realms by creating a real-time bidirectional connection between the physical entity and its digital counterpart, whereas a DS is typically an evolving digital representation that mirrors the current state and behavior of a physical entity in a delayed manner rather than in a real-time manner. Nevertheless, in the field of civil engineering, a DS model collects data from a structure through sensors and represents the entity with a sufficient level of detail in terms of both geometric and mechanical properties. Hence, through DS technology, engineers can establish an FE model that is consistent with the structural dynamics of a real building in digital space. For example, Zheng et al. [12] established a DS model of a seven-story building and used the model to perform a collapse simulation. Marienkov et al. [13] constructed a DS for a 24-story building and modeled the building response to seismic impacts. Compared to design-document-based FE models, DS-based FE models enable more accurate predictions of the structural behavior of buildings in service [14], [15].
The core objective of a DS is to achieve convergence of a real structure and its digital counterpart. This requires that the apparent geometries and inherent mechanical properties of physical entities be truly reflected by virtual entities. This usually depends on the accurate identification of the mechanical features of physical entities in their current service stages.
The conventional method for monitoring structural dynamics involves deployment of physical sensors (e.g., linear variable differential transformers (LVDTs) and laser displacement sensors) and structural health monitoring (SHM) systems [16], [17], [18]. However, physical sensors have limitations, such as their high cost, limited number of monitoring points, and high probability of failure during service. Recently, computer-vision-based SHM systems have gained attention [19], [20]. For example, Ye et al. [19] conducted vision-based displacement measurements of a scale-model arch bridge and validated the measurements using LVDTs. Park et al. [21] enhanced the quality of dynamic displacement measurements using data fusion of vision-based displacement measurements with acceleration. Vision-based monitoring systems offer at least three advantages over physical sensors [22]: ① ease of installation: a vision-based monitoring system can be placed far from a structure without considering its accessibility; ② full-field measurement: a vision-based monitoring system can use a camera to measure multiple points and obtain full-field information about the structure; and ③ low cost: a vision-based monitoring system requires neither complex sensor arrays nor supporting facilities. Provided that environmental conditions are good, vision-based monitoring systems can provide the same or even higher accuracy than physical sensors.
A large number of surveillance camera systems have been deployed in cities throughout worldwide. They constantly record extensive video data of buildings without additional installations, exhibiting the potential to compose a city-scale SHM system and serve DS-based health monitoring of existing building structures. However, vision-based DS and health monitoring of buildings are mainly limited to laboratory experiments. Feng and Feng [23] utilized modal parameters identified from a vision sensor to update the interstory stiffness of a laboratory frame structure. Dworakowski et al. [24] obtained the deflection curves of small-scale laboratory beams by means of digital image correlation. Yoon et al. [25] implemented a Kanade-Lucas-Tomasi (KLT) tracker to identify modal shapes for a laboratory-scale six-story building. Yang et al. [26] demonstrated the potential for modal identification using video measurements at low frame rates based on a laboratory three-story building structure. In contrast, few studies have reported the application of computer-vision-based SHM technology in real building structures owing to various environmental and hardware limitations. In real engineering projects, in-plane and out-of-plane displacements of structures occur simultaneously relative to the observation plane. However, the camera position is relatively fixed and generally fails to form an appropriate angular relationship with the measured structural displacement [27]. In addition, in many cases, the cameras surrounding a target building cannot form a suitable multi-view camera system to measure three-dimensional (3D) displacements because of their limited quantity or uncoordinated positions [27]. Moreover, the cameras used in real projects are sometimes outdated devices with low resolution, which significantly affects their measurement accuracy [28].
With the rapid advancements in deep learning, super-resolution (SR) [29] and pose estimation [30] techniques have been developed in recent years. By applying the SR technique, high-resolution (HR) images can be obtained from low-resolution (LR) images [31], [32]. Through the application of deep-learning-based pose estimation, the 6D poses of target objects can be outlined from monocular visual images, thereby transforming the recognized pixel displacements into 3D displacements [33], [34]. Therefore, the combination of deep-learning-based SR and pose estimation techniques enables the measurement of 3D structural displacement using only LR monocular visual images or videos, thereby providing a feasible roadmap for the implementation of vision-based DS in real-world structures based on low-cost camera equipment.
To this end, this paper proposes a low-cost vision-based DS workflow and introduces its successful application to a real-world engineering case. In this case, a 345.8 m supertall building experienced unexpected shaking under normal meteorological conditions, resulting in the emergency evacuation of personnel and suspension of service. This event had unexpected social and economic effects. This study establishes the DS of a building using 3D displacement measurements based on SR monocular vision. The DS-based simulation uncovered hidden structural dynamics and inherent mechanical reasons for abnormal shaking.
The main contributions of this study are the realization of a vision-based DS model and mechanical simulations using LR surveillance footage. The proposed workflow provides a feasible roadmap for implementing vision-based DS in real-world structures using low-cost camera equipment. Furthermore, the method was successfully implemented to investigate the causes of anomalous vibrations in a famous supertall building. The abnormal vibration event in a supertall building described in this study is the first of its kind internationally; however, such risks exist worldwide. Supertall buildings are ubiquitous globally, and their rooftop ancillary facilities are susceptible to deterioration and consequent anomalous vibrations over long periods of service. Subtle vibrations in ancillary facilities can trigger anomalous dynamic responses in supertall buildings, thereby affecting their functionality. The results of this study offer practical strategies and invaluable insights into the prevention and mitigation of this type of risk in buildings, thereby contributing to the lifespan extension of in-use buildings worldwide. Additionally, with the increasing number of general sensing devices, such as surveillance cameras in cities, the proposed method may unleash the immense potential of general sensing devices in achieving a leap from SHM to city health monitoring (CHM).
The remainder of this paper is organized as follows. Section 2 introduces the basic information on the study object. Section 3 describes the methods used. Section 4 presents the DS-based simulation results. Discussion and conclusions are presented in 5 Discussions, 6 Conclusions, respectively.
2. Basic information of study object
In May 2021, a super high-rise building in China experienced notable vibrations, causing the emergency evacuation of personnel. Consequently, the building was out of service for more than 100 days until the cause of the shaking was determined. This building vibration event is the first of its kind to occur internationally. There is no prior global experience regarding the causes of building swaying. The 72-story building (Fig. 1(a)) was built in 2000 and has a site area of 9653 m2 and a floor area of 169 834 m2. The building consists of a main structure and a steel frame structure constructed on the roof (Fig. 1(a)). According to the design document, the height of the main structure is 291.6 m, and the height of the building, including the steel frame reaches 345.8 m.
Maximum horizontal acceleration of the main structure when the building shakes exceeds 35 mm·s−2. During the shaking of the main structure, the camera that was originally used for security purposes recorded that the two masts of the top-roof steel frame shook violently (Fig. 1(b); the north mast is referred to as Mast N, while the south mast is named Mast S hereinafter). Owing to the poor hardware configuration of the security camera, the resolution of the raw monitoring video was low, as shown in Fig. 1(b).
To determine the cause of the building vibrations, the event investigation team headed by the second author performed on-site tests, interviews with relevant people, and basic numerical computations. The event investigation team excluded several potential causes, including ① vibration of the surrounding metro; ② vibration of elevators, computer station clusters, air conditioners, and other equipment inside the building; and ③ vibration of surrounding construction sites. After a careful and comprehensive investigation, the event investigation team focused on the causes of building shaking under wind loads. This study answers this question using the monitoring video shown in Fig. 1(b).
3. Methods
3.1. Vision-based DS workflow
Considering that the cameras surrounding a real building are possibly LR monocular devices, this study employs a deep-learning SR technique to generate HR video data and proposes a monocular vision-based 3D displacement measurement method to identify the vibration characteristics of the target building. Fig. 2 presents the conceptual architecture of the proposed vision-based DS workflow. Specifically, the design-document-based FE model can be easily constructed for the physical entity (i.e., the target building), which is the foundation digital model for performing the DS workflow. Meanwhile, the LR surveillance footage is constantly recorded by a monocular camera surrounding the target building, which can be easily realized at a low cost. Subsequently, the corresponding HR monitoring data were synthesized based on the LR surveillance footage using the deep-learning-based SR technique. Then, the 3D displacement of the target building was recognized using the proposed deep-learning-driven measurement method based on the generated HR monocular vision data. Finally, by integrating the design-document-based FE model with the identified displacement data, a DS model representing the up-to-date state of the physical entity was established after implementing the model update process for the original FE model. Consequently, a DS-based FE simulation can be performed to uncover structural dynamics and guide risk management. Details of the underlying methodologies, that is, deep-learning-based SR, monocular-vision-based 3D displacement measurement, and FE model updating, are introduced in 3.2 SR based on generative adversarial network, 3.3 Monocular vision-based 3D displacement measurement, 3.4 FE model updating.
Currently, owing to the difficulty in achieving near-real-time FE model updates and simulations, the method proposed in this study cannot be attributed to DT. Hence, this study objectively refers to the proposed workflow as a DS process rather than a DT process. Nonetheless, with the advancement of FE technology, especially surrogate modeling methods, the process shown in Fig. 2 may be completed in near real time in the foreseeable future, thereby achieving vision-based DT.
3.2. SR based on generative adversarial network
3.2.1. SR neural network
In this study, the SR neural network SRGAN [31] was used to realize the SR of LR-monitoring video sequences. The SRGAN, designed based on the concept of a generative adversarial network (GAN) [35], was the leading model among the SR neural networks during the investigation of building shaking events. Therefore, this approach was adopted in this study.
Similar to the classical GAN model, the SRGAN consists of a generator network and a discriminator network [31]. The generator network was built on residual blocks with skip connections, where each residual block comprised two convolutional layers with batch normalization and the activation function of a parametric ReLU (ReLU means rectified linear unit). A total of 16 residual blocks were used in this study. Image resolution upscaling in the SRGAN was achieved through subpixel convolutional layers, with each layer upsampled by a factor of two. For the 8× SR employed in this study, three sets of subpixel convolutional layers were utilized. The discriminator network of the SRGAN consists of eight convolutional layers using Leaky ReLU as the activation function. The extracted feature maps were processed through two fully connected layers and a sigmoid activation function to determine whether the generated image was a natural HR image or a super-resolved image. For the detailed network architecture and parameters of the SRGAN, please refer to Ledig et al. [31].
3.2.2. Neural network training
In general, an SRGAN can be trained using public SR datasets (e.g., the BSD100 dataset [36] generated by the University of California, Berkeley). However, the SR neural network used in this study does not require a generalization ability. This implies that only an SR operation on a single target object of the mast in the aforementioned video sequences is required. Accordingly, in this study, the SRGAN was trained using image pairs comprising paired HR and LR images of the target mast. Although the network trained in this manner lost its generalization ability, it was endowed with superior accuracy in the specific task of SR for the mast in the monitoring video.
Specifically, the method for constructing the training dataset was as follows:
(1) An HR image of the mast was captured using a high-definition camera.
(2) The first frame of the LR video was extracted. The extracted LR images were identified as a pair of HR images.
(3) Through image registration, the HR image captured by the high-definition camera was transformed into a viewpoint similar to that of the LR image. The region of interest (ROI) for the SR operations in the video sequences was determined. Consequently, both HR and LR images were cropped based on the ROI to form paired data.
By applying random translations and rotations within a certain pixel range to the extracted ROI, the motion of the mast within the ROI can be simulated, thereby generating an arbitrary number of LR-HR paired datasets.
Using the aforementioned methods, this study obtained a training set comprising 600 pairs of LR-HR images. Network training was conducted using the Adam optimizer [37] with a learning rate of 0.0001. The batch size was set to 16. The training process was initialized for 100 epochs and completed after 200 epochs. The training was performed on a computer equipped with a Xeon E5-2682 @2.50 GHz CPU (Intel Corporation, USA) and a GeForce RTX 3090 GPU (NVIDIA Corporation, USA) with 24 GB of video random-access memory (VRAM).
Once the training is completed, subsequent frames of the monitoring video can be fed into the model to obtain a super-resolved ROI image of the mast. Examples of SR frames are shown in Fig. 3(a). It is evident that the texture details in the monitoring video are significantly improved. In addition, the KLT optical flow tracking method [38], [39] was applied to measure the displacement in dynamic sequences (Section 3.3.3). When applying KLT optical flow tracking, the more trackable and stable the feature points on the target object in dynamic sequences, the more accurate the displacement measurement. Fig. 3(b) presents the feature point status of the target object in both the raw and SR videos. Notably, compared to the raw video, the SR video indicated more trackable and stable feature points on the mast. The influence of the SR on the displacement measurement accuracy is discussed in Section 5.1.
3.3. Monocular vision-based 3D displacement measurement
3.3.1. Pose-estimation neural network
The 3D displacement measurement relies on the pose matrix of the target object (Section 3.3.3). In this study, the pose matrix was captured using a deep-learning-based pose estimation method. Deep-learning-based pose estimation methods can be divided into two categories according to their generalization ability: ① instance-level methods trained on specific target objects [33]; and ② category-level methods with the ability to recognize similar objects of the same class [40]. Because this study only required pose estimation for the mast as the target object, an instance-level method was adopted.
In this study, the dense pose object detector (DPOD) model proposed by Zakharov et al. [33] was employed as the deep learning-based pose estimation model. The main reasons for choosing the DPOD are as follows:
(1) DPOD is an instance-level pose estimation method based on monocular red-green-blue (RGB) images that do not require depth information.
(2) DPOD demonstrated good performance on commonly used datasets in the field of deep-learning-based pose estimation, such as Linemod and its occluded version Linemod-Occluded [41], [42].
(3) As a two-stage method, the DPOD provides explicit and intuitive geometric information in the first stage. This establishes the relationship between the 2D and 3D coordinates, which is crucial for subsequent 3D displacement measurements.
The DPOD network uses a single RGB image as input. In the first stage, it outputs an object mask and a 2D-3D correspondence map. In the second stage, the pose of the object is estimated. The 2D-3D correspondence map establishes a corresponding relationship between 2D pixels and 3D model vertices using texture colors. In this study, UVW mapping was used as the output of the first stage of DPOD. The range of values for each channel in the UVW mapping was [0,255], as displayed in this study as RGB colors in the images.
The first stage of the DPOD adopts a classic encoder-decoder architecture. The encoder utilizes a pretrained ResNet18 model [43]. The decoder consists of four branches corresponding to the three channels of UVW mapping and the object mask. In the second stage, DPOD solves the perspective-n-point (known widely as PnP) problem to obtain the object pose. For more details on the DPOD network architecture, please refer to Zakharov et al. [33].
3.3.2. Neural network training
As an instance-level pose estimation method, the training dataset of the DPOD should include RGB images of the target object (i.e., the steel frame) and the corresponding UVW mapping. In this study, virtual rendering was used to construct the training dataset. The training dataset was generated by combining multi-view-rendered images of the mast with random backgrounds. The purpose of using random background images to train a deep-learning model is to enhance its ability to recognize a target object in diverse real-world scene images. By including a variety of backgrounds, the model can learn to extract relevant features from the mast while ignoring background variations. The process of generating the training dataset through virtual rendering involves the following steps.
(1) A 3D model of the mast was obtained using oblique photography, as shown in Fig. 4(a).
(2) The open-source 3D graphics software Blender (Blender Foundation, the Netherlands) [44] was used for virtual rendering. During the rendering process, the intrinsic parameters of the virtual camera were set to match those of the surveillance camera. The random range of the camera poses should cover the poses of the surveillance camera. Because the exact relative position between the surveillance camera and mast could not be determined, random variations were introduced to the virtual camera position coordinates. The horizontal and vertical coordinates of the virtual camera were designed to fluctuate within ±1 and ±0.2 m, respectively, which could compensate for camera position errors. As for the rotation degree of freedom in the camera extrinsic parameters, the ranges of the three Euler angles were manually adjusted to cover a random range within ±5°. This adjustment ensured that the rendered data domain was aligned with the actual surveillance images. Additionally, a slight radial distortion was added using Blender to match the real-world images in the virtual rendering process. Horizontal image offsets within ±5% were also set to introduce further randomness. The lighting in the virtual rendering utilized the “SUN” mode provided by Blender, with the random range of intensity set from 2 to 10 and the parallel lighting set to originate from a random direction in the upper hemisphere of the world coordinate system. During the virtual rendering of the steel frame images, the corresponding UVW mapping was simultaneously obtained using the same camera pose parameters. Random values were assigned to the parameters, resulting in a set of 1000 rendered images. Examples of the virtual-rendering results are shown in Fig. 4(b).
(3) In the monitored video sequences, the background of the steel frame is cloudy. Therefore, similar images were used as random backgrounds in the training dataset. To this end, the SWINySEG dataset [45], which contains 6768 cloudy sky images covering both day and night, was chosen. A virtual rendering training dataset was established by combining the rendered mast images with random backgrounds from the SWINySEG dataset. Examples of the generated datasets are shown in Fig. 5. The resolution of the images in the training dataset was set to 768 × 432 pixels.
The training process utilized the Adam optimizer [37] with a learning rate of 3 × 10−4 and a weight decay rate of 4 × 10−5. The batch size was set to 3, and the model was trained for 100 epochs. Each epoch comprised 334 batches. The training was conducted on a computer equipped with an Intel Xeon E5-2682 @2.50 GHz CPU and an NVIDIA GeForce RTX 3090 GPU with 24 GB of VRAM. After the training was completed, the first frame of the monitoring sequence was fed into the model to obtain the pose of the steel frame. The pose result constituted the input for the subsequent 3D displacement measurements.
3.3.3. 3D displacement measurement
This study selected the most prominent 10 s segment in the monitoring sequences for analysis. The sequences featured a frame rate of 25 frames of per second (FPS), resulting in a total of 250 frames. This study utilizes the pose estimation results and keypoint matching (KPM) between the initial and final states to calculate the 3D displacement of the top of the mast.
Considering that the axial deformation of the two masts can be neglected, the top of each mast was assumed to undergo planar motion within its horizontal plane. The direction of the line connecting the tops of the two masts is defined as the x-direction of this horizontal plane, whereas the direction perpendicular to x within this horizontal plane is defined as the y-direction.
The pose matrix T derived from the DPOD network is defined as follows:
where R is the rotation matrix (rij (i = 1, 2 ,3; j = 1, 2, 3) is the element in the matrix), and t is the translation vector (tx, ty, and tz are the three elements in the vector). In any frame image, the homogeneous coordinates Pi = [ui, vi, 1]T of an arbitrary feature point in the pixel coordinate system can be transformed into homogeneous coordinates Qi = [Xi, Yi, Zi, 1]T in the world coordinate system according to the following equations:
where s is the scaling factor of the homogeneous coordinates; K denotes the camera intrinsic matrix, which includes the focal lengths fx and fy and the optical center positions cx and cy; K can be obtained through ex-factory parameters or camera calibration; and Zi is the vertical coordinate of the motion plane of the feature point, which can be calculated using the 2D–3D coordinate mapping provided by UVW mapping in conjunction with Pi.
Assuming that the homogeneous coordinates of a particular feature point in the world coordinate system are Qi and Qj in two different frames, the displacement of this feature point is given by the Euclidean norm of the vector [Xj − Xi, Yj − Yi, 0]T. Methods for feature point detection and matching have been well established in previous studies. In this study, feature-point detection and matching were implemented based on the KLT optical flow tracking method.
The displacement measurement results at the tops of the two masts based on the aforementioned method are shown in Fig. 6(a). The in-plane and out-of-plane amplitudes of Mast N were approximately 80.3 and 17.5 mm, respectively. For Mast S, the in-plane and out-of-plane amplitudes were approximately 122.9 and 13.2 mm, respectively. Mast S exhibits more intense in-plane vibrations than Mast N, whereas their out-of-plane vibrations are similar. Fig. 6(b) shows the corresponding power spectral density (PSD) of the displacement, highlighting a dominant frequency of 2.12 Hz.
Furthermore, based on the identified mast displacements, the first, second, third, and fourth orders of the natural vibration modes of the mast were obtained using the stochastic subspace identification method [46], with corresponding vibration frequencies of 1.60, 1.79, 1.96, and 2.12 Hz (Fig. 6(c)). The first and second orders of the modes were the swings of the two masts outside the main plane of the steel frame (i.e., the main plane was defined as the plane formed by the straight lines of both masts). The third- and fourth-order modes exhibited the same and opposite directional swings of the two masts in the main plane, respectively (Fig. 6(c)). The frequency and displacement patterns of the fourth mode were consistent with the observations during the mast vibration, indicating that the mast in the monitoring video sequences primarily underwent vortex-induced vibrations in the fourth mode. The aforementioned mode data were used to update the FE model to create a DS for the steel frame (Section 3.4.2).
3.4. FE model updating
3.4.1. Design-document-based FE model of the steel frame
The general-purpose FE software package MSC.Marc (MSC Software Company, USA) is widely used in the FE modeling and analysis of building structures [3], [5], [8], [14], [15], [47]. In this study, an FE model was established using the MSC.Marc software based on the design document of the steel frame. The steel tubes of the frame were modeled using thin-walled beam sections with fixed constraints applied at the bottom of the model.
Table 1 presents a comparison of the modal analysis results obtained from the design document-based FE model and the vision-based identification results. The updated FE model results are also listed in Table 1 and discussed in Section 3.4.2. The fourth modal frequency obtained from the design-document-based FE model is 2.40 Hz, which deviates from the actual value of 2.12 Hz by 13.2%. The average relative error of the first four modal frequencies is 17.6%. This suggests that the stiffness of the steel frame may have experienced a certain degree of degradation since its construction, leading to a decrease in natural frequencies. In conclusion, the design-document-based FE model failed to accurately reflect the dynamic characteristics of a steel frame. This is not the DS of a real steel frame and requires updating based on the monitoring video-based identification results.
3.4.2. FE model updating of the steel frame
The design-document-based FE model was updated using the following steps:
(1) Determination of the objective function. Following Lin et al. [7], this study adopted a least-squares-based objective function and set the limit of the objective function to 10−4:where OBJ(X) is the objective function, X represents a vector comprising the updating parameters, fi(X) is the frequency of the ith vibration mode of the FE model, and fi,SSI denotes the corresponding observed value for that mode. The total number of vibration modes considered, denoted n, was set to four.
The widely used modal assurance criterion (MAC) was used as a discriminant indicator to determine the correspondence between the simulated mode shapes obtained from the eigenvalue analysis of the FE model and the observed mode shapes obtained from video-based recognition. The MAC calculation is based on the mode shapes of the FE model, , and the observed mode shapes, . This provides a measure of confidence in determining the similarity between two sets of mode shapes.
Following Lin et al. [7], the acceptance criterion for MAC was set to 0.85 in this study. This threshold value served as a reference for evaluating mode shape similarity.
(2) Determination of update parameters. The updating parameter selected in this study was the elastic modulus of the mast steel tube. Theoretically, parameters such as mass distribution and boundary conditions are key factors that affect the mast vibration pattern. The rationale for excluding these parameters from the update process stems from the field investigation findings of expert engineers, which indicated that the mass and boundary conditions of the steel frame exhibited negligible deviation from their initial construction state. Moreover, apart from the two masts, the remaining part of the steel frame was a robust truss structure that was barely displaced under daily wind loads. Field investigations showed no signs of degradation in the truss sections. Therefore, the elastic moduli of other parts of the steel frame were not considered in the model-updating process.
Because it was impossible to determine which section of the mast experienced stiffness degradation, the two masts in the FE model were discretized into 16 segments along the vertical direction. During the model updating process, the optimal values of the parameters for each discrete segment were determined.
(3) Determination of optimization algorithm. An optimization algorithm was used to minimize the objective function. This study employed a genetic algorithm (GA) [48] as the optimization algorithm to update the FE model. The GA is a heuristic algorithm that reduces the computational time required for model updating through parallel computations. Therefore, this approach was adopted in this study. The initial elastic modulus of the mast steel tube is 206 GPa. Table 2 presents the updated elastic moduli of each segment of the two masts.
(4) Verification of updated FE model. As shown in Table 1, the natural frequencies of the updated model agree well with the identification results based on the monitoring video. The average relative errors of the first four natural frequencies were all less than 2%, indicating that the updated FE model can reflect the dynamic characteristics of the steel frame more accurately than the design-document-based FE model. Hence, the updated FE model represents the DS of the real steel frame. The subsequent simulations described in Section 4 were conducted based on the updated FE model.
4. Structural dynamic response results
This study obtained the wind loads acting on a steel frame during building shaking through a computational fluid dynamics (CFD) analysis. Subsequently, the DS of the building was constructed by combining the steel-frame-updated FE model and the main-structure FE model established on on-site survey data, which was used to simulate the building's dynamic behavior during shaking. The corresponding details are presented in 4.1 CFD simulations, 4.2 DS-based FE simulations of the entire building.
4.1. CFD simulations
CFD simulations have been widely employed to estimate the static or time-varying wind loads experienced by buildings and their auxiliary structures [49], [50], [51], [52]. In this study, the time-averaged wind environment upstream of the masts was obtained through a CFD simulation based on the Reynolds-averaged Navier-Stokes (RANS) approach for a building complex within approximately two square kilometers around a supertall building. Subsequently, a transient CFD simulation using the k-w SST (k and w represent turbulent kinetic energy and turbulent dissipation rate, respectively; SST means shear stress transport) turbulence model was conducted to compute the crosswind loads acting on both masts.
Specifically, oblique photography was employed to acquire a 3D digital model of a building complex within the aforementioned area. Based on this 3D model, a CFD model was established using Fluent software (ANSYS, Inc., USA) [53]. As shown in Fig. 7(a), the dimensions of the CFD computational domain, that is, 6500 m (length) × 5500 m (width) × 2250 m (height), were designed according to best practice guidelines [54], [55]. A tetrahedral cell was used to discretize the domains (Fig. 7(b)). The cell edge length on the building façades is approximately 0.5 m, whereas that on the steel frame is smaller than 0.1 m. The CFD simulation adopted the steady-state RANS equations and employed the k-w turbulence model to close the equations. For the inlet boundary, the mean wind-speed profile U(z) was generated based on monitoring data from nearby meteorological stations, which were given by U(z) = 1.50z0.3 m·s−1, here z is the height above ground. For the ground and building surfaces, a nonslip boundary condition and standard wall function were applied. A symmetric boundary condition was assigned to the lateral and top boundaries. A constant static pressure was applied at the outflow boundary.
Fig. 8 shows the simulated wind pressure results, which indicate that both the windward and leeward sides of the target building experienced relatively low wind pressures. Given these wind-pressure conditions, the building was unlikely to exhibit significant oscillations. Fig. 9 shows the simulated wind speed results at the height of the steel frame. A good agreement was observed between the average wind speed obtained from the CFD simulation and the wind speed monitoring data from a nearby anemometer, confirming the reliability of the CFD simulation results. Based on the CFD simulation, the wind speed at the height of the mast was identified as approximately 12 m·s−1, exceeding the critical flutter speed of 11.66 m·s−1 calculated based on the Strouhal number for the cylinder vortex-induced resonance. This further confirmed the occurrence of vortex-induced vibrations in the two masts of the steel frame under wind loads.
Based on the wind-speed profile in the windward direction at the height of the mast obtained from the RANS simulation, a transient CFD simulation was conducted for the mast. A total of 38 measurement sections were arranged along the axial direction of each mast with 12 points distributed along the circumferential direction in each circular section. The wind pressure obtained from CFD simulations was multiplied by the control area at each measurement point. Subsequently, vector summation was performed using the normal vector at the measurement point to obtain the crosswind aerodynamic force acting on the mast, as shown in Fig. 10. The mast experienced a stable periodic load with a frequency of approximately 2.10 Hz, which is close to the fourth natural frequency of the steel frame at 2.12 Hz. Moreover, the wind loads on the two masts exhibit a phase difference of 180°.
4.2. DS-based FE simulations of the entire building
Based on the as-built drawings and on-site survey data, an FE model of the main structure of the building was established using MSC.Marc software. This FE model was combined with the updated FE model of the steel frame, as described in Section 3.4.2, to obtain the DS model of the building (Fig. 11(a)). The FE model of the main structure adopted the method proposed by Lu and Guan [47] for frame-core tube super-tall buildings.
A comparison between the natural frequencies obtained from the DS model and field measurement results is shown in Fig. 11(b), demonstrating good agreement. It is noteworthy that the 7th and 11th modes were not identified using the DS model. The simulated 13th natural frequency of the building was 2.135 Hz, which is close to the frequency of the wind loads acting on the mast (2.12 Hz). The 13th mode corresponded to the 4th torsional mode. Applying the wind loads on the mast obtained from Section 4.1 to the overall FE model for time history analysis allows for the computation of the acceleration response of different stories in the structure.
Fig. 12 shows the acceleration results for the 30th and 50th stories. In addition, the acceleration results are provided for both the vicinity of the core tube and the side with the steel frame for each story. The acceleration amplitudes on the side of the steel frame for the 30th and 50th stories reach 53.3 and 55.5 mm·s−2, respectively. According to the evaluation criteria for indoor occupant comfort provided by AIJ-GEH-2004 [56], this level of acceleration exceeds approximately 1.7 times the acceleration (i.e., 32.0 mm·s−2) that would make 90% of indoor occupants perceive the building vibration.
Meanwhile, it is worth noting that, for the same story, the acceleration on the side with the steel frame is greater than that near the core tube. Post-event investigations of the building occupants also revealed that individuals located on the outer side of the story experienced more pronounced building vibrations than those near the core tube. This was because the steel frame was in an eccentric position relative to the main structure of the building, causing asymmetric vortex-induced vibrations of the steel frame mast to exert eccentric forces on the main structure. This eccentric force had a frequency very close to the resonant frequency of the building's 4th torsional mode, leading to the excitation of torsional resonance in the building. Consequently, the torsional effect of the building caused the acceleration to be greater on the outer side of the story than near the core tube.
The aforementioned DS-based simulation and analysis revealed the hidden structural dynamics behind the abnormal vibrations of buildings. The steel frame at the top of the building experienced stiffness degradation during prolonged service, resulting in vortex-induced vibration of the two masts under stable wind loads. Owing to the inconsistent degree of stiffness degradation between the two masts, their vibration displacement amplitudes were uneven. Consequently, the asymmetric vortex-induced vibrations of the two masts exerted a periodic force on the main structure of the building with a frequency close to its 4th torsional mode frequency. This force ultimately causes torsional resonance in the building, leading to significant shaking felt by the occupants inside the building, especially those located at the periphery of the stories.
Finally, the event investigation team decided to demolish the steel frame at the top of the building based on the abovementioned results. The DS method based on 3D displacement measurement with SR monocular vision introduced in this study pointed out the correct direction for the investigation, playing a significant role in the event investigation. To date, the buildings have not experienced any further abnormal vibrations.
5. Discussions
5.1. SR vs LR
Fig. 13 shows the mast displacement results obtained through the monocular vision-based 3D displacement measurement method using raw monitoring video sequences without SR processing. Without SR processing, an accumulation of errors occurred, resulting in a drift in the displacement time history of the two masts. A comparison between Figs. 6(a) and 13 highlights the capability of the SR technique to improve the accuracy of displacement measurements based on surveillance videos. Table 3 presents the story acceleration simulation results of the DS models derived from the LR- and SR-based displacement measurements, demonstrating that the story acceleration results derived from the LR-based DS model are significantly smaller than those obtained from the SR-based DS model. This indicates that the LR-based displacement measurement cannot accurately identify the structural dynamic features.
5.2. DS vs design-document-based simulation
Table 3 also lists a comparison between the SR-powered DS and design-document-based FE. It can be observed that the model based on design documents fails to accurately simulate the mechanical behavior of the building, significantly underestimating the floor acceleration amplitude. This is because the FE model of the steel frame based on the design data could not reproduce the asymmetric vortex-induced vibrations of the two masts, thus failing to accurately capture the dynamic response characteristics of the main structure of the building. This highlights the importance of DS technology for the performance assessment of existing building structures, especially those that have experienced long-term service.
5.3. Potential of general sensing devices in city health monitoring
The implementation of health monitoring of aging building structures is of significant importance in urban areas. Traditional SHM techniques rely on physical sensors such as displacement transducers and accelerometers. While some newly constructed buildings may have been equipped with dedicated sensor devices to monitor their safety status, there is a wide prevalence of buildings that have been in service for several decades in cities. These buildings were typically not equipped with specialized sensor devices from the beginning of their construction. Few cities can afford the investment cost of installing specialized SHM sensor devices in these buildings. Therefore, it may not be feasible to conduct SHM of existing buildings throughout the city using physical sensors.
With the rapid development of digitalization and information technologies, general sensing devices, such as fixed closed-circuit television cameras, are widely available in cities. These devices constantly collect large amounts of data from their built environments. In recent years, advancements in deep learning have made it possible to process and analyze big data efficiently. If the information about existing buildings encoded in these data can be fully decoded and analyzed, low-cost health monitoring of existing buildings at the city scale can be achieved. Drawing upon the concept of SHM, this study introduces the term “city health monitoring” (CHM) to describe this envisioned application. CHM extends beyond SHM and encompasses a broader scope of building and infrastructure monitoring. The present research makes initial attempts in this field and is expected to promote the development and achievement of CHM.
6. Conclusions
This study proposes a novel vision-based DS workflow and presents its successful application in a real engineering case. In this case, a supertall building with a height of 345.8 m experienced unexpected shaking under normal meteorological conditions, resulting in the emergency evacuation of personnel and suspension of service. This event had unexpected social and economic effects. This study employed a 3D displacement measurement technique based on SR monocular vision to identify the structural dynamic characteristics of a building, based on which the DS of the building was established through model updating. The DS-based simulation in the digital space uncovered the hidden structural dynamics and inherent mechanical reasons behind the building vibration phenomenon, thus guiding risk mitigation work for the physical entity.
This study demonstrates the necessity of applying DS technology to the performance assessment of existing building structures, especially those that have experienced long-term service. The technical roadmap demonstrated in this study provides a feasible solution for real-structure DS applications based on computer vision. The abnormal vibration event in a supertall building described in this study is the first of its type worldwide. The results of this study offer practical strategies and invaluable insights into the prevention and mitigation of this type of risk in buildings, thereby contributing to the lifespan extension of in-use buildings worldwide. The investigation process reported here provides a valuable reference for tracing similar future events. Furthermore, with the increasing number of general sensing devices, such as surveillance cameras in cities, the proposed method may unleash the immense potential of general sensing devices in achieving the leap from SHM to CHM.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (52238011, 52208456, and 52279145), the China National Postdoctoral Program for Innovative Talents (BX20220031), the Shenzhen Science and Technology Program (ZDSYS20210929115800001), and the Shenzhen Major Science and Technology Program (KJZD20230923114310021). The authors are grateful to Beijing PARATERA Tech Co., Ltd. for providing the computational hardware and software used in this study. Finally, the authors thank Prof. Jianguo Nie, Prof. Xin Nie, Prof. Muxuan Tao, Prof. Ran Ding, Hongjing Xue, and Jizhi Zhao for their help in developing the FE model.
Compliance with ethics guidelines
Donglian Gu, Qingrui Yue, Li Li, Chujin Sun, and Xinzheng Lu declare that they have no conflict of interest or financial conflicts to disclose.
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