Changes In Structural Stiffness Research Articles

Fault Detection of Linear Guide Preload of a Positioning Stage with Vibration–Acoustic Analysis

The vibration analysis method has been widely used to detect faults in the components of a machine. For a linear positioning stage, its vibration characteristics are closely related to and affected by the preload of linear guides. To clarify the meaning of the vibration signals coming out from an abnormal machine, in this study we aimed to investigate the influence of a faulty linear guide on the vibration and acoustic characteristics of a positioning stage through experimental and finite element modeling approaches. Experimental measurements indicate that stages equipped with abnormal or damaged linear guides indeed exhibit different vibration behavior compared to stages with intact guides. According to finite element analysis, the variation in vibration characteristics can be attributed to the changes in the structural stiffness of linear guides because of rolling ball defects. This phenomenon was also found in the acoustic characteristics measured for stages under various preloaded conditions, providing further correlations between the variations in acoustic characteristics and changes in structural stiffness. The present results clearly show that faulty conditions of linear guides can be effectively detected by means of monitoring the vibration and acoustic characteristics of the stage.

Recursive subspace identification for on-line tracking of structural modal parameter

The objective of this paper is to develop an on-line tracking of system parameter estimation and damage detection techniques using response measurements. To avoid the singular-value-decomposition in data Hankel matrix, a new subspace identification algorithm was developed. Seismic response data of a 3-story steel frame with abrupt change of inter-story stiffness from the shaking table test was used to verify the proposed recursive subspace identification (RSI) method by using both input and output measurements. With the implementation of forgetting factor in RSI method the ability of on-line damage detection of the abrupt change of structural stiffness can be enhanced. Then, the recursive stochastic subspace identification (RSSI) algorithm is also developed for continuous structural health monitor of structure by using the output-only measurements. Verification of the proposed RSSI method by using the white noise response data of a 2-story reinforced concrete frame from its low level white noise excitation was used. Discussion of the subspace identification model parameters is also investigated.

Detecting sudden changes in stiffness using high-pass filters

SUMMARY It is often of interest to detect the time of occurrence of sudden change in structural parameters, particularly the changes in structural stiffness for health monitoring purposes as a change in stiffness also implies some damage in one or more structural elements. Although well known, it is formally shown here that a sudden change in stiffness induces a sudden change in the acceleration response. Several methods have been used in the literature to detect such sudden changes. The wavelet transform, in particular the discrete wavelets transform, is one of the popular approaches. In this approach, the sudden changes have been shown to manifest themselves as spikes in the plots of the details of the discrete wavelet transform of the acceleration response. In this paper, we provide an analytical rationale to explain what constitutes these spikes and their relationship to the discontinuity being detected. In particular, it is shown that a spike corresponds to the scaled step-response of a high-pass filter and that a step discontinuity can be detected using a high-pass filter with properly chosen cut-off frequency where the discontinuity manifests as a clear spike in the filtered output. How the measurement error and sampling frequency affect the detection is discussed. An example of a multi-degree-of-freedom system subjected to the base excitation, with sudden changes in its structural elements, is presented to illustrate the approach. Copyright © 2011 John Wiley & Sons, Ltd.

Localized Trabecular Damage Adjacent to Interbody Fusion Devices

An in vitro cadaveric study of interbody fusion devices (IFDs) with differing interface geometries. To quantify the trabecular damage and mechanical property degradation resulting from mechanical testing of bone-implant constructs and evaluate the dependence on the interface geometry. The success of an orthopedic implant depends, in part, on the interaction between the implant and the bone at its interface. IFDs must safely and effectively transfer load between the device and the neighboring vertebral cancellous bone on which the device is supported. Twenty-four vertebral pairs implanted with bilateral cylindrical or hexahedral IFDs were subjected to either 1% or 2.5% compressive strain. The change in structural stiffness and the presence of residual deformation caused by damage processes were measured. Histologic evidence of trabecular damage was quantified using polychromatic labeling and an image processing scheme. Statistical comparisons between groups within a strain level were made using the Mann-Whitney U test. RESULTS.: Permanent deformation and/or decreased structural stiffness was found in all specimens. The overall changes in mechanical stiffness properties were inconsistent with regard to the device interface geometry. Histologic damage was found in all specimens located in a region immediately adjacent to the implant. The distribution of the damage relative to the center of the device cross-section was significantly different for the 2 interface geometries. At the higher strain, damage and the mechanical effect of damage were greater for the cylindrical devices. Histologic damage was found in close proximity to the bone-implant interface and in all specimens, including those which did not demonstrate mechanical damage. Patterns of histologic damage corresponded directly to the bone-implant interface geometry. Gross structural measurements do not reliably detect changes caused by damage at the bone-implant interface.

APPLICATION OF EMPIRICAL MODE DECOMPOSITION IN STRUCTURAL HEALTH MONITORING: SOME EXPERIENCE

The installation of long-term structural health monitoring (SHM) system on super-tall buildings, long span bridges and large space structures has become a worldwide trend since last decade to monitor loading conditions, to detect damage, to assess structural safety and to guide maintenance during their service life. The core part of an SHM system is the function of data processing and structural parameter/damage identification that extracts useful information from huge amount of raw data and provides reliable knowledge for proper decision. Recently emerged data processing technique empirical mode decomposition (EMD) in conjunction with Hilbert transform (HT) provides a more better and powerful tool for SHM. This paper summarizes some research experience gained from application of EMD + HT in SHM with focuses on pre-processing raw data, structural parameter identification and damage detection. In particular, EMD is applied to determining time varying mean wind speed for wind data and to extract multipath effect from GPS data. For structural parameter identification, the EMD + HT approach is employed to identify natural frequencies and modal damping ratios of long span bridge during passage of strong typhoon and of structures with closely spaced modes of vibration. The results manifest the advantages of EMD + HT over traditional FFT-based methods in damping estimation. Furthermore, experimental investigation has been carried out to study the applicability of EMD for identifying structural damage caused by a sudden change of structural stiffness. It is concluded from all these investigations that EMD approach is a promising tool for structural health monitoring of large civil structures. Finally, some issues concerned for further practical application of EMD are highlighted and discussed based on these academic researches.

The Effects of Structural and Localized Resonances on Induction Motor Performance

Troubleshooting resonance problems within alternating current induction motor systems has always presented difficult challenges for motor manufacturers and end users alike. Often, the changes in structural stiffness from a motor manufacturer's rigid foundation to a less stiff field base can produce drastically different vibration performance. In most cases, a structural natural frequency of a motor or foundation that coincides with a motor forcing function will provide detrimental results to the motor vibration. Many times the effects of undesirable system resonances may be detected after the motor has been installed, causing costly down time, or even motor failure if the problem remains undetected. Additionally, natural frequencies of motor components, such as fans, may cause a catastrophic fatigue failure when the motor is subjected to forcing functions with frequencies in the vicinity of these localized resonances. This paper will provide insight on motor system resonances and localized resonances that may be damaging to an induction motor's operation.

Long-term Structural Health Monitoring System for a FRP Composite Highway Bridge Structure

This article discusses the implementation of a long-term structural health monitoring system for a FRP highway bridge using vibration-based monitoring techniques. The design and installation of such a system is prompted by the need to present a quantitative assessment of structural response to owners and operators in order to provide early warnings for major changes in response in the case of impending catastrophic failures. The bridge under discussion is instrumented with accelerometers as well as corresponding data acquisition and transmission equipment for automatic data collection. Ambient vibration based techniques are used to extract modal parameters from measured bridge response. Information regarding the change of internal structural characteristics is then obtained through a mode shape curvature based approach. Structural stiffness change is based on the analysis of collected data. A finite element model updating technique is used to provide an improved baseline model. The updated model is then used for simulation of damage effects.

A new damage index for detecting sudden change of structural stiffness

A sudden change of stiffness in a structure, associated with the events such as weld fracture and brace breakage, will cause a discontinuity in acceleration response time histories recorded in the vicinity of damage location at damage time instant. A new damage index is proposed and implemented in this paper to detect the damage time instant, location, and severity of a structure due to a sudden change of structural stiffness. The proposed damage index is suitable for online structural health monitoring applications. It can also be used in conjunction with the empirical mode decomposition (EMD) for damage detection without using the intermittency check. Numerical simulation using a five-story shear building under different types of excitation is executed to assess the effectiveness and reliability of the proposed damage index and damage detection approach for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also examined. The results from this study demonstrate that the damage index and damage detection approach proposed can accurately identify the damage time instant and location in the building due to a sudden loss of stiffness if measurement noise is below a certain level. The relation between the damage severity and the proposed damage index is linear. The wavelet-transform (WT) and the EMD with intermittency check are also applied to the same building for the comparison of detection efficiency between the proposed approach, the WT and the EMD.

A damage index for structural health monitoring based on the empirical mode decomposition

This paper presents two novel damage indices based on empirical mode decomposition (EMD) and fast Fourier integration for identifying structural damage caused by a change in structural stiffness. The paper also demonstrates the effectiveness of the proposed damage indices formulated based on a series of coupled mathematical/engineering approaches that are used to detect damage in pipes reliably and accurately. The main approach is based on monitoring the vibration response of pipes using piezoelectric sensors and the first intrinsic mode functions (IMFs). Finite element analysis is used to simulate the response of a healthy pipe, as well as pipes with various sizes of damage. Damages are meant to represent the outcome of local corrosion (damage) with varying reduction in areas around the circumference of the pipe. The evaluated damage indices could effectively establish the location of the defects. Moreover, the evaluated energy indices could also distinguish various size defects. To demonstrate further the effectiveness of our proposed damage indices, the results are compared with other effective indices based on wavelet packet and other statistical methods reported in the literature.

Investigation into the use of low cost MEMS accelerometers for vibration based damage detection

When a structure is damaged there is often a concomitant localized change in structural stiffness, which may affect the dynamic characteristics of the structure. One characteristic that has proved suitable for damage identification and location is the operational curvature shape which exhibits changing features at locations of stiffness change. A method that finds theses features, SIDER, employs an algorithm that operates on broadband operational curvature shapes. To obtain data for SIDER, a small number of accelerometers, typically about four, is installed on the structure and the structure is then excited at a large array of test points using a ‘roving hammer’ technique. Frequency response functions are individually measured between each excitation point and the reference accelerometers, and the required operating curvature shapes are determined from the resulting array of frequency response functions. While setup of the experiment is reasonably quick, data acquisition can be time consuming and it is not easily amenable to automation. This paper investigates an alternative approach, which relies on the reciprocity theorem. An array of response transducers is installed on the structure, and then only a few locations are excited. There are significant benefits to this method, including the possibility of automation and remote sensing. The cost of hundreds of conventional accelerometers can be prohibitive, and therefore this project investigated using an array of low cost MEMS accelerometers. MEMS are also attractive in that they may be embedded into a composite structure during manufacture. In the study reported here the roving hammer and MEMS array methods are compared by testing a composite vertical stabilizer (tail plane) from an Airbus A320 aircraft. Despite the different test procedures, and the lower quality of the MEMS transducers, it is shown that an array of low cost MEMS transducers can determine results comparable with those obtained using high performance transducers.

フィルタ理論に基づくフレーム構造物の損傷同定解析

The structural damage identification analysis of structure models were performed by filtering algorithms as a frame work of inverse problem. In this study, three kinds of filtering algorithm based on the Wiener filter, the projection filter and the parametric projection filter were employed to detect the structural damage of a five-story frame model defined by the reduction of lateral stiffness. Natural frequencies corresponding to each eigen-mode measured by the experimental modal analysis are effectively used as the observation data characterized by the change of structural stiffness. The notable characteristics of each filtering algorithm in applying the structural damage identification analysis are made clear through several numerical calculations.

Design sensitivity analysis in large deformation elasto‐plastic and elasto‐viscoplastic problems

AbstractImplicit time integration algorithm derived by Simo for his large‐deformation elasto‐plastic constitutive model is generalized, for the case of isotropy and associative flow rule, towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters. Combining it with the general formulation of design sensitivity analysis (DSA) for non‐linear finite element transient equilibrium problem, we come at a numerically efficient, closed‐form finite element formulation of DSA for large deformation elasto‐plastic and elasto‐viscoplastic problems, with various types of design variables (material constants, shape parameters). The paper handles several specific issues, like the use of a non‐algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change. Computational examples demonstrate abilities of the formulation and quality of results. Copyright © 2005 John Wiley & Sons, Ltd.

An effective method of determining the residual stress gradients in a micro-cantilever

A method of determining the micro-cantilever residual stress gradients by studying its deflection and curvature is presented. The stress gradients contribute to both axial load and bending moment, which, in prebuckling regime, cause the structural stiffness change and curving up/down, respectively. As the axial load corresponds to the even polynomial terms of stress gradients and bending moment corresponds to the the odd polynomial terms, the deflection itself is not enough to determine the axial load and bending moment. Curvature together with the deflection can uniquely determine these two parameters. Both linear analysis and nonlinear analysis of micro-cantilever deflection under axial load and bending moment are presented. Because of the stiffening effect due to the nonlinearity of (large) deformation, the difference between linear and nonlinear analyses enlarges as the micro-cantilever deflection increases. The model developed in this paper determines the resultant axial load and bending moment due to the stress gradients. Under proper assumptions, the stress gradients profile is obtained through the resultant axial load and bending moment.

Efficient structural health monitoring for a benchmark structure using adaptive RLS filters

Structural health monitoring is the process of implementing a damage detection strategy for civil and mechanical engineering infrastructure. In this research, the structure’s health or the level of damage is monitored by identifying changes in structural parameters, by comparing the stiffness matrix of a structure with the undamaged model matrix. The two methods developed employ adaptive recursive least squares (RLS) filtering using measured or estimated structural responses and a reasonable estimate of the input force, such as an earthquake, to directly identify changes in structural stiffness for the ASCE benchmark structure health monitoring (SHM) problem. These methods focus on minimal computation to enable real-time implementation and are computationally simple, requiring 0.03 Mcycles of computation for a 4 degree of freedom (DOF) structure at a 100 Hz sampling rate and 520 Mcycles for 120-DOF at 100 Hz. These values assume no parallelisation for super-scalar digital signal processing chips and are within the capability of current digital signal processing devices. The identified changes in stiffness matrix converge to within 1.5% of the true value within 1.6 s, with an average of 0.56 s for the twelve 4-DOF and 12-DOF cases and damage patterns examined from the ASCE SHM benchmark problem.

LMS-based structural health monitoring of a non-linear rocking structure

A structure's health or level of damage can be monitored by identifying changes in structural or modal parameters. This research directly identifies changes in structural stiffness due to modelling error or damage for a post-tensioned pre-cast reinforced concrete frame building with rocking beam column connections and added damping and stiffness (ADAS) elements. A structural health monitoring (SHM) method based on adaptive least mean squares (LMS) filtering theory is presented that identifies changes from a simple baseline model of the structure. This method is able to track changes in the stiffness matrix, identifying when the building is (1) rocking, (2) moving in a hybrid rocking–elastic regime, or (3) responding linearly. Results are compared for two different LMS-based SHM methods using an L2 error norm metric. In addition, two baseline models of the structure, one using tangential stiffness and the second a more accurate bi-linear stiffness model, are employed. The impact of baseline model complexity is then delineated. The LMS-based methods are able to track the non-linearity of the system to within 15% using this metric, with the error due primarily to filter convergence rates as the structural response changes regimes while undergoing the El Centro ground motion record. The use of a bi-linear baseline model for the SHM problem is shown to result in error metrics that are at least 50% lower than those for the tangential baseline model. Errors of 5–15% with this L2 error norm are fairly stringent compared to the greater than 2 × changes in stiffness undergone by the structure, however, in practice the usefulness of the results is dependent on the resolution required by the user. The impact of sampling rate is shown to be negligible over the range of 200–1000Hz, along with the choice of LMS-based SHM method. The choice of baseline model and its level of knowledge about the actual structure is seen to be the dominant factor in achieving good results. The methods presented require 2.8–14.0 Mcycles of computation and therefore could easily be implemented in real time. Copyright © 2005 John Wiley & Sons, Ltd.

A simple LMS-based approach to the structural health monitoring benchmark problem

A structure's health or level of damage can be monitored by identifying changes in structural or modal parameters. However, the fundamental modal frequencies can sometimes be less sensitive to (localized) damage in large civil structures, although there are developing algorithms that seek to reduce this difficulty. This research directly identifies changes in structural stiffness due to modeling error or damage using a structural health monitoring method based on adaptive least mean square (LMS) filtering theory. The focus is on computational simplicity to enable real-time implementation. Several adaptive LMS filtering based approaches are used to analyze the data from the IASC–ASCE Structural Health Monitoring Task Group Benchmark problem. Results are compared with those from the task group and other published results. The proposed methods are shown to be very effective, accurately identifying damage to within 1%, with convergence times of 0.4–13.0 s for the twelve different 4 and 12 degree of freedom benchmark problems. The resulting modal parameters match to within 1% those from the benchmark problem definition. Finally, the methods developed require 1.4–14.0 Mcycles of computation and therefore could easily be implemented in real time. Copyright © 2004 John Wiley & Sons, Ltd.

Structural Damage Detection Using Empirical Mode Decomposition: Experimental Investigation

This paper presents an experimental investigation on the applicability of the empirical mode decomposition (EMD) for identifying structural damage caused by a sudden change of structural stiffness. A three-story shear building model was constructed and installed on a shaking table with two springs horizontally connected to the first floor of the building to provide additional structural stiffness. Structural damage was simulated by suddenly releasing two pretensioned springs either simultaneously or successively. Various damage severities were produced using springs of different stiffness. A series of free vibration, random vibration, and earthquake simulation tests were performed on the building with sudden stiffness changes. Dynamic responses including floor accelerations and displacements, column strains, and spring releasing time instants were measured. The EMD was then applied to measured time histories to identify damage time instant and damage location for various test cases. The comparison of identified results with measured ones showed that damage time instants could be accurately detected in terms of damage spikes extracted directly from the measurement data by EMD. The damage location could be determined by the spatial distribution of the spikes along the building. The influence of damage severity, sampling frequency, and measured quantities on the performance of EMD for damage detection was also discussed.

瞬間吸収エネルギーに基づく粘性系制振補強構造の入力低減率

A simplified method to assess the seismic performance of structures with added viscous or viscoelastic dampers is proposed. It is based on the momentary energy dissipated in structures with/without additional dampers and evaluates the reduction ratio of maximum acceleration of earthquake ground motions. The changes in structural stiffness, damping factor and seismic momentary induced energy are considered to relate the proposed method to the maximum displacement response of damped structures. Extensive time history analyses on the single-degree-of-freedom system with additional viscous or viscoelastic dampers are performed and results have shown a good agreement with those predicted by the proposed method.

Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.

Nonlinear reduced models for beam damage detection using data on moving oscillator–beam interactions

The problem of detecting local and/or distributed loss of stiffness in beam structures using vibration data generated by passage of a moving oscillator is considered. A time domain structural damage detection scheme, within finite element modeling framework, that takes into account time varying structural matrices, structural nonlinearities and spatial incompleteness of measured data, is developed. The damage parameters associated with changes in structural stiffness are shown to be governed by a set of overdetermined nonlinear equations which are solved iteratively. Illustrative examples on a geometrically nonlinear Euler–Bernoulli beam carrying a moving single degree of freedom oscillator are provided.