Cross-Modal Strain Energy Method for Estimating Damage Severity

A newly developed damage severity estimation method, termed as cross-modal strain energy (CMSE) method, which is capable of accurately estimating the damage magnitude of multiple damaged members, is presented. While all existing damage severity estimation methods that utilize modal strain energy are either employing an iterative solution procedure or involving significant approximations, the CMSE method is an exact, noniterative solution method. Furthermore, the development of the CMSE method is under the assumption that the mass distributions of the baseline and damaged structures are unknown, but identical. Implementing this method requires only the information of a few modes measured from the damaged structure. Numerical studies are demonstrated for a three-dimensional five-story frame structure based on synthetic data generated from finite element models.     

Damage Diagnosis of Frame Structures Using Modified Modal Strain Energy Change Method

This work presents a modified modal strain energy change (M-MSEC) method and its corresponding iteration process to detect damage to frame structures. Analytical results of a three-dimensional frame structure demonstrate that the quantity of damage can be identified correctly by using different modes in the M-MSEC method. A full-scale experimental study is also performed to evaluate the robustness of the M-MSEC method on damage detection as well as damage quantification. Satisfactory results are shown in relation to the modeling error, noise effect, and limited measurements.     

Damage Localization and Finite-Element Model Updating Using Multiresponse NDT Data

New techniques for both finite-element model updating and damage localization are presented using multiresponse nondestructive test (NDT) data. A new protocol for combining multiple parameter estimation algorithms for model updating is presented along with an illustrative example. This approach allows for the simultaneous use of both static and modal NDT data to perform model updating at the element level. A new damage index based on multiresponse NDT data is presented for damage localization of structures. This index is based on static and modal strain energy changes in a structure as a result of damage. This method depicts changes in physical properties of each structural element compared to its initial state using NDT data. Deficient or potentially damaged structural elements are then selected as the unknown parameters to be updated by parameter estimation. Error function normalization, error function stacking, and multiresponse parameter estimation methods are proposed for using multiple data types for simultaneous stiffness and mass parameter estimation. Also, multiple sets of measurements with various sizes and missing data points can be utilized. This paper uses a laboratory grid model of a bridge deck built at the University of Cincinnati Infrastructure Institute and the corresponding NDT data for validation of the above damage localization and model updating methods. Multiresponse parameter estimation has been utilized to update the stiffness of bearing pads, and both the stiffness and mass of the connections, using static and dynamic NDT data. The static and modal responses of the updated grid model presented a closer match with the NDT data than the responses from the initial model.     

Structural Damage Detection from Modal Strain Energy Change

A structural damage detection method based on modal strain energy (MSE) change before and after damage is presented in this paper. The localization of damage based on MSE of each structural element is briefly presented, and the sensitivity of the MSE with respect to a damage is derived. The sensitivity is not based on any series expansion and is a function of the analytical mode shape changes and the stiffness matrix. Only incomplete measured mode shapes and analytical system matrices are required in this damage localization and quantification approach. Results from a numerical example and an experiment on a single-bay, two-story portal steel frame structure are investigated. The effects of measurement noise and truncated analytical mode shapes are discussed. Results indicate that the proposed approach is noise sensitive, but it can localize single and multiple damages. Damage quantification of two damages is successful with a maximum of 14% error under a 5% measurement noise.     

Improved Damage Quantification from Elemental Modal Strain Energy Change

An improved structural damage quantification algorithm is presented based on the elemental modal strain energy change before and after the occurrence of damage in a structure. The algorithm includes the analytical stiffness and mass matrices of the system in the damage quantification. It reduces significantly the modal truncation error and the finite-element modeling error from higher analytical modes in the computation, and it improves the convergence properties of the existing algorithm by Shi et al. (2000). “Structural damage detection from elemental modal strain energy change.” J. Eng. Mech., 126(12), 1216–1223]. The effectiveness of the proposed algorithm is demonstrated via a numerical example and experimental results from a two-storey steel portal frame, and it is demonstrated to be an efficient and robust method for damage quantification.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.     

Numerical Simulation of Damage Localization in Polyester Mooring Ropes

This paper presents the derivation of a mechanical model to estimate the effects of damage on the response of ropes. Damage can be represented through a degradation of the properties of individual rope elements, and it can also include the complete rupture of one or more elements. The general assumptions made to estimate the length over which damage propagates along the length of a rope and how this length is considered in modeling damaged rope behavior are explained. Consistent with tests on damaged polyester (PET) mooring ropes, numerical simulations demonstrate the existence of strain localization around the failure region and, due to degradation of rope element properties, damage localization as well. This damage localization causes the premature failure of rope elements, reducing the maximum load capacity and maximum failure strain that a damaged rope is capable of resisting relative to that of an intact rope. The proposed model suggests that some of the variables that affect damaged rope behavior are the degree of damage present at a given cross-section, the location of broken rope elements, and the length over which damage propagates along the rope length. Experimental data are used to validate the model.     

轻质混凝土拼装墙板填充钢框架协同抗震性能试验研究

为了研究墙板与钢框架结构之间的协同抗震性能,对采用不同墙框连接节点的轻质混凝土拼装墙板填充钢框架进行了低周往复荷载试验。通过对比试件的承载力、滞回性能、刚度、耗能以及延性性能,探讨了轻质混凝土拼装墙板及其整体性对结构抗震性能的影响。结果表明:填充墙板钢框架结构的最终破坏形态以墙板挤压开裂,框架梁柱端部翼缘屈曲为主;轻质混凝土拼装墙板与钢框架协同工作,有利于提高结构整体的承载力和变形能力,减轻钢框架在平面内的屈曲破坏;与刚性节点相比,采用柔性节点连接墙板与钢框架对结构的承载力、层间刚度和耗能能力更为有利;增强拼装墙板的整体性,有助于提高结构整体刚度、变形和耗能能力。研究结果可为轻质混凝土拼装墙板填充钢框架结构的抗震设计提供参考。      

轴承外圈裂纹损伤的模态参数对比研究

轴承结构的表面损伤对其振动特性具有显著影响。以6307滚动轴承为研究对象,采用有限单元法分析了轴承外圈出现不同尺度的裂纹缺陷后,其固有特性的变化情况。其中,着重探讨了系统固有频率、位移模态以及应变模态参数对外圈损伤的敏感程度。     

General Approach to Dynamic Analysis of Rotorcraft

This paper presents a general‐purpose mathematical formulation for the dynamic analysis of a rotorcraft consisting of flexible or rigid components, or both, that may undergo large rotations. In this formulation, two sets of coordinates are used, namely rigid‐body coordinates and elastic coordinates. The rigid‐body coordinates define the location and the orientation of a body frame with respect to an inertial frame. The rigid‐body rotational coordinates may be Euler angles, Euler‐like angles, or Euler parameters. The elastic coordinates define the elastic deformations with respect to the body frame. Nonlinear strain‐displacement relations are considered in order to be able to incorporate the effect of geometric stiffening. A systematic methodology that combines the traditional finite element and multibody approaches is developed to obtain a set of differential and algebraic equations governing the dynamics of the system. The resulting set of equations is highly nonlinear. Numerical schemes to solve this set of equations are also discussed. The formulation presented is general and allows the development of a modular code. The formulation also allows the code to be updated and grow without reformulation of the problem.     

Explosion and Fire Analysis of Steel Frames Using Mixed Element Approach

This paper presents a mixed element approach for analyzing steel frame structures subjected to a localized explosion and followed by fire. Critical members that are subjected to direct action of explosion and fire are modeled using shell elements. Noncritical members that are away from the affected area are modeled using beam elements. The proposed approach is computationally efficient for modeling large-scale structures and accurate enough to capture detailed behavior of member inelasticity and instability associated with the effects of blast and fires. Section classification may change from static load to blast load because of the enhanced yield strength due to high strain rate. The beam element approach is found to overpredict the overall resistance of steel frame structures if local deformation of cross section occurred after the blast loads. Detailed finite element modeling of critical frame members is necessary to improve the accuracy of predicting the ultimate resistance of structures. The proposed approach is applied to study the ultimate behaviors of a steel column and a three-story steel frame under explosion and fire.     

Bayesian Probabilistic Approach to Structural Health Monitoring

A Bayesian probabilistic methodology for structural health monitoring is presented. The method uses a sequence of identified modal parameter data sets to compute the probability that continually updated model stiffness parameters are less than a specified fraction of the corresponding initial model stiffness parameters. In this approach, a high likelihood of reduction in model stiffness at a location is taken as a proxy for damage at the corresponding structural location. The concept extends the idea of using as indicators of damage the changes in structural model parameters that are identified from modal parameter data sets when the structure is initially in an undamaged state and then later in a possibly damaged state. The extension is needed, since effects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable model error, lead to uncertainties in the updated model parameters that in practice obscure health assessment. The method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified on a regular basis and the probability of damage for each substructure is continually updated.     

Natural Excitation Technique and Eigensystem Realization Algorithm for Phase I of the IASC-ASCE Benchmark Problem: Simulated Data

A benchmark study in structural health monitoring based on simulated structural response data was developed by the joint IASC–ASCE Task Group on Structural Health Monitoring. This benchmark study was created to facilitate a comparison of various methods employed for the health monitoring of structures. The focus of the problem is simulated acceleration response data from an analytical model of an existing physical structure. Noise in the sensors is simulated in the benchmark problem by adding a stationary, broadband signal to the responses. A structural health monitoring method for determining the location and severity of damage is developed and implemented herein. The method uses the natural excitation technique in conjunction with the eigensystem realization algorithm for identification of modal parameters, and a least squares optimization to estimate the stiffness parameters. Applying this method to both undamaged and damaged response data, a comparison of results gives indication of the location and extent of damage. This method is then applied using the structural response data generated with two different models, different excitations, and various damage patterns. The proposed method is shown to be effective for damage identification. Additionally the method is found to be relatively insensitive to the simulated sensor noise.     

Improved Damage Localization and Quantification Using Subset Selection

Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.     

Structural Damage Detection and Assessment from Modal Response

This paper presents a global damage detection and assessment algorithm based on a parameter estimation method using a finite-element model and the measured modal response of a structure. Damage is characterized as a reduction of the member constitutive parameter from a known baseline value. An optimization scheme is proposed to localize damaged parts of the structure. The algorithm accounts for the possibility of multiple solutions to the parameter estimation problem that arises from using spatially sparse measurements. Errors in parameter estimates caused by sensitivity to measurement noise are reduced by selecting a near-optimal measurement set from the data at each stage of the localization algorithm. Damage probability functions are computed upon completion of the localization process for candidate elements. Monte Carlo methods are used to compute the required probabilities based on the statistical distributions of the parameters for the damaged and the associated baseline structure. The algorithm is tested in a numerical simulation environment using a planar bridge truss as a model problem.     

Uncoupling of Potential Energy in Nonlinear Seismic Analysis of Framed Structures

A computational analysis method is presented to investigate the potential energy of fully nonlinear framed structures and other energy characteristics due to earthquake ground motions. The overall potential energy is directly related to the stiffness of the structure, and it consists of three components in a fully nonlinear system: (1) strain energy representing the storing energy that is associated with the linear elastic portion of the structural response; (2) higher-order energy representing the energy associated with the geometric nonlinear effect of the overall structural response, which is derived from finite element method; and (3) plastic energy representing the energy dissipated by material inelasticity of the structure, and it is being derived analytically. The merit of proposed analysis method lies in the uncoupling of geometric nonlinearity and material inelasticity effects before solving for the equation of motion, and this leads directly to the analytical representations of each energy form. Both plastic energy and higher-order energy based on single-degree-of-freedom system are studied in detail to demonstrate the beauty of the proposed analysis method. In addition, a method of generating energy density spectra is also proposed, which is useful to enhance the understanding energy characteristics in seismic analysis. Finally, a five-story frame is used as a numerical example to illustrate the effectiveness and robustness of the proposed method.     

Three-Dimensional Micromechanical Finite-Element Network Model for Elastic Damage Behavior of Idealized Stone-Based Composite Materials

This paper presents a three-dimensional (3D) micromechanical finite-element (FE) network model for predicting elastic damage behavior of the idealized stone-based materials. Stone-based composite materials have multiphase structures: an aggregate (or stone) skeleton, a binding medium, fillers, and air voids. Numerical simulation of the micromechanical behavior of the idealized stone-based materials was accomplished by using a microframe element network model that incorporated the mechanical load transfer between adjacent particles. The elastic stiffness matrix of this special element was obtained from an approximate elastic stress-strain analysis of straight cement between particle pairs. A damage-coupled microframe element was then formulated with bilinear damage laws, including elastic and softening behavior based on the equivalent fracture release energy. Indirect tension and compression simulations were conducted with developed FE models on the idealized digital samples of the stone-based materials. These simulations predicted the internal microdamage distribution and global fracture behavior of these samples, which qualitatively agree with the laboratory observations. The results indicate that the developed FE models have the capability to predict the typical loading-related damage behavior observed from the stone-based materials.     

Damage Detection in Composite Materials Using Identification Techniques

The present paper describes an approach for damage detection in composite structures that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from a mathematical model of the original structure, where such a model is typically a finite‐element representation of the structure. In the present work dealing with composite materials, two distinct analytical models, one using two‐dimensional (2D) elements in conjunction with the classical lamination theory and another using three‐dimensional (3D) elements were considered. The output error approach of system identification was employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. The proposed method is an extension of the stiffness‐reduction approach for damage detection to realistic structures. Numerical simulation of measurements of static deflections, strains, and vibration modes were used in the identification procedure. The methodology was implemented for representative composite structures. Principal shortcomings in the proposed approach and possible methods to circumvent these problems are discussed in the paper.     

Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames.?I: Theoretical Considerations Based on Semitangential Property

To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguez' rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the thin-walled space frame element are derived using Hermitian polynomials considering shear deformation effects, and a new scheme to evaluate incremental member forces and load correction stiffness matrices due to off-axis loads is presented and its physical meaning is addressed. Furthermore, finite-element solutions displaying spatial postbuckling behaviors are evaluated and compared with available solutions.