Changes In Modal Parameters Research Articles

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.

Nondestructive Detection of Internal Delamination by Vibration-based Method for Composite Plates

A method for locating internal delamination in multilayer composite plates is presented. A finite element method for composite plates is developed to investigate the relationship between delamination and change of modal parameters. The mechanism of the mode-dependent energy dissipation of composite plates is revealed by numerical analysis of delamination-induced variations of modal parameters. Experiments are carried out using piezoelectric actuator and accelerometer to measure the dynamic response to sinusoidal sweep excitation for several cantilever composite plates. The results show that the region of internal delamination in composite plates can be predicted according to the measured acceleration response and the computed modal strain energy.

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The rotation of spacecraft flexible appendage may cause changes in modal parameters. For this time-varying system, the computation cost of the frequently-used singular value decomposition (SVD) identification method is high. Some control problems, such as the self-adaptive control, need the latest modal parameters to update the controller parameters in time. In this paper, the projection approximation subspace tracking (PAST) recursive algorithm is applied as an alternative method to identify the time-varying modal parameters. This method avoids the SVD by signal subspace projection and improves the computational efficiency. To verify the ability of this recursive algorithm in spacecraft modal parameters identification, a spacecraft model with rapid rotational appendage, Soil Moisture Active/Passive (SMAP) satellite, is established, and the time-varying modal parameters of the satellite are identified recursively by designing the input and output signals. The results illustrate that this recursive algorithm can obtain the modal parameters in the high signal noise ratio (SNR) and it has better computational efficiency than the SVD method. Moreover, to improve the identification precision of this recursive algorithm in the low SNR, the wavelet de-noising technology is used to decrease the effect of noises.

Increased reliability of reference-based damage identification techniques by using output-only data

During the past few years, a considerable number of damage identification techniques have been proposed and successfully tested on vibration data obtained from mechanical structures. Most vibration-based methods identify damage by interpreting measured changes in modal parameters. In practice, damage identification problems can occur due to minor changes in the boundary conditions of the test set-up especially if classic input–output vibration measurements are required for the diagnosis of a lightweight structure. In this contribution, a comparison is made between an input–output and output-only damage identification set-up for an aluminum beam structure suffering from fatigue-induced crack formation.

The dynamic analysis of a cracked Timoshenko beam by the spectral element method

The aim of this paper is to introduce a new finite spectral element of a cracked Timoshenko beam for modal and elastic wave propagation analysis. The proposed approach deals with the spectral element method. This method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure. In the paper, the results of the change in modal parameters due to crack appearance are presented. The influence of the crack parameters, especially of the changing location of the crack, on the wave propagation is examined. Responses obtained at different points of the beam are presented. Proper analysis of these responses allows one to indicate the crack location in a very precise way. This fact is very promising for the future work in the damage detection field.

Application of ARMAV models to the identification and damagedetection of mechanical and civil engineering structures

In this paper, the application of auto-regressive moving averagevector models to system identification and damage detection isinvestigated. These parametric models have already been applied for theanalysis of multiple input-output systems under ambient excitation. Theirmain advantage consists in the capability of extracting modal parametersfrom the recorded time signals, without the requirement of excitationmeasurement. The excitation is supposed to be a stationary Gaussian whitenoise. The method also allows the estimation of modal parameteruncertainties. On the basis of these uncertainties, a statistically baseddamage detection scheme is performed and it becomes possible to assesswhether changes of modal parameters are caused by, e.g. some damage orsimply by estimation inaccuracies. The paper reports first an example ofidentification and damage detection applied to a simulated system underrandom excitation. The `Steel-Quake' benchmark proposed in the framework ofCOST Action F3 `Structural Dynamics' is also analysed. This structure wasdefined by the Joint Research Centre in Ispra (Italy) to test steelbuilding performance during earthquakes. The proposed method gives anexcellent identification of frequencies and mode shapes, while dampingratios are estimated with less accuracy.

Time Domain Identification of Frames under Earthquake Loadings

The purpose of this paper is to examine the adaptive identification method and the nonlinear system identification technique through numerical simulation on seismic response of building structures. For the identification of a time-variant system and a system with an abrupt change of modal parameters, two parameter adaptation algorithms in recursive identification methods are discussed: recursive least square algorithm with constant trace and adaptive fading Kalman filter method. Based on the equivalent linear model, the time-variant model parameters can be identified. The tracking ability on the identification of a time-variant system is discussed. For the identification of the nonlinear system, the forward including algorithm and the neural network training algorithm were used to estimate the modal parameter of the nonlinear autoregressive moving average model, and the accuracy on the predicted output of nonlinear model identification was discussed.

Use of modal testing to identify damage on steel members

There is a need to construct a structural monitoring system for assessment of current health condition of deteriorating structures and the prediction of their response under load. In this paper, basic experimental tests and numerical analysis are performed to investigate the feasibility of using modal testing techniques as a tool for structural health monitoring and damage detection. The objective of this study is to investigate the change of modal parameters due to imposed damage, and to verify the most sensitive modal parameters for identifying and locating the damage. Rectangular tudes, twelve feet in length, were tested for this purpose. They have either one or two spans and each of three cases has its own damage scenario. The modal parameters considered are modal frequency, displacement mode shape (DMS) and strain mode shape (SMS). The coordinate modal assurance criterion (CoMAC), and the modal vector error (MVE) are used to quantify the change of mode shape between the undamaged and damaged structures. The change of frequency can be measured rather precisely in this experimental test, but the location of damage could not be detected by use of DMS change with CoMAC. It is suggested that the DMS or preferably the SMS be used in collaboration with MVE as a more effective method of locating damage.

IDENTIFICATION FOR CRITICAL FLUTTER LOAD AND BOUNDARY CONDITIONS OF A BEAM USING NEURAL NETWORKS

With the increasing size and complexity of machines and vessels, the inverse problems of continuous bodies are becoming important. In this paper, the possibility of using a Multilayer Perceptron network trained with the Backpropagation Algorithm for detecting the critical flutter load and boundary conditions of tapered beams is studied. The beam model considered is a Timoshenko beam, which, with the use of the transfer matrix method, estimates the changes in various modal parameters caused by the shape parameters and boundary conditions of beams.

An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge

Damage detection techniques have been proposed to exploit changes in modal parameters and to identify the extent and location of damage in large structures. Most of such techniques, however, generally neglect the environmental effects on modal parameters. Such environmental effects include changes in loads, boundary conditions, temperature, and humidity. In fact, the changes due to environmental effects can often mask more subtle structural changes caused by damage. This paper examines a linear adaptive model to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Data from the Alamosa Canyon Bridge in the state of New Mexico were used to demonstrate the effectiveness of the adaptive filter for this problem. Results indicate that a linear four-input (two time and two spatial dimensions) filter to temperature can reproduce the natural variability of the frequencies with respect to time of day. Using this simple model, we attempt to establish a confidence interval of the frequencies for a new temperature profile in order to discriminate the natural variation due to temperature. Copyright © 1999 John Wiley & Sons, Ltd.

DYNAMIC BENDING AND TORSION STIFFNESS DERIVATION FROM MODAL CURVATURES AND TORSION RATES

In order to maintain the reliability of civil engineering structures, considerable effort is currently spent on developing a non-destructive vibration testing method for monitoring the structural integrity of constructions. The technique must be able to observe damage, secondly to localize the damage; and finally to give an idea of the severity of the damage. Within the framework of relating changes of measured modal parameters to changes in the integrity of the structure, it is important to be able to determine the dynamic stiffness in each section of the structure from measured modal characteristics.A damaged structure results in a dynamic stiffness reduction of the cracked sections. The dynamic stiffnesses provide directly an indication of the extension of the cracked zones in the structure. The dynamic stiffness reduction can also be associated with a degree of cracking in a particular zone.In an experimental programme, a concrete beam of 6 m length is subjected to an increasing static load to produce cracks. After each static perload, the beam is tested dynamically in a free–free set-up. The change in modal parameters is then related to damage in the beam.The technique that will be presented in the paper to predict the damage location and intensity is a direct stiffness derivation from measured modal displacement derivatives. Using the bending modes, the dynamic bending stiffness can be derived from modal curvatures. Using the torsional modes, the dynamic torsion stiffness can be derived from modal torsion rates.

An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge

Damage detection techniques have been proposed to exploit changes in modal parameters and to identify the extent and location of damage in large structures. Most of such techniques, however, generally neglect the environmental effects on modal parameters. Such environmental effects include changes in loads, boundary conditions, temperature, and humidity. In fact, the changes due to environmental effects can often mask more subtle structural changes caused by damage. This paper examines a linear adaptive model to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Data from the Alamosa Canyon Bridge in the state of New Mexico were used to demonstrate the effectiveness of the adaptive filter for this problem. Results indicate that a linear four-input (two time and two spatial dimensions) filter to temperature can reproduce the natural variability of the frequencies with respect to time of day. Using this simple model, we attempt to establish a confidence interval of the frequencies for a new temperature profile in order to discriminate the natural variation due to temperature. Copyright © 1999 John Wiley & Sons, Ltd.

Effect of excitation type on dynamic system parameters of a reinforced concrete bridge

Damage detection in civil engineering structures using the change in dynamic system parameters has gained a lot of scientific interest during the last decade. By repeating a dynamic test on a structure after a certain time of use, the change in modal parameters can be used to quantify and qualify damages. To be able to use the modal parameters confidentially for damage evaluation, the effect of other parameters such as excitation type, ambient conditions,... should be considered. In this paper, the influence of excitation type on the dynamic system parameters of a highway prestressed concrete bridge is investigated. The bridge, B13, lies between the villages Vilvoorde and Melsbroek and crosses the highway E19 between Brussels and Antwerpen in Belgium. A drop weight and ambient vibration are used to excite the bridge and the response at selected points is recorded. A finite element model is constructed to support and verify the dynamic measurements. It is found that the difference between the natural frequencies measured using impact weight and ambient vibration is in general less than 1%.

DETECTION OF STRUCTURAL FAULTS BY MODAL DATA, LOWER BOUNDS AND SHADOW SITES

Different algorithms have recently been developed for the diagnosis of many types of civil and mechanical structures using modal data, such as natural frequencies and mode shapes. Although many solutions have been proposed, some important questions seem to be absent in the technical literature. If changes in a structure's modal parameters are able to reflect structural faults, it is important to know what is the smallest detectable physical change in that structure.It is suggested that damage detection by means of modal data can be useful for macro-damage rather than for micro-damage. This resulted from numerical and experimental tests using a simple correlation between measurement noise and sensitivity of modal data, with respect to structural changes in different parts of a system. An automatic sensitivity approach is presented to obtain the lower bound of structural faults for the particular structure under study. The same automatic procedure is able to detect possible shadow sites within the frequency range analyzed.

Effect of fatigue loading on the modal properties of composite structures and its utilization for prediction of residual life

The design of composite structures for fatigue loading utilizes S- N curves to predict the fatigue life based on coupon testing. Due to the complex manufacturing process, the initial fabrication inconsistencies may cause the predicted number of cycles to failure to be off by one or two orders of magnitude. An experimental method is developed to predict the residual fatigue life of composite structures and continuously refine the prediction during the service life of these structures. Global effects on modal parameters, natural frequencies and damping ratios are investigated during the fatigue process. The Random Decrement signal processing technique is used. Changes of modal parameters are correlated with the prediction of fatigue failure life for selected graphite/epoxy composite specimens. The nature of the proposed method lends itself to real-time applications, especially, in service structures, as a nondestructive indicator.

Damage Identification in Continuum Structures From Vibration Modal Data

ABSTRACTA novel procedure for damage identification of continuum structures is proposed, where both the location and the extent of structural damage in continuum structures can be correctly determined using only a limited amount of measurements of incomplete modal data. On the basis of the exact relationship between the changes of structural parameters and modal parameters, a computational technique based on direct iteration and directly using incomplete modal data is developed to determine damage in structure. Structural damage is assumed to be associated ith a proportional (scalar) reduction of the original element stiffness matrices, equivalent to a scalar reduction of the material modulus, which characterises at Gauss point level. Finally, numerical examples for plane stress problem and plate bending problem are utilised to demonstrate the effectiveness of the proposed approach.

Nondestructive Evaluation of Thermally Shocked Silicon Carbide by Impact-Acoustic Resonance

Monolithic ceramics are under consideration as structural components for hot-stage sections of gas-fired turbine engines. In addition to manufacturing quality control, other important aspects for this application include life prediction modeling and time between engine overhauls. One nondestructive evaluation (NDE) method that provides information about material condition involves an analysis of resonant vibrations. In previous work by this general approach, changes in modal parameters have been related to bulk defect mechanisms such as microcracking due to thermal shock damage. In this work resonant vibrations from monolithic ceramic specimens were excited by an instrumented impact hammer and detected by a noncontact acoustic microphone over frequencies up to 100 kHz. Computer-based analysis of vibration signatures from test specimens allowed extraction of modal frequencies and damping constants. Downward shifts in detected resonant frequencies and increases in internal friction or (specific) damping capacity measurements were obtained from SiC cylindrical rings, and these measurements were shown to relate to thermal shock severity. This NDE method not only provides measurable parameters that could be used as accept–reject criteria for in-line process inspection, it also provides a means for tracking the mechanical integrity of in-service engine components to support life prediction modeling.

Measurement of the modal parameters of a space structure in zero gravity

An analytic and experimental study of the changes in the modal parameters of space structural test articles from 1 to 0 g is presented. Deployable, erectable, and rotary modules were assembled to form three one- and two-dimensional structures in which variations in bracing wire and rotary joint preload could be introduced. The structures were modeled as if hanging from a suspension system in 1 g, and unconstrained, as if free floating in 0 g. The analysis is compared with ground experimental measurements made on a spring/wire suspension system with a nominal plunge frequency of 1 Hz and with measurements made on the Shuttle middeck. The degree of change in linear modal parameters, as well as the change in nonlinear nature of the response, is examined. Trends in modal parameters are presented as a function of force amplitude, joint preload, and ambient gravity level.

Perturbation method applied to vibration monitoring of slotted beams

Vibration signals can be used in monitoring the structural integrity of steel beams. If the beams are cracked or slotted, the resonant frequencies will decrease and the mode shapes will change depending on the size and the location of the defects. The current study involves applying a perturbation method in prediction of resonant frequencies and mode shapes of a slotted beam. Modal analysis techniques are used in estimation of modal parameters including resonant frequencies, damping, and mode shapes. The effect of using the modal analysis method on the frequency resolution will be discussed. A large discrepancy was observed between experimental frequency shifts and those predicted by the perturbation method for relatively large slots. As required by the method itself, perturbation to the system (in this case is slot) should be small, which will lead to small changes in modal parameters. These results are compared with those obtained previously [Man etal., J. Acoust. Soc. Am. 95, 2029–2037 (1994)] by solving the exact vibration equation for a slotted beam. It is clear that the perturbation technique is not accurate, although it does give correct qualitative predictions which are not readily apparent with the other approach.

Modal Analysis Of Stepped Beams With Piezoelectric Materials

A stepped beam model is developed to predict analytically the natural frequencies and mode shapes of a uniform flexible beam with surface bonded piezoelectric materials. The stepped portion includes the inertia and stiffness of the piezoelectric material and bonding layer, and the shear deformation and rotary inertia of the beam are also considered. By using the analytical modal solution, the stepped beam model is further extended to investigate its modal parameter changes under piezoelectric actuation. It is shown that for a length ratio of 16·67 and thickness ratio of four between the beam and piezoelectric material, the first natural frequency can be increased by as much as 5% compared with that of a uniform beam model. In addition, there exists a generalized stiffness from piezoelectric actuation, and it can be either positive or negative, depending on the locations of the piezoelectric actuators. The analytical predictions are verified by experiments.