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Surface Damage Detection and Localization for Bridge Visual Inspection Based on Deep Learning and 3D Reconstruction 基于深度学习和三维重建的桥梁目测表面损伤检测与定位
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-29 DOI: 10.1155/2024/9988793
Youhao Ni, Jianxiao Mao, Hao Wang, Zhuo Xi, Zhengyi Chen

In the process of infrastructure construction in recent decades, there exist millions of bridges in service that need safety inspection for performance assessment. Currently, computer vision and deep learning-based surface damage detection methods can achieve classification and localization of damages at the image level, but achieving precise localization in three-dimensional space is more challenging. To overcome aforementioned limitations, this study proposes a three-stage method of bridge surface damage detection and localization based on three-dimensional (3D) reconstruction. In stage 1, the UAV flight path planning of the bridge is carried out, and the 3D reconstruction model of the bridge is formed based on the structure from motion (SfM) algorithm. In stage 2, you-only-look-once version 7 (YOLOv7) network is adopted to detect multiple damages, and scale invariant feature transform (SIFT) detector is used to match the identical damage in image level. In stage 3, based on solution of epipolar geometric constraint, the matched damage was mapped to the 3D model, and the 3D damage localization is realized and visualized. The quality of the 3D model has been analyzed, and it is recommended that inspection distance is determined at 20 m. Moreover, the reconstruction model of bridges achieves centimeter-level positioning accuracy, and the positioning accuracy of damage reaches the meter level. The mapped model effectively showcases surface damages, providing bridge owners with intuitive insights.

在近几十年的基础设施建设过程中,有数百万座在役桥梁需要进行安全检测以评估性能。目前,基于计算机视觉和深度学习的表面损伤检测方法可以在图像层面实现损伤的分类和定位,但在三维空间实现精确定位更具挑战性。为克服上述局限性,本研究提出了一种基于三维(3D)重建的三阶段桥梁表面损伤检测和定位方法。在第一阶段,对桥梁进行无人机飞行路径规划,并基于运动结构(SfM)算法形成桥梁的三维重建模型。第 2 阶段,采用 YOLOv7 网络(you-only-look-once version 7,YOLOv7)检测多个损坏点,并使用尺度不变特征变换(SIFT)检测器在图像层面匹配相同的损坏点。在第三阶段,基于外极几何约束的求解,将匹配的损伤映射到三维模型中,实现三维损伤定位和可视化。分析了三维模型的质量,建议将检测距离确定为 20 米。此外,桥梁重建模型的定位精度达到了厘米级,损伤定位精度达到了米级。绘制的模型有效地展示了表面损伤,为桥梁业主提供了直观的见解。
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引用次数: 0
Experimental and Theoretical Investigations on an Asynchronized Parallel Double-Stage Viscous Fluid Damper 异步并联双级粘滞流体阻尼器的实验和理论研究
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-26 DOI: 10.1155/2024/6921518
Cantian Yang, Haoxiang Wang, Linlin Xie, Aiqun Li, Xinyu Wang

The parameters of most conventional passive dampers are constant, which may not sufficiently satisfy the different energy dissipation capacity demands of the structure under different load conditions. The development of passive dampers with variable performances has become an emerging and vital trend in energy dissipation technologies and smart structures. This study proposes a novel passive viscous fluid damper with variable performance under different deformation levels called an asynchronized parallel double-stage viscous fluid damper (APDVFD). It is expected to exhibit an asynchronized double-stage working mechanism based on a variable annular gap. In the first stage, only the primary piston provides the damping force. When the deformation reaches a preset value, the primary and second pistons work in parallel, providing a damping force concurrently. Circular orifices are adopted for the piston head to provide a sufficient damping force. The double-stage operating mechanism and fatigue performance of the APDVFD were validated and investigated through a full-scale experiment with 46 load cases. Based on these, a theoretical model capable of predicting the hysteretic behavior of the APDVFD was developed and validated against test data.

大多数传统无源阻尼器的参数都是恒定的,这可能无法充分满足结构在不同荷载条件下的不同消能能力需求。开发性能可变的被动阻尼器已成为消能技术和智能结构的一个新兴和重要趋势。本研究提出了一种在不同变形水平下性能可变的新型被动粘滞流体阻尼器,称为异步并联双级粘滞流体阻尼器(APDVFD)。它有望在可变环形间隙的基础上表现出异步双级工作机制。在第一阶段,只有主活塞提供阻尼力。当变形达到预设值时,第一和第二活塞并行工作,同时提供阻尼力。活塞头采用圆孔设计,以提供足够的阻尼力。APDVFD 的双级工作机制和疲劳性能通过 46 种负载情况下的全尺寸实验进行了验证和研究。在此基础上,建立了能够预测 APDVFD 滞后行为的理论模型,并根据测试数据进行了验证。
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引用次数: 0
Temperature-Dependent Modulus and Ultrasonic Velocity of Concrete 混凝土随温度变化的模量和超声波速度
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-25 DOI: 10.1155/2024/9051219
Ding Wang, Jing Tang

The temperature dependence of the internal structure and elastic properties of concrete is revealed by subjecting concrete to different heating conditions. The variation trend of wave velocity in the concrete medium with temperature is analyzed through ultrasonic properties. The decrease in cement matrix modulus and the increase in crack density in concrete are the main factors leading to a decrease in wave velocity. The changes in the composition of the concrete matrix after dehydration are obtained using a thermal decomposition model. Based on the effective medium model, the calculation results of the effective modulus at different temperatures are presented, with a focus on analyzing the influences of the temperature-dependent changes in the matrix elastic properties and the randomly distributed cracks on the effective modulus. The experimental tests and the presentation of the model results indicate a relatively satisfactory agreement, thereby verifying the reliability of the models. The results of this study can explain the basic propagation mechanism of waves in concrete and have promising applications in the ultrasonic testing of thermal damage to cement-based materials.

通过将混凝土置于不同的加热条件下,揭示了混凝土内部结构和弹性特性与温度的关系。通过超声波特性分析了混凝土介质中波速随温度的变化趋势。混凝土中水泥基体模量的降低和裂缝密度的增加是导致波速降低的主要因素。利用热分解模型得出了脱水后混凝土基体成分的变化。在有效介质模型的基础上,介绍了不同温度下有效模量的计算结果,重点分析了基体弹性特性随温度变化的影响以及随机分布的裂缝对有效模量的影响。实验测试和模型结果表明两者的一致性比较令人满意,从而验证了模型的可靠性。这项研究的结果可以解释波在混凝土中的基本传播机制,在水泥基材料热损伤超声波测试中具有广阔的应用前景。
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引用次数: 0
Robustness Evaluation of Negative Stiffness Damper for Cable Vibration Mitigation Based on Interval Model with Experimental Validation 基于区间模型和实验验证的用于电缆减振的负刚度阻尼器鲁棒性评估
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-24 DOI: 10.1155/2024/1258183
Xiang Shi, Xiaolin Wei, Jin-Yang Li, Heming Xing, Qinlin Cai

The negative stiffness damper (NSD) has emerged as a promising passive vibration control device for cable structures due to its simplicity and effectiveness. However, uncertainties stemming from both internal and external environmental factors can potentially compromise the NSD’s performance in real-world applications, posing risks to cable safety. In response, this paper conducts a robustness evaluation on an integrated cable-NSD system, taking into account various potential uncertainties. Specifically, the uncertain parameters are described by interval variables. Consequently, an interval model is constructed to delineate the boundaries of cable dynamic responses when subjected to these uncertainties. The model’s accuracy is validated against experimental results. Subsequent simulations involve assessing interval responses for both single- and multimode cable vibrations under varying uncertainties. Finally, the NSD’s robustness concerning cable vibration control is evaluated using the model, which incorporates the first-passage theory. This analysis delves into the relationships among confidence levels, performance measures, and the variation range of uncertainties. The results indicate that for single-mode vibration control, there is a 90% confidence level that the damping ratio reduction remains within 10%. As for multimode vibration control, a 90% confidence level is established that the amplification falls within 17%.

负刚度阻尼器(NSD)因其简单有效,已成为一种很有前途的电缆结构被动振动控制装置。然而,由内部和外部环境因素引起的不确定性可能会影响 NSD 在实际应用中的性能,从而给电缆安全带来风险。为此,本文考虑到各种潜在的不确定性,对集成电缆-NSD 系统进行了鲁棒性评估。具体来说,不确定参数由区间变量描述。因此,本文构建了一个区间模型,以划定电缆在受到这些不确定性影响时的动态响应边界。该模型的准确性根据实验结果进行了验证。随后的模拟包括评估不同不确定性下单模和多模电缆振动的区间响应。最后,使用包含第一通道理论的模型对 NSD 在电缆振动控制方面的稳健性进行评估。该分析深入探讨了置信度、性能指标和不确定性变化范围之间的关系。结果表明,对于单模振动控制,有 90% 的置信度可以确保阻尼比的减小保持在 10% 以内。至于多模式振动控制,90% 的置信度为放大率在 17% 以内。
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引用次数: 0
Analytical Solution and Energy Flow Analysis of a Vertical Vibration-Controlled System Using the Nonlinear Energy Sink 利用非线性能量汇对垂直振动控制系统进行分析求解和能量流分析
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-18 DOI: 10.1155/2024/5549289
Decheng Lu, Peng Chen, Dingsong Zhou

The nonlinear energy sink (NES) has drawn increasing research attention in recent years. In this study, we investigated a novel disc spring-based vertical NES device capable of counterbalancing payload gravity and providing a combination of linear and cubic restoring forces. The vertical NES device is used to mitigate vibration responses in vertically flexible structures caused by human or machinery-induced actions. To simplify the NES controlled system, a two-degree-of-freedom model was used to account for harmonic forces acting on the primary structure. Using the complexification-averaging (CX-A) method, we obtained the frequency-amplitude solution and subsequently derived the force transmissibility (Tf). Parametric comparisons between the NES and traditional tuned mass damper (TMD)-controlled systems were performed by comparing the Tf curves and numerically verifying the theoretical solutions. Results confirmed the accuracy of the theoretical force transmissibility solutions and affirmed the advantage of the NES system by overcoming the limited operating frequency bandwidth of the traditional TMD system. The inclusion of a linear stiffness term in an NES system has been shown to enhance the vibration control performance within the resonant frequency bandwidth. In addition, the time history energy analysis for the NES and TMD systems was conducted. The energy flow analysis elucidated the broad operating bandwidth of the NES system. This finding suggests that the vibration energy flow to the attachment in the NES system is irreversible, thereby preventing amplification of the response in the primary structure, even when the system is mistuned.

近年来,非线性能量汇(NES)引起了越来越多的研究关注。在本研究中,我们研究了一种基于碟形弹簧的新型垂直 NES 装置,该装置能够平衡有效载荷重力,并提供线性和立方恢复力组合。垂直 NES 装置可用于减轻垂直柔性结构中由人为或机械引起的振动响应。为了简化 NES 受控系统,使用了一个双自由度模型来考虑作用在主结构上的谐波力。我们使用复合平均(CX-A)方法获得了频率-振幅解,随后得出了力传递率(Tf)。通过比较 Tf 曲线和对理论解进行数值验证,我们对 NES 和传统的调谐质量阻尼器 (TMD) 控制系统进行了参数比较。结果证实了力传递理论解的准确性,并肯定了 NES 系统克服传统 TMD 系统有限工作频率带宽的优势。事实证明,在 NES 系统中加入线性刚度项可以提高共振频率带宽内的振动控制性能。此外,还对 NES 和 TMD 系统进行了时间历程能量分析。能量流分析阐明了 NES 系统宽广的工作带宽。这一发现表明,在 NES 系统中,流向附件的振动能量是不可逆的,因此即使在系统失谐的情况下,也能防止主结构的响应放大。
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引用次数: 0
Unsupervised Vision-Based Structural Anomaly Detection and Localization with Reverse Knowledge Distillation 基于视觉的无监督结构异常检测和定位与反向知识提炼
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-11 DOI: 10.1155/2024/8933148
Xiaoming Lei, Mengjin Sun, Rongxin Zhao, Huayong Wu, Zijie Zhou, You Dong, Limin Sun

Most of vision-based methods for structural damage detection rely on supervised learning, requiring a substantial number of labeled images for model training, which is labor-intensive and time-consuming. To address these challenges, this study introduces a vision-based structural anomaly detection and localization approach using unsupervised learning and reverse knowledge distillation. The proposed model incorporates a teacher model, a student model, and a trainable one-class bottleneck embedding module. The asymmetrical architecture of the teacher and student models forms an encoder-decoder structure for parameter transfer and feature extraction. The student network receives a specific embedding from the teacher network as input and target, facilitating the recovery of multiscale information from the teacher. Training images only contain the undamaged structures, and the teacher model, a pretrained model, instructs the student model to remember their undamaged features to detect and localize damages in unseen testing images. Through experiments, including a comparison among five candidate backbones for pretrained teacher models based on the residual network and testing across various structural damage types, the optimal model is identified, demonstrating good performance in both anomaly detection and localization. Furthermore, the model’s generalization performance is thoroughly validated, confirming its efficacy across diverse scenarios.

大多数基于视觉的结构损伤检测方法都依赖于监督学习,需要大量的标注图像进行模型训练,耗费大量人力和时间。为了应对这些挑战,本研究采用无监督学习和反向知识提炼的方法,介绍了一种基于视觉的结构异常检测和定位方法。所提出的模型包含一个教师模型、一个学生模型和一个可训练的一类瓶颈嵌入模块。教师模型和学生模型的非对称结构形成了一个用于参数传输和特征提取的编码器-解码器结构。学生网络接收教师网络的特定嵌入作为输入和目标,便于从教师网络中恢复多尺度信息。训练图像只包含未损坏的结构,教师模型作为一个预训练模型,指示学生模型记住未损坏的特征,以检测和定位未见测试图像中的损坏。通过实验,包括对基于残差网络的预训练教师模型的五个候选骨架进行比较,以及对各种结构损伤类型进行测试,最终确定了最佳模型,在异常检测和定位方面都表现出了良好的性能。此外,该模型的泛化性能也得到了全面验证,证实了其在不同场景下的有效性。
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引用次数: 0
Optimization of Pipeline Leakage Detection System in Utility Tunnel Based on Finite Element Method 基于有限元法的公用事业隧道管道泄漏检测系统优化
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-09 DOI: 10.1155/2024/9626974
Yongli Liu, Jiao Wang, Tiantian Xue, Henglin Xiao, Yanshuang Yang

In addressing the problems of delayed detection, inefficient identification, and coverage blind spots in optical fiber-based pipeline leakage detection within pipe galleries, this study proposes a leakage detection strategy utilizing distributed optical fiber temperature measurement technology. Finite element method is employed to analyze the temperature influence radius around the pipeline leakage hole and a model test is conducted as a validation. The results show that the temperature field image at the leakage site is elliptical, influenced by temperature differences between ambient and liquid. An increase in this temperature difference accelerates changes in the temperature field’s range. Adjustments to the optical fiber’s winding angle and pitch demonstrated that an optimal pitch is 1/24 of the pipeline’s length, with a 45° winding angle. This configuration maximizes the optical fiber’s distribution in detection while maintaining its cost-effectiveness. When the leakage site is constant, and only the winding mode is altered, it is observed that when the ambient temperature exceeds the liquid temperature in the pipeline, the temperature of the escaping liquid impacts the temperature-measuring fiber due to gravity, registering approximately 2°C higher than the temperature measured directly at the leakage site. The temperature anomaly from field diffusion is significantly less than that caused by the water flow from the leakage impacting the fiber due to gravity. Conversely, when the ambient temperature is lower than the pipeline’s liquid temperature, the opposite occurs. These research findings offer a novel approach for distributed detection in water supply and drainage pipeline leakage.

针对基于光纤的管廊内管道泄漏检测中存在的检测延迟、识别效率低和覆盖盲区等问题,本研究提出了一种利用分布式光纤测温技术的泄漏检测策略。采用有限元法分析了管道泄漏孔周围的温度影响半径,并进行了模型试验验证。结果表明,泄漏点的温度场图像是椭圆形的,受环境温度和液体温度差的影响。温差的增加会加速温度场范围的变化。对光纤缠绕角度和间距的调整表明,最佳间距为管道长度的 1/24,缠绕角度为 45°。这种配置既能最大限度地扩大光纤在检测中的分布范围,又能保持其成本效益。当泄漏点不变,仅改变缠绕模式时,可以观察到当环境温度超过管道中的液体温度时,逸出液体的温度由于重力作用会影响测温光纤,比直接在泄漏点测量的温度高出约 2°C。现场扩散造成的温度异常明显小于泄漏水流在重力作用下冲击测温光纤造成的温度异常。相反,当环境温度低于管道的液体温度时,则会出现相反的情况。这些研究成果为给排水管道泄漏的分布式检测提供了一种新方法。
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引用次数: 0
Effect of Bidirectional Ground Motion on the Response of Double Concave Friction Pendulum Systems 双向地面运动对双凹摩擦摆系统响应的影响
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-05 DOI: 10.1155/2024/1011161
Jiaxi Li, Ping Tan, Kui Yang, Haowen Zheng, Shinsuke Yamazaki, Shoichi Kishiki

Recent destructions of structures due to insufficient isolator deformation capacity have led to demands for greater seismic redundancy in seismic isolation design. For a friction pendulum system (FPS), the effect of bidirectional behavior of earthquakes on the maximum response and its effect on friction heating, temperature, and in turn on the maximum response can be significant. However, the extent of these effects under different FPS design parameters and different types of ground motions (GMs) is still not clear. In this study, an analytical model of double concave FPS considering the coupling effect of friction heating and bidirectional behavior was proposed and validated by bidirectional earthquake response orbits, which reflect the characteristics of both GMs and FPSs. Then, the effects of bidirectional GM and corresponding bidirectional temperature change on the response were investigated under different types of strong GMs. Finally, a performance-based design method with a bidirectional-effect-compensation mechanism was proposed. For double concave friction pendulum bearings with PTFE-related layers, it was found that the bidirectional behavior of earthquakes will amplify the maximum isolator displacement by an average of 110–210% (60 MPa) and the maximum superstructure acceleration by an average of 100–140% (60 MPa) under strong GMs (PGV-C1 > 0.2 m/s) and optimum design parameters. The amplification ratio is not only influenced by GM characteristics but also highly related to the design parameters and friction-heating effect of DCFPS.

最近由于隔震装置变形能力不足而造成的结构破坏,促使人们要求在隔震设计中增加抗震冗余。对于摩擦摆系统(FPS)来说,地震的双向行为对最大响应的影响及其对摩擦加热、温度的影响,进而对最大响应的影响可能是显著的。然而,在不同的 FPS 设计参数和不同类型的地面运动(GMs)下,这些影响的程度仍不明确。本研究提出了考虑摩擦加热和双向行为耦合效应的双凹面 FPS 分析模型,并通过双向地震响应轨道进行了验证。然后,研究了不同类型强 GM 下双向 GM 和相应双向温度变化对响应的影响。最后,提出了一种具有双向效应补偿机制的基于性能的设计方法。对于带有聚四氟乙烯相关层的双凹摩擦摆式支座,研究发现,在强 GM(PGV-C1 > 0.2 m/s)和最佳设计参数下,地震的双向行为将使最大隔震器位移平均放大 110-210% (60 MPa),最大上部结构加速度平均放大 100-140% (60 MPa)。放大率不仅受 GM 特性的影响,还与 DCFPS 的设计参数和摩擦热效应密切相关。
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引用次数: 0
A Novel Method for Full-Field Scale Factor Calculation under Off-Axis Measurements for Vision-Based Structural Multipoint Displacement Measurement and Health Monitoring 基于视觉的结构多点位移测量和健康监测离轴测量下的全场比例因子计算新方法
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-07-01 DOI: 10.1155/2024/8416971
Guohua Zhai, Zhisen Tan, Yabin Liang

For vision-based structural displacement measurement and health monitoring, the scale factor (SF) calculation plays a pivotal role in converting the pixel displacement into the actual one. On the other hand, for the current SF calculation methods, the object distance, between the to-be-measured points on the object plane and the optical center of the shooting instrument, has to be measured in advance due to the existence of the pitch and horizontal angle under off-axis measurement. Unfortunately, it is usually inefficient, difficult, and even impossible to obtain the object distances for all the to-be-measured points, especially for the full-field displacement monitoring on huge scale structures. In this paper, a novel SF calculation method was proposed to calculate the full-field scale factor of the host structure under off-axis measurement by combining with the similarity relation of the camera imaging model. With the help of this method, all the scale factors of the to-be-measured points can be calculated accurately and highly efficiently, as long as the object distance of any one point or the geometric dimensions of any feature object on the object surface is provided. In addition, to quantitatively assess the SF calculation accuracy of the method, a static vision-based measurement investigation was firstly conducted, and then, two experimental investigations about the multipoint and full-field structural displacement measurement on a cable-stayed bridge model and a simply supported beam model were conducted to validate the effectiveness and feasibility of the proposed method. Finally, all the results demonstrated that the proposed method exhibits an excellent performance on the SF calculation under off-axis measurement and provides a great potential to be utilized for the vision-based structural multipoint and full-field displacement measurement and health monitoring.

在基于视觉的结构位移测量和健康监测中,比例因子(SF)计算在将像素位移转换为实际位移方面起着关键作用。另一方面,由于离轴测量存在俯仰角和水平角,目前的 SF 计算方法必须提前测量物体平面上的待测点与拍摄仪器光学中心之间的物体距离。遗憾的是,要获得所有待测点的物距通常是低效、困难甚至不可能的,尤其是在对巨型结构进行全场位移监测时。本文提出了一种新颖的 SF 计算方法,结合相机成像模型的相似性关系,计算离轴测量下主结构的全场比例因子。在该方法的帮助下,只要提供任意一点的物距或物体表面任意特征物体的几何尺寸,就能准确高效地计算出所有待测点的比例因子。此外,为了定量评估该方法的SF计算精度,首先进行了基于视觉的静态测量研究,然后对斜拉桥模型和简支梁模型进行了多点和全场结构位移测量的实验研究,以验证所提方法的有效性和可行性。最后,所有结果表明,所提出的方法在离轴测量条件下的 SF 计算中表现优异,为基于视觉的结构多点全场位移测量和健康监测提供了巨大的应用潜力。
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引用次数: 0
Analytical Bayesian Copula-Based Uncertainty Quantification (A-BASIC-UQ) Using Data with Missing Values in Structural Health Monitoring 利用结构健康监测中的缺失值数据进行基于贝叶斯 Copula 的不确定性量化分析 (A-BASIC-UQ)
IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY Pub Date : 2024-06-30 DOI: 10.1155/2024/5410581
Ka-Veng Yuen, Zi-Tong Zhao, He-Qing Mu, Wei Shao

The presence of missing values is common in real-world datasets, so modeling and uncertainty quantification (UQ) of incomplete datasets have gained increasing attention in various research areas, including structural health monitoring (SHM). However, modeling and UQ utilizing incomplete datasets are nontrivial tasks. On the other hand, prediction based on a set of incomplete measured input variables is also an important task, but most existing methods, which are discriminative models, do not possess this capability. Aiming to tackle these two challenges, we propose the two-stage analytical Bayesian copula-based uncertainty quantification (A-BASIC-UQ) using incomplete SHM data. In the modeling stage, the copula-based multivariate joint probability density function (PDF) is modeled directly according to an incomplete dataset without imputation or disposal of any data points. For the univariate marginal PDF, using the measured (nonmissing) values of the corresponding random variable (RV), Bayesian model class selection is conducted to select the most suitable model class. For the Gaussian copula PDF, using the bivariate complete data points of entry-by-entry pairwise data, the optimal parameter vector is obtained from the estimation of the Pearson correlation coefficient. In the prediction stage, the analytical expressions of the predictive PDF, the predicted value and the credible region of the output variables are derived according to a set of incomplete measured input variables. The analytical expression of the predictive PDF is obtained based on the analytical operations on the auxiliary RVs and that of the predicted value and the credible region are obtained based on the analysis of multivariate Gaussian distribution. Therefore, the proposed method does not require numerical integration nor Monte Carlo simulation and does not suffer from computational burden even when there are many variables (say 4 or above). Examples using simulated data and real SHM data are presented to illustrate the capability of the proposed A-BASIC-UQ.

在现实世界的数据集中普遍存在缺失值,因此不完整数据集的建模和不确定性量化(UQ)在结构健康监测(SHM)等多个研究领域受到越来越多的关注。然而,利用不完整数据集建模和不确定性量化并非易事。另一方面,基于一组不完整的测量输入变量进行预测也是一项重要任务,但大多数现有的判别模型方法都不具备这种能力。为了解决这两个难题,我们提出了使用不完整 SHM 数据的两阶段贝叶斯共轭不确定性量化分析方法(A-BASIC-UQ)。在建模阶段,基于 copula 的多变量联合概率密度函数 (PDF) 直接根据不完整数据集建模,无需估算或处理任何数据点。对于单变量边际概率密度函数,利用相应随机变量(RV)的测量值(非缺失值)进行贝叶斯模型分类选择,以选出最合适的模型分类。对于高斯协方差 PDF,利用逐个入口配对数据的二维完整数据点,通过估计皮尔逊相关系数获得最佳参数向量。在预测阶段,根据一组不完整的测量输入变量,得出预测 PDF、预测值和输出变量可信区域的分析表达式。预测 PDF 的解析表达式基于对辅助 RV 的解析运算,预测值和可信区域的解析表达式基于对多元高斯分布的分析。因此,所提出的方法既不需要数值积分,也不需要蒙特卡罗模拟,即使变量较多(如 4 个或以上)也不会造成计算负担。本报告使用模拟数据和真实的 SHM 数据举例说明了所提出的 A-BASIC-UQ 的能力。
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Structural Control & Health Monitoring
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