Modal Strain Energy Decomposition Method for Damage Localization in 3D Frame Structures

This article presents a newly developed modal strain energy decomposition method for damage localization that is capable of identifying damage to individual members of three-dimensional (3D) frame structures. This method is based on decomposing the modal strain energy of each structural member (or element) into two parts, one associated with the element’s axial coordinates and the other with its transverse coordinates. In turn, two damage indicators are calculated for each member to perform the damage localization analysis. Implementing this method requires only a small number of mode shapes identified from both the damaged and baseline structures. Numerical studies are conducted of a 3D five-story frame structure and also a complicated offshore template platform, based on synthetic data generated from finite-element models. In addition to providing theoretical insights to illustrate the advantages of using this newly developed method, this article also demonstrates numerically that the new method is capable of localizing various kinds of damaged elements (a vertical pile, horizontal beam, or slanted brace) at a template offshore structure.     

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 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.     

Investigation of the load sequence effects in fatigue of damaged composite laminate & characterization of fatigue damage

Carbon fiber reinforced composites are widely used today in various areas and specially in aerospace industry for structural applications. This investigation focuses on the effect of different load sequencing and impact damage on the fatigue behaviour of CFC laminates. The specimens made from plain CFC laminates and low energy impact damaged CFC laminates were subjected to a typical flight block loading sequence and the fatigue strength degradation was monitored through stiffness measurement using load displacement data obtained during block loading. Three different stress/strain levels were used in testing. All the tests were performed using a computer controlled 100 kN servo-hydraulic test machine in load mode at room temperature and in lab air atmosphere on undamaged and low energy impact damaged composite laminates. Fatigue tests were performed with a sinusoidal waveform at 3 Hz. It was observed that lower strain levels did not show any significant effect on the fatigue properties in both the type of loading i.e. low to high and in high to low block loading in case of both the undamaged and impact damaged CFC specimens. Significant.reduction in stiffness was seen at higher strain level i.e. 6500me in both the undamaged and impact damaged CFC specimens. The low energy impact damaged specimens showed early failure at higher strain levels compared to undamaged specimens. The specimens were observed to have delaminated in the high stress fatigue cycling. The observed stiffness reduction due to fatigue cycling and the presence of delamination provide a means of macroscopic identification of fatigue strength degradation in composite materials. The energy plots appear useful tool to assess the damage growth.     

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.     

Thermal stress fracture of refractory lining components: Part III. Analysis of Fracture

The fracture behavior of refractory components heated from one end is simulated using a twodimensional constant heating rate thermoelastic model and the maximum principal tensile stress fracture criterion. Dimensionless graphical relationships that can be used to predict location of fracture and orientation of cracking are presented. Dimensional analysis and the finite element numerical method are used to develop a general solution for the total strain energy. Based on the premise that extent of crack propagation is directly related to available strain energy at fracture and inversely related to the surface energy per unit area, the solution for total strain energy is used to derive a damage resistance parameter useful for the design and selection of refractory components that accounts for material properties, geometry, and heating and cooling rate. Model predictions of location of fracture, orientation of cracking, and extent of crack propagation are in general agreement with experimental results previously reported in the literature. Limitations of the two-dimensional thermoelastic model are discussed.     

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.     

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.     

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.     

起爆方式对间隔装药应力场分布及裂纹扩展的影响

通过模型实验研究了不同起爆方式对空气间隔装药炮孔两侧损伤分布的影响规律,借助数字图像相关实验系统,获取了全场应变场演化过程及空气段应变衰减规律,同时借助透射式焦散线实验系统,探究了起爆方式对预制裂纹动态断裂行为的影响.实验结果表明：柱状药包炮孔两侧产生的损伤范围具有显著的分形特征.采用外侧起爆时,空气段中心两侧均产生损伤,而采用其他起爆方式时,空气段均未出现损伤.不同起爆方式对空气段应变场径向压应变的影响主要体现在应变大小、衰减速度两个方面,对轴向拉应变的影响主要体现在时效性、衰减速度两个方面.不同起爆方式下预制裂纹端部断裂行为差别较大.采用内侧起爆、外侧起爆时,裂纹均为水平扩展,呈现典型Ⅰ型裂纹,裂纹起裂主要由拉伸破坏引起,异侧起爆时裂纹起裂为Ⅰ-Ⅱ混合型,具体表现为拉-剪破坏.基于数值模拟软件LS-DYNA,解释了预制裂纹端部起裂成因,得到了孔壁处应力场分布规律,不同起爆方式对炮孔轴向孔壁处压力分布影响显著,装药段主要体现在压力峰值位置和压力分布形态两个方面,空气段主要体现在压力峰值大小和压力分布形态两个方面.     

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.     

Damage Detection and Damage Detectability— Analysis and Experiments

A technique to identify structural damage in real time using limited instrumentation is presented. Contrast maximization is used to find the excitation forces that create maximum differences in the response of the damaged structure and the analytical response of the undamaged structure. The optimal excitations for the damage structure are then matched against a database of optimal excitations to locate the damage. To increase the reliability of the approach under modeling and measurement errors, the contrast maximization approach is combined with an approach based on changes in frequency signature. The detectability of any particular damage with the proposed technique depends on the ratio of the magnitude of damage and the magnitude of errors in the measurements, as well as on how much the damage influences the measurements. A damage detectability prediction measure, that incorporates these effects, is developed. The technique is first tested numerically on a 36 degree-of-freedom space truss. To simulate experimental conditions, an extensive study is carried out in the presence of noise. A similar truss is then built and the finite-element method (FEM) model of the structure is corrected using experimental data. The technique is applied to locate the damage in several members. The experimental results indicate that this technique can robustly identify the damaged member with limited measurements and real-time computation. The effectiveness of the damage detection measure is also demonstrated.     

Bridge Structural Condition Assessment Using Systematically Validated Finite-Element Model

The structural condition assessment of highway bridges is largely based on visual observations described by subjective indices, and it is necessary to develop a methodology for an accurate and reliable condition assessment of aging and damaged structures. This paper presents a method using a systematically validated finite-element model for the quantitative condition assessment of a damaged reinforced concrete bridge deck structure, including damage location and extent, residual stiffness evaluation, and load-carrying capacity assessment. In a trial of the method in a cracked bridge beam, the residual stiffness distribution was determined by model updating, thereby locating the damage in the structure. Furthermore, the damage extent was identified through a defined damage index and the residual load-carrying capacity was estimated.     

Stiffness Evaluation and Damage Detection of Ceramic Candle Filters

This paper presents a nondestructive evaluation method to identify the structural stiffness of ceramic candle filters. A ceramic candle filter is a hollow cylindrical structure made of a porous ceramic material used in advanced, coal-fired power generation systems. The candle filters need to sustain an extreme thermal and chemical environment over a great period of time to protect the gas turbine components from exposure to particulate matter. A total of 92 new candle filters and 29 used candle filters have been tested nondestructively using a dynamic characterization technique. All filters were subjected to an excitation force, and the response was picked up by an accelerometer in a free-free boundary condition. The frequency response function and vibration mode shapes of each filter were evaluated. Beam vibration equations and finite-element models were built to calculate the filter's dynamic response. Results indicate that the vibration signatures can be used as an index to quantify the structural properties of ceramic candle filters. The results also show estimations of the overall bending stiffness values for four different types of candle filters. The used filters show a trend of stiffness degradation, which was related to the filter's exposure time. Damage detection procedures using modal strain energy and finite-element simulation were studied for detection of a localized damage in the candle filter. The location and the size of the damaged section can be identified using the measured model strain energy.     

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.     

Use of Thermodynamic Formalism in Generalized Continuum Theories and a Model for Damage Evolution

A technique for setting up generalized continuum theories based on a balance law and nonlocal thermodynamics is suggested. The methodology does not require the introduction of gradients of the internal variable in the free energy, while allowing for its possibility. Elements of a generalized (brittle) damage model with porosity as the internal variable are developed as an example. The notion of a flux of porosity arises, and we distinguish between the physical notion of a flux of voids (with underpinnings of corpuscular transport) and a flux of void volume that can arise merely due to void expansion. A hypothetical, local free energy function with classical limits for the damaged stress and modulus is constructed to show that the model admits a nonlinear diffusion-advection equation with positive diffusivity for the porosity as a governing equation. This equation is shown to be intimately related to Burgers equation of fluid dynamics, and an analytical solution of the corresponding constant-coefficient, semilinear equation without source term is solved by the Hopf–Cole transformation, that admits the Hopf–Lax entropy weak solution for the corresponding Hamilton–Jacobi equation in the limit of vanishing diffusion. Constraints on the class of admissible porosity and strain-dependent free energy functions arising from the mathematical structure of the theory are deduced. This work may be thought of as providing a continuum thermodynamic formalism for the internal variable gradient models proposed by Aifantis in 1984 in the context of local stress and free-energy functions. However, the degree of diffusive smoothing is not found to be arbitrarily specifiable as mechanical coupling produces an “antidiffusion” effect, and the model also inextricably links propagation of regions of high gradients with their diffusive smoothing.     

Damage Detection Utilizing the Damage Index Method to a Benchmark Structure

This paper addresses the first generation benchmark problem on structural health monitoring developed by the ASCE Task Group on Structural Health Monitoring. The focus of the problem is a four-story model of an existing physical model at the University of British Columbia where simulated data are used for the system identification. Modal parameters were extracted using the frequency domain decomposition method. Rather than relying on data from the undamaged structure, a new proposed methodology based on ratios between stiffness and mass values from the eigenvalue problem is presented to identify the undamaged state of the structure. Once the structural identification is complete, the damage index method is used to detect the location and severity of damage. By not relying on undamaged structure information, this approach may be applicable to existing structures that may already incorporate some amount of damage.     

Experimental and theoretical evidence for carbon-vacancy binding in austenite

Our research and results from the literature all consistently suggest a binding energy of nearest-neighbor carbon-vacancy (C-V) pairs of the order 35 to 40 kJ/mole in austenitic alloys. Results examined include point-defect anelasticity, self-diffusion, high-temperature creep, strain aging, strain-age hardening, radiation damage, and point-defect structure modeling. Increases in the height of carbon-based anelastic peaks by quenching, cold work, and electron irradiation are consistent with a substantial nonexclusive contribution of C-V complexes. Increased carbon content in austenite increases the iron self-diffusivity and the high-temperature creep rate of fcc Fe, implying a C-V binding energy of ∼40 kJ/mol. Dynamic strain aging of carbon-containing austenites occurs in temperature ranges too low to involve interstitial solute mobility and requires an interpretation of large C-V binding wherein the vacancy is the more mobile component. Strengthening in heavily deformed austenitic stainless steels associated with strain aging or long-term aging near room temperature implies solution hardening by tetragonal-like C-V complexes formed at these temperatures. Results on radiation damage of austenitic steels show effects of carbon on irradiation susceptibility. Finally, we have performed first-principles gradient-corrected density functional calculations to determine the binding energy of nearest-neighbor C-V pairs in fcc iron; a value of ∼35 kJ/mol is obtained. This article is based on a presentation in the symposium “Terence E. Mitchell Symposium on the Magic of Materials: Structures and Properties” from the TMS Annual Meeting in San Diego, CA in March 2003.     

Application of Wavelet Approach for ASCE Structural Health Monitoring Benchmark Studies

This paper presents an application of wavelet analysis for damage detection and locating damage region(s) for the ASCE structural health monitoring benchmark data. The response simulation data were generated basically by a FEM program provided by the ASCE Task Group on Health Monitoring for a four-story prototype building structure subjected to simulated stochastic wind loading. Damage was introduced in the middle of response by breaking one or more structure elements such as interstory braces. Wavelets were used to analyze the simulation data. It was found that structural damage due to sudden breakage of structural elements and the time when it occurred can be clearly detected by spikes in the wavelet details. The damaged region can be determined by the spatial distribution pattern of the observed spikes. The effects of measurement noise and the severity of damage were investigated. The results in this paper illustrate a great promise of wavelet analysis for structural health monitoring, especially for an on-line application.     

Identification of Parametric Variations of Structures Based on Least Squares Estimation and Adaptive Tracking Technique

An important objective of health monitoring systems for civil infrastructures is to identify the state of the structure and to detect the damage when it occurs. System identification and damage detection, based on measured vibration data, have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some parameters in structural elements, such as a degradation of the stiffness. Hence it is important to develop data analysis techniques that are capable of detecting the parametric changes of structural elements during a severe event, such as the earthquake. In this paper, we propose a new adaptive tracking technique, based on the least-squares estimation approach, to identify the time-varying structural parameters. In particular, the new technique proposed is capable of tracking the abrupt changes of system parameters from which the event and the severity of the structural damage may be detected. The proposed technique is applied to linear structures, including the Phase I ASCE structural health monitoring benchmark building, and a nonlinear elastic structure to demonstrate its performance and advantages. Simulation results demonstrate that the proposed technique is capable of tracking the parametric change of structures due to damages.