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There are three main research conducted in this paper, including using deep learning methods with vision-based technologies on Structural Damage Detection (SDD), Structural Health Monitoring (SHM) and progressive collapse study. During the learning and improvement process, many goals of automation in SDD and SHM have been achieved, although there will be a large room for further improvement and development on these studies. In progressive collapse study, remote sensing technologies and data fusion are applied on a field experiment of a real building at the Central Campus of the Ohio State University. The major contributions of this paper are shown as follows:A few comprehensive experimental studies for automated SDD in extreme events using deep learning methods for processing 2D images. In the first study, a 152-layer Residual Network (ResNet) is utilized to identify multiple classes in eight SDD tasks, which include identification of scene levels, damage levels, material types, etc. The proposed ResNet achieved high accuracy for each task while the positions of the damage are not identifiable. In the second study, the existing ResNet and a segmentation network (U-Net) are combined into a new pipeline, cascaded networks, for categorizing and locating structural damage. The results show that the accuracy of damage detection is significantly improved compared to only using a segmentation network. In the third and fourth studies, end-to-end networks are developed and tested as a new solution to directly detect cracks and spalling in the image collections of recent large earthquakes. One of the proposed networks can achieve an accuracy above $67.6\%$ for all tested images at various scales and resolutions, and shows its robustness for these human-free detection tasks.Studies are conducted with a pipeline to automatically track and measure displacements and vibrations of structures or structural components in laboratory and field experiments. This novel framework that uses computer vision and deep learning methods to mimic human vision system for the dynamic performance assessment of in-service infrastructure with various camera placements. On one hand, the static deformations of cylinders and small-scale reinforced concrete beams in the laboratory tests are captured and measured by the proposed framework at first. Then two shaking table tests in the lab are utilized to assess the dynamic performance of the simulated structures. On the other hand, several bridges, including pedestrian, railway, and traffic bridges, are tested for their dynamic performance in field experiments with different camera placements: remote, structure-mounted, and drone-mounted cameras. To remove systematic motions of cameras and to capture the fundamental frequency of these tested structures, two techniques, displacement subtraction and frequency subtraction, are applied. To better understanding of practical applications, critical parameters for camera settings and data processing techniques, such as video frame-rates, window size and locations, and sampling rates on visual data are studied. It shows that not only the vibrations and the frequencies of the simulated structures (i.e., in lab tests) or the in-service structures (i.e., in filed experiments), but also the static deformation of structures or structural components, can be tracked and measured accurately by our proposed framework.The performance of a building in progressive collapse study is monitored and analyzed with the methods developed in previous studies. On one hand, we applied the proposed methods to detect structural damage on this reinforced concrete (RC) structure that was tested, including visual data from cell phones, inside and outside cameras, and drones. The experiments indicate that these solutions for automatic detection of structural damage using deep learning methods are feasible and promising. On the other hand, the proposed methods to measure the deformations and vibrations are utilized to process visual data from outside and inside cameras, and drones. Data from different sources are fused for capturing the performance of the structural elements under the scenarios of the sudden loss of the columns and slabs. The data fusion technique is useful to investigate the characteristics of this framed structure, especially when the traditional sensors such as strain gauges and Linear Variable Displacement Transducers (LVDTs) didn't work in the experiments. Since visual data acquisition and preparation, and techniques of data processing have been inclusively researched for real applications with deep learning, many experimental studies on SDD and SHM are carried out and promising results are obtained in this paper. In addition, the vibration-based technologies or traditional sensors are used as the reference. Our goal is to meet the needs for automatic detection of structural damage and accurate measurements for the performance of the structures or structural elements, thus, the efficiency and effectiveness of these frameworks are tested and analyzed. In summary, these research in this paper indicate that vision-based technologies with deep learning can be applied well on structural engineering domain, and facilitate structural engineers' job by providing reliable data and credential results. The methodologies developed in this paper can fill the gap of research and engineering applications in the future.

Abstract: With the increase in the number of deep learning networks, many excellent methods have been proposed for video segmentation tasks. However, most of the these methods are for learning pattern information. Not as much work has been done in the area of distribution information, which is also useful for video segmentation. Therefore, this work focuses on learning statistical distributions via neural networks for video segmentation tasks including background subtraction, vessel segmentation and crack detection. In this thesis, we discuss four proposed methods in order to identify an effective way to learn statistical distributions. First, we propose a dynamic deep pixel distribution learning (D-DPDL) method for background subtraction. In D-DPDL, a random permutation of temporal pixels feature is used to force the network to learn the statistical distributions. Compared with previous background subtraction methods based on deep learning networks, the D-DPDL model only requires limited ground-truth frames for training, and it is effective even when training videos and testing videos are captured from different scenes. Then, we improve the D-DPDL method and apply it to vessel segmentation and crack detection, and we found that a wide rather than deep network works better. Finally, we proposed an arithmetic distribution neural network (ADNNet), which is based on arithmetic distribution layers, for learning distributions. The arithmetic distribution layers is the first work to propose network layers based on arithmetic distribution operations, which perform even better than convolutional layers in distribution classification.

For health and safety monitoring in civil constructions such as bridges, roads and pavements, segmenting the regions of interest is the fundamental requirement for image analysis at high-level semantic. One of the major structural problems in concrete and asphalt surfaces are cracks, which start with harming the visual aspect of the construction and further lead to failure of the construction. This study makes four contributions to extract the image foreground from the background in order to address the crack detection task on the asphalt and concrete surfaces. Specifically, we model cracks as foreground objects and concrete or asphalt surfaces as textured background. The first contribution of this research is a hybrid image processing method for crack detection. In this method, the cracks are modelled as linear structures on the background of textured concrete or asphalt surfaces, which can be extracted by combining structure extraction with global pattern distribution. There are two phases in this model towards creating the final structure-texture map. The first phase is extracting strong structures or edges using relative total variation measures, which produces a structure feature map by preserving the edges and suppressing the background noises. The second phase calculates the spatial distribution of textures across the image. A bag-of-words model is used in this phase to quantise the texture pattern, which in crack detection application is the widely distributed road texture background. The local structure map and the global distribution map extract the crack structure and the textured background, respectively. The final crack is extracted by fusing these two maps and applying binarisation as the post-processing step. This model achieved a better result compared with the local structure extraction and the saliency method. As the second contribution, a large-scale dataset of asphalt and concrete crack images is prepared, including images with their corresponding high-resolution pixel-wise labels. To the best of our knowledge, until the completion of this thesis, there has not been any crack image dataset with pixel-wise ground truth labels available. The original crack image set includes 2532 images of cracks on brick and asphalt surfaces. This image set is split into training, validation and testing sets with the ratio of 50/25/25. Two augmentation techniques of rotation and ipping are applied to only the training set while validation and testing sets are locked in order to prevent the data leakage. All models are learned on the training set after fine-tuning the hyper-parameters. After each tuning, an early estimate of the model accuracy is obtained using the validation set. Finally, an unbiased performance estimation of the fitted model is provided on the testing set. The third contribution of this thesis is developing two encoder-decoder networks by exploring the recent advances of deep learning research for crack detection and applying them on our crack dataset. The first network is inspired by DeepLab, which is a modified ResNet architecture. In this network the last pooling layer is replaced with an Atrous Spatial Pyramid Pooling (ASPP) module. This encoder-decoder structure is designed to classify each image pixel into two foreground cracks or textured background. The second model is inspired by Full Resolution Residual Network (FRRN), which is a ResNetlike network with two residual and pooling streams to extract the high- and low-level features, respectively. The combination of di erent level features in this model improves the localization of crack pixels as well as the recognition of the crack structure as a whole. As FRRN outperforms DeepLab on crack classification, we select it as the baseline for further research. In our last contribution, we optimise the FRRN model by reducing the number of parameters. Inspired by the Inception module which significantly improved the utilization of the computing resources inside the GoogLeNet, we proposed Incepted FRRN (I-FRRN) network by embedding the Inception module inside the FRRN. Combining these two structures, our proposed model records 88.14% accuracy in classifying the positive class with 0.22% improvement, while having less than half the number of parameters compared with FRRN. The results show that the proposed architecture achieves significant computational e ciency gains and comparable or higher class-accuracy in crack classification task over the baseline model.

Corrosion damage reduces the load-carrying capacity of bridges which poses a threat to passenger safety. The objective of this research was to reduce the resources involved in conventional bridge inspections which are an important tool in the condition assessment of bridges and to help in determining if live load testing is necessary. This research proposes a framework to link semi-automated damage detection on prestressed concrete bridge girders with the estimation of their residual flexural capacity. The framework was implemented on four full-scale corrosion damaged girders from decommissioned bridges in Virginia. 3D point clouds of the girders reconstructed from images using Structure from Motion (SfM) approach were textured with images containing cracks detected at pixel level using a U-Net (Fully Convolutional Network). Spalls were detected by identifying the locations where normals associated with the points in the 3D point cloud deviated from being perpendicular to the reference directions chosen, by an amount greater than a threshold angle. 3D textured mesh models, overlaid with the detected cracks and spalls were used as 3D damage maps to determine reduced cross-sectional areas of prestressing strands to account for the corrosion damage as per the recommendations of Naito, Jones, and Hodgson (2011). Scaling them to real-world dimensions enabled the measurement of any required dimension, eliminating the need for physical contact. The flexural capacities of a box beam and an I-beam estimated using strain compatibility analysis were validated with the actual capacities at failure sections determined from four destructive tests conducted by Al Rufaydah (2020). Along with the reduction in the cross-sectional areas of strands, limiting the ultimate strain that heavily corroded strands can develop was explored as a possible way to improve the results of the analysis. Strain compatibility analysis was used to estimate the ultimate rupture strain, in the heavily corroded bottommost layer prestressing strands exposed before the box beam was tested. More research is required to associate each level of strand corrosion with an average ultimate strain at which the corroded strands rupture. This framework was found to give satisfactory estimates of the residual strength. Reduction in resources involved in current visual inspection practices and eliminating the need for physical access, make this approach worthwhile to be explored further to improve the output of each step in the proposed framework.

Structural health monitoring (SHM) is a rapidly growing field focused on detecting damage in complex systems before catastrophic failure occurs. SHM systems provide the potential to improve safety and significantly reduced costs. Advanced sensor technologies are necessary to fully harness SHM in applications involving harsh or remote environments, life-critical systems, mass production vehicles, robotic systems, and others. Fiber Bragg grating (FBG) sensors are an attractive solution for in-situ health monitoring due to their low weight, resistance to electromagnetic noise, ability to be multiplexed, and accuracy for real-time measurements. However, effective embedment of FBG sensors into metal has proved challenging. Ultrasonic additive manufacturing (UAM) has been demonstrated for solid-state fabrication of 3D structures with embedded FBG sensors. In this thesis, UAM embedded FBG sensors for SHM applications are investigated. Embedment of a fiber using UAM was shown to have little effect on the tensile and fatigue properties of aluminum coupons. Furthermore, the ability of UAM embedded FBG sensors to detect and monitor crack growth in Compact Tension (CT) specimens is demonstrated. UAM embedded FBG sensors 3 mm from the initiation site were able to accurately detect cracks of length 0.286 ± 0.033 mm. UAM embedded FBG sensors are shown to accurately track crack growth until near failure. Furthermore, UAM embedded FBG sensors 3 mm, 6 mm, and 9 mm from the initiation site detected a crack that initiated to 0.350 mm. Finally, the potential for high temperature applications is also examined through elevated temperature testing. Fiber optics embedded into aluminum using UAM are shown to be more resilient to degradation at elevated temperatures than exposed fibers. UAM embedded FBG sensors are therefore shown to be an effective type of sensor for SHM applications.

Novel experimental capabilities to study hydraulic fracturing in the laboratory are developed and utilized in this research. Fracturing experiments are conducted using two-dimensional (2-D) test specimens that are made from synthetic, porous materials with well-characterized properties. Fracture growth during the experiments is captured with clear, high resolution images and subsequent image processing using Digital Image Correlation (DIC) analyses. First, we investigated the problem of a hydraulic fracture induced in a soft layer bounded by harder layers. The experiments reveal a clear tendency for induced fractures to avoid harder bounding layers. This is seen as fracture deflection or kinking away from the harder layers, fracture curving between the harder bounding layers, and fracture tilt from the maximum far-field stress direction. In addition, when a fracture is induced in a relatively thin layer, the fracture avoids the harder bounding layers by initiating and propagating parallel to the bounding interfaces. Fracture propagation parallel to the bounding layers is also observed in relatively wide layers when the far-field stress is isotropic or very low. Complex fracture trajectories are induced in layered specimens when the far-field differential stress is low or intermediate. In a second set of experiments, we used homogeneous specimens with multiple fluid injection ports. It is clearly shown that injection-induced stresses can appreciably affect hydraulic fracture trajectories and fracturing pressures. We show that induced hydraulic fractures, under our laboratory conditions, are attracted to regions of high pore pressure. Induced fractures tend to propagate towards neighboring high pore pressure injection ports. The recorded breakdown pressure in the fracturing experiments decreases significantly as the number of neighboring injectors increases. The influence of an adjacent fluid injection source on the hydraulic fracture trajectory can be minimized or suppressed when the applied far-field differential stress is relatively high. Preferential fracture growth due to changes in pore pressure in field applications as compared to our laboratory observations is also discussed. In a third set of experiments, we show that the breakdown pressure of test specimens can be reduced markedly with low injection rates, cyclic borehole pressurization, and/or constant pressure injection. This is largely related to the extent of pressurized region around the borehole caused by fluid leakoff in dry specimens and possible specimen weakening by fluid contact. The breakdown pressure can also be reduced by notching the specimen borehole when the injection fluid is allowed to flow and leak off along the borehole notch. In a fourth set of experiments, we compared fracture growth induced by a viscous liquid and a gas which are glycerin and nitrogen, respectively. The experiments show that fractures propagate through test specimens in a gradual manner when induced by glycerin at various injection rates. By contrast, nitrogen injection induces fractures that grow much more rapidly, which we attribute to its compressible nature and ultralow viscosity. The breakdown pressure is also shown to be markedly lower for nitrogen fractures compared to glycerin fractures. Moreover, an experimental evidence of fluid lag when fractures are induced with viscous fluids is demonstrated. Lastly, experiments were conducted to examine the behavior of an induced hydraulic fracture as it approaches a cemented natural fracture. We show a tendency for the induced hydraulic fracture to cross thick natural fractures filled with softer materials than the host rock and to be diverted by thick natural fractures with harder filling materials. The induced hydraulic fracture also tends to cross hard natural fractures when the natural fractures are relatively thin. In addition, the induced hydraulic fracture from the injection port is shown to be diverted by a thin, hard natural fracture that is placed relatively close to the injection port but crosses the same natural fracture when placed farther away from the injection port. These observations, and numerous others, documented in this dissertation provide fundamental insights on various aspects of hydraulic fracture propagation. Our extensive set of laboratory observations are also very useful in validating numerical hydraulic fracturing simulators due to the small-scale, 2-D nature, and characterized properties of the test specimens used in the experiments.

This thesis introduces a multi-Bayesian framework for detection and classification of features in environments abundant with error-inducing noise. The approach takes advantage of Bayesian correction and classification in three distinct stages. The corrective scheme described here extracts useful but highly stochastic features from a data source, whether vision-based or otherwise, to aid in higher-level classification. Unlike many conventional methods, these features’ uncertainties are characterized so that test data can be correctively cast into the feature space with probability distribution functions that can be integrated over class decision boundaries created by a quadratic Bayesian classifier. The proposed approach is specifically formulated for road crack detection and characterization, which is one of the potential applications. For test images assessed with this technique, ground truth was estimated accurately and consistently with effective Bayesian correction, showing a 33% improvement in recall rate over standard classification. Application to road cracks demonstrated successful detection and classification in a practical domain. The proposed approach is extremely effective in characterizing highly probabilistic features in noisy environments when several correlated observations are available either from multiple sensors or from data sequentially obtained by a single sensor.

This research introduces and applies the concept of digital state models for civil infrastructure condition assessment and structural testing. Digital state models are defined herein as any transient or permanent 3D model of an object (e.g. textured meshes and point clouds) combined with any electromagnetic radiation (e.g., visible light, infrared, X-ray) or other two-dimensional image-like representation. In this study, digital state models are built using visible light and used to document the transient state of a wide variety of structures (ranging from concrete elements to cold-formed steel columns and hot-rolled steel shear-walls) and civil infrastructures (bridges). The accuracy of digital state models was validated in comparison to traditional sensors (e.g., digital caliper, crack microscope, wire potentiometer). Overall, features measured from the 3D point clouds data presented a maximum error of ±0.10 in. (±2.5 mm); and surface features (i.e., crack widths) measured from the texture information in textured polygon meshes had a maximum error of ±0.010 in. (±0.25 mm). Results showed that digital state models have a similar performance between all specimen surface types and between laboratory and field experiments. Also, it is shown that digital state models have great potential for structural assessment by significantly improving data collection, automation, change detection, visualization, and augmented reality, with significant opportunities for commercial development. Algorithms to analyze and extract information from digital state models such as cracks, displacement, and buckling deformation are developed and tested. Finally, the extensive data sets collected in this effort are shared for research development in computer vision-based infrastructure condition assessment, eliminating the major obstacle for advancing in this field, the absence of publicly available data sets.

Many components of existing civil infrastructure systems, such as road pavement, bridges, and buildings, are suffered from rapid aging, which require enormous nation's resources from federal and state agencies to inspect and maintain them. Crack is one of important material and structural defects, which must be inspected not only for good maintenance of civil infrastructure with a high quality of safety and serviceability, but also for the opportunity to provide early warning against failure. Conventional human visual inspection is still considered as the primary inspection method. However, it is well established that human visual inspection is subjective and often inaccurate. In order to improve current manual visual inspection for crack detection and evaluation of civil infrastructure, this study explores the application of computer vision techniques as a non-destructive evaluation and testing (NDE&T) method for automated crack detection and quantification for different civil infrastructures. In this study, computer vision-based algorithms were developed and evaluated to deal with different situations of field inspection that inspectors could face with in crack detection and quantification. The depth, the distance between camera and object, is a necessary extrinsic parameter that has to be measured to quantify crack size since other parameters, such as focal length, resolution, and camera sensor size are intrinsic, which are usually known by camera manufacturers. Thus, computer vision techniques were evaluated with different crack inspection applications with constant and variable depths. For the fixed-depth applications, computer vision techniques were applied to two field studies, including 1) automated crack detection and quantification for road pavement using the Laser Road Imaging System (LRIS), and 2) automated crack detection on bridge cables surfaces, using a cable inspection robot. For the various-depth applications, two field studies were conducted, including 3) automated crack recognition and width measurement of concrete bridges' cracks using a high-magnification telescopic lens, and 4) automated crack quantification and depth estimation using wearable glasses with stereovision cameras. From the realistic field applications of computer vision techniques, a novel self-adaptive image-processing algorithm was developed using a series of morphological transformations to connect fragmented crack pixels in digital images. The crack-defragmentation algorithm was evaluated with road pavement images. The results showed that the accuracy of automated crack detection, associated with artificial neural network classifier, was significantly improved by reducing both false positive and false negative. Using up to six crack features, including area, length, orientation, texture, intensity, and wheel-path location, crack detection accuracy was evaluated to find the optimal sets of crack features. Lab and field test results of different inspection applications show that proposed compute vision-based crack detection and quantification algorithms can detect and quantify cracks from different structures' surface and depth. Some guidelines of applying computer vision techniques are also suggested for each crack inspection application.

Structural health monitoring (SHM) methods are being explored as techniques to assess the integrity of mechanical, civil, and aerospace structures. Most of these methods detect or quantify damage by comparing current structural state measurements to stored baseline measurements collected from an undamaged structure. These baseline dependent methods assume that measured signals will not change when exposed to varying environmental and usage conditions. To avoid limitations of this assumption, baseline-free techniques such as vibro-acoustic modulation (VAM) are being explored.VAM is a nonlinear vibration technique in which the structure of interest is excited using a combination of specific frequencies and the response recorded. The VAM technique assumes that an undamaged structure can be represented by a linear system while the representation of a damaged structure must include nonlinearity. A nonlinearity is assumed to result in the generation of sideband responses.To demonstrate the use of VAM to detect fatigue cracking, experimental testing has been performed on existing damaged and undamaged specimens, as well as on fatigue specimens where cracks have been initiated and grown. Initial testing of the damaged and undamaged specimens provides validation for using VAM as a baseline-free SHM technique. Subsequent measurements during fatigue testing confirm this result. Two rectangular coupons were fatigue cycled to initiate and grow cracks. The VAM method detected cracks at 6.42 percent and 12.24 percent damaged cross-sectional area. Potential advantages and limitation of the use of VAM for fatigue crack detection are discussed, and recommendations for additional research efforts to improve or refine the technique are given.

In this research, the fault detection and diagnosis using a model-based technique for the cracked rotor vibration system is developed and implemented. More specifically, the observer based or filter bank approach is employed in the fault detection and diagnosis process in order to detect the occurrence of a crack and diagnose the position and the depth of the crack in rotating machinery. The fault detection and diagnosis process is consisted of two parts. The first part is the filter bank or the residual generation which generates the residual vectors corresponding to each observer. The second part is a voting algorithm which searches the observer that corresponds to the behavior of the real system. The type of filter contained in the filter bank is the discrete time-variant Kalman filter. The filter is specifically designed to track the cracked rotor vibration system. Since the filter is time-variant, the state matrix at the current time step of the filter is updated by the state estimated value from the previous time step. Constructing the filter bank with the presented filter allows the fault detection and diagnosis process to perform very well under the environment of the process and measurement noises which is unavoidable in real systems.The voting algorithm evaluates every observer to find the observer behaving the closest to the real system based on the score achieved by each observer. The score is calculated by the information of the residual mean, the residual autocorrelation of each observer, the correlation coefficient between the real system measurements, and the observer outputs.In order to evaluate the fault detection and diagnosis process performance,the fault detection and diagnosis process is tested with the simulated real system containing various sets of system parameters. The results and discussions are presented.

Crack failure is among the most dreaded failures experienced in rotating machinery. It is therefore important to be able to detect a crack before failure occurs and cost effective to know the location and severity of a crack making it possible to predict the behavior and life of the machinery. This dissertation outlines a method of crack detection using the elastic wave created by the snapping shut of a radial crack to determine these characteristics. To determine the feasibility of such a method, preliminary research is performed by examining the behavior of a crack in 4-point-bending. A theoretical solution for the elastic wave behavior is determined by modeling the behavior as the collinear impact between two shafts. A theoretical impact velocity is found using finite element modeling to examine crack geometry. A pendulum experiment is performed in order to examine the validity of the assumed theoretical acceleration at the shaft end. The experimental acceleration response is smaller than the theory because the volume of air caught between the shaft face and the wall has to be expelled. This is explained by Reynolds lubrication equation which proves this hypothesis. An experiment to test the 4-point-bending theory is presented. More work is needed to determine the feasibility of such a crack detection method, such as running a 4-point-bending experiment as the design for which is presented.

The ability to monitor the structural health of rotordynamic systems is becoming increasingly important as critical components continue to be used despite aging and the associated potential for damage accumulation. The aim of this thesis is to investigate a novel structural health monitoring approach for the detection of damage in rotating shafts, which utilizes a magnetic force actuator for applying multiple types of force inputs on to a rotating structure for analysis of resulting outputs. The magnetic actuator will be used in conjunction with conventional support bearings and also be applied to rotor under full magnetic levitation. The results of numerical simulations of the cracked rotor system will be compared with experimental data obtained with the crack detection dedicated test rig.

An analytical model of cracked composite beams vibrating in coupled bending-torsion is developed. The beam is made of fiber-reinforced composite with fiber angles in each ply aligned in the same direction. The crack is assumed open. The local flexibility concept is implemented to model the open crack and the associated compliance matrix is derived. The crack introduces additional boundary conditions at the crack location and these effects in conjunction with those of material properties are investigated. Free vibration analysis of the cracked composite beam is presented. The results indicate that variation of natural frequencies in the presence of a crack is affected by the crack ratio and location, as well as the fiber orientation. In particular, the variation pattern is different as the magnitude of bending-torsion coupling changes due to different fiber angles. When bending and torsional modes are essentially decoupled at a certain fiber angle if there is no crack, the crack introduces coupling to the initially uncoupled bending and torsion. Based on the crack model, aeroelastic characteristics of an unswept composite wing with an edge crack are investigated. The cracked composite wing is modeled by a cracked composite cantilever and the inertia coupling terms are included in the model. An approximate solution on critical flutter and divergence speeds is obtained by Galerkin's method in which the fundamental mode shapes of the cracked wing model in free vibration are used. It is shown that the critical divergence/flutter speed is affected by the elastic axis location, the inertia axis location, fiber angles, and the crack ratio and location. Moreover, model-based crack detection (size and location) by changes in natural frequencies is addressed. The Cawley-Adams criterion is implemented and a new strategy in grouping frequencies is proposed to reduce the probability of measurement errors. Finally, sensitivity of natural frequencies to model parameter uncertainties is investigated. Uncertainties are modeled by information-gap theory and represented with a collection of nested sets. Five model parameters that may have larger uncertainties are selected in the analysis, and the frequency sensitivities to uncertainties in the five model parameters are compared in terms of two immunity functions.