Changes In Modal Parameters Research Articles

Estimation of structural static displacements based on vibration data using known mass perturbation

This note presents a new method for conveniently estimating static displacements of a structure based on its vibration data. In the proposed method, structural static displacements can be estimated using a normalized modal flexibility matrix assisted by a known mass perturbation method in order to overcome several shortcomings of existing displacement sensors (e.g., linear variable differential transformers, laser Doppler vibrometer, etc) such as limitations on installation due to surrounding environments and inconvenience to the public during static loading tests. For validating the feasibility of the proposed method, experimental validation was carried out on a simply-supported beam model. In the experimental tests, the vibration data under excitation by wind loads was first measured with eight accelerometers. Then the known masses were added on a specific location on the beam and the measurements were carried out under the same settings as the first experiment. The determination of the changes in modal parameters allows estimation of the scaling constants to obtain mass-normalized mode shapes. Finally, the normalized modal flexibility matrix was calculated by using the mass-normalized mode shapes based on the scaling constants and the displacements were estimated by the normalized modal flexibility matrix. These results were compared with real static displacements estimated from the laser-type displacement sensor. It was found that they matched each other well. Therefore, the proposed method can be an effective alternative to conventional static displacement estimation.

Structural Damage Detection Based on Modal Parameters Using Continuous Ant Colony Optimization

A method is presented to detect and quantify structural damages from changes in modal parameters (such as natural frequencies and mode shapes). An inverse problem is formulated to minimize the objective function, defined in terms of discrepancy between the vibration data identified by modal testing and those computed from analytical model, which then solved to locate and assess the structural damage using continuous ant colony optimization algorithm. The damage is formulated as stiffness reduction factor. The study indicates potentiality of the developed code to solve a wide range of inverse identification problems.

Application of Bayesian-Designed Artificial Neural Networks in Phase II Structural Health Monitoring Benchmark Studies

This paper presents the results of a study into the use of pattern recognition as a method for detecting damage in structures. Pattern recognition is achieved by the use of artificial neural networks (ANNs), however, these require careful design because the number of hidden layers and the number of neurons in each hidden layer are critical to the ANN’s performance. In the current study, a Bayesian model class selection method was employed to select an optimal ANN model class that avoids ad hoc assumptions and subjective decisions in the ANN design. The objective of the research was to provide an extended study of the proposed method using the IASC-ASCE Structural Health Monitoring Phase II Simulated Benchmark Structure. Damage-induced modal parameter changes were used as a pattern feature in damage detection. Analysis showed that the proposed method is able to successfully identify damages in the benchmark structure.

Methods of Gear Damage Assessment Based on Modal Parameter Identification

With the evolution and degradation of mechanical fault, changes of the structural inherent characteristics will directly affect the overall response of system. Spur gear, which worked as the research object, is to be explored on the changes of modal parameters under different damage state. Optimum driving-point mobility and modal parameter identification is achieved by comprehensive utilization of experimental modal analysis and finite element analysis. is used to determine the experiment results is whether accurate or not. Then comparing with the differences of modal parameters, the preliminary judgment of gear damage can be made. According to the experimental data of different gears, theis taken to complete the correlation analysis and to judge the degree of the damage. The results shows that provide an effective basis for the identification of vibration mechanism and vibration characteristic of fault gear.

Modal Analysis for Crack Detection in Small Wind Turbine Blades

The aim of the present paper is to evaluate structural health monitoring (SHM) techniques based on modal analysis for crack detection in small wind turbine blades. A finite element (FE) model calibrated to measured modal parameters will be introduced to cracks with different sizes along one edge of the blade. Changes in modal parameters from the FE model are compared with data obtained from experimental tests. These comparisons will be used to validate the FE model and subsequently discuss the usability of SHM techniques based on modal parameters for condition monitoring of wind turbine blades.

Statistical decision making for damage localization with stochastic load vectors

Mechanical systems under vibration excitation are prime candidates for being modeled by linear time invariant systems. Damage detection in such systems relates to the monitoring of the changes in the eigenstructure of the corresponding linear system, and thus reflects changes in modal parameters (frequencies, damping, mode shapes) and finally in the finite element model of the structure. Damage localization using both finite element information and modal parameters estimated from ambient vibration data collected from sensors is possible by the Stochastic Dynamic Damage Location Vector (SDDLV) approach. Damage is related to some residual derived from the kernel of the difference between transfer matrices in both reference and damage states and a model of the reference state. Deciding that this residual is zero is up to now done using an empirically defined threshold. In this paper, we show how the uncertainty in the estimates of the state space system can be used to derive uncertainty bounds on the damage localization residuals to decide about the damage location with a hypothesis test.

The Analysis of Long‐Term Frequency and Damping Wandering in Buildings Using the Random Decrement Technique

The characterization and monitoring of buildings is an issue that has attracted the interest of many sectors over the last two decades. With the increasing use of permanent, continuous and real-time networks, ambient vibrations can provide a simple tool for the identification of dynamic building parameters. This study is focused on the long-term variation of frequency and damping in several buildings, using the Random Decrement Technique (RDT). RDT provides a fast, robust and accurate long-term analysis and improves the reliability of frequency and damping measurements for structural health monitoring. This reveals particularly useful information in finding out precisely how far changes in modal parameters can be related to changes in physical properties. This paper highlights the reversible changes of the structure's dynamic parameters, correlated with external forces, such as temperature and exposure to the sun. Contrasting behaviors are observed, including correlation and anti-correlation with temperature variations.

Prediction of fatigue life of glass fiber reinforced polyester composites using modal testing

The main objective of the present work is to investigate the capability of experimental modal analysis as a nondestructive tool to characterize and quantify the fatigue behavior of laminated composite beam with different lamina orientations and cantilevered boundary condition. In the present work, experimental modal analysis was conducted on the specimens previously subjected to fatigue loading to determine the modal parameters (natural frequency, damping ratio and mode shape). This was achieved through studying the response of modal testing with different specimens of different lamina orientations as a main factor affecting fatigue life. This correlates modal parameters such as: damping ratio, natural frequency and mode shape to fatigue behavior. The composite material used in experiments is glass fiber reinforced polyester (GFRP) laminate. Plane bending fatigue tests were performed on standard fatigue specimens. The fatigue test was interrupted at different fatigue life ratios (n/Nf) and modal testing was conducted to determine the change in modal parameters. The results showed that the changes of modal parameters provide a proper means for predicting the fatigue behavior of composite structures. From the experimental results of both dynamic and fatigue tests, curve fitting technique was used to correlate modal parameters to fatigue life. An exponential and quadratic equations have been obtained which correlate fatigue life ratio to damping ratio and resonant frequency respectively. It was noticed from the curves representing exponential and quadratic equations that the value of damping ratio ξ is more noticeable than the value of frequency, which means that the extent of fatigue damage determines the damping ratio, hence damping ratio could be said to be a good indicator of the fatigue life ratio.

Shaking table test and numerical damage behaviour analysis of a steel portal frame with bolted connections

This paper presents shaking-table test results of a two-story steel portal frame with bolted connections. The aim of these tests is to understand the inelastic behaviour of frame structures subjected to dynamic loads. Moreover, the purpose of these tests is to study changes in modal parameters due to the development of Low-Cycle Fatigue damage in frame connections. A nonlinear numerical simulation is performed using a Fatigue Damage-Based Hysteretic model. A comparison of results obtained from numerical analysis and those of shaking-table tests is presented. The paper concludes that the proposed numerical method can predict the response of the damaged frame.

Numerical robust stability estimation in milling process

The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.

실험 모드해석을 이용한 균열 적층복합판의 손상평가

본 연구에서는 실험적 모드해석 기법을 이용하여 캔틸레버 및 양단고정 직사각형 적층복합판의 동적 테스트가 수행되었다. 균열 성장으로 인한 손상평가를 위하여 적층복합판에 인위적인 단계별 손상(균열)을 가하였으며, 충격해머 모드실험에 의해 얻어진 주파수응답함수(FRF), MAC(Modal Assurance Criterion) 값 및 모드매개변수(진동수, 모드형상, 감쇠비)의 변화를 분석하였다. 각 단계별 손상에 대한 적층복합판의 실험적 모드매개변수를 검증하기 위하여 유한요소해석으로부터 구한 고유진동수와 모드형상을 비교하였다. 손상은 벤치마크로서의 유한요소모델을 보정하는 과정으로부터 얻게 되는 적층복합판의 기하학적 특성 및 구조적 거동의 변화를 통하여 평가될 수 있음을 보여주었다. In this study, vibration tests are performed on cantilevered and clamped-clamped laminated composite rectangular plates using experimental modal analysis technique. The damages are simulated by applying progressive line cracks to the laminated composite plates for damage evaluations due to crack growth. The changes of frequency response functions(FRFs), MAC values, and modal parameters (frequency, mode shape and damping ratio) of the damaged composite plates, which are obtained by the modal testing of impact hammer, are investigated. Each experimental modal parameter of the progressively damaged composite plates is compared with natural frequencies and mode shapes obtained by finite element analysis. It is seen that the damage can be evaluated from the changes in the geometric properties and structural behaviors of the laminated composite plates resulting from the model updating process of the finite element model as a benchmark.

Long-term monitoring of a PSC box girder bridge: Operational modal analysis, data normalization and structural modification assessment

For reliable performance of vibration-based damage detection algorithms, it is important to distinguish abnormal changes in modal parameters caused by structural damage from normal changes due to environmental fluctuations. This paper firstly addresses the modeling of temperature effects on modal frequencies of a PSC box girder bridge located on the A1 motorway in France. Based on a six-month monitoring experimental program, modal frequencies of the first seven mode shapes and temperatures have been measured at three hour intervals. Neural networks are then introduced to formulate regression models for quantifying the effect of temperature on modal parameters (frequencies and mode shapes). In 2009, this bridge underwent a strengthening procedure. In order to assess the effect of strengthening on the vibration characteristics of the bridge, modal properties had to be corrected from temperature influence. Thus, the first goal is to assess the changes on the vibration signature of this bridge induced by the strengthening. For this purpose, classical statistical analysis and clustering methods are applied to the data recorded over the period after strengthening. The second goal is to evaluate the influence of temperature effects on the clustering results. It comes that the temperature correction significantly improves the confidence in the novelty detection and in the strengthening efficiency.

Uninterrupted and accelerated vibrational fatigue testing with simultaneous monitoring of the natural frequency and damping

A mechanical system's modal parameters change when fatigue loading is applied to the system. In order to perform an accelerated vibration-based fatigue test these changes must be taken into account in order to maintain constant-stress loading. This paper presents an improved accelerated fatigue-testing methodology based on the dynamic response of the test specimen to the harmonic excitation in the near-resonant area with simultaneous monitoring of the modal parameters. The measurements of the phase angle and the stress amplitude in the fatigue zone are used for the real-time adjustment of the excitation signal according to the changes in the specimen's modal parameters. The presented methodology ensures a constant load level throughout the fatigue process until the final failure occurs. With the proposed testing methodology it is possible to obtain a S-N point of the Woehler curve relatively quickly and to simultaneously monitor the changes of the specimen's natural frequency and damping loss factor. The presented methodology with real-time control is verified on an aluminum Y-shaped specimen (106 load cycles are achieved in 21min) and is applicable to a specimen with arbitrary geometry. Besides the faster completion of the fatigue test the methodology can be adopted for the validation of the vibrational fatigue analysis.

Prestress-Force Estimation in PSC Girder Using Modal Parameters and System Identification

In this paper, a vibration-based method to estimate prestress-forces in a prestressed concrete (PSC) girder by using vibration characteristics and system identification (SID) approaches is presented. Firstly, a prestress-force monitoring method is formulated to estimate the change in prestress forces by measuring the change in modal parameters of a PSC beam. Secondly, a multi-phase SID scheme is designed on the basis of eigenvalue sensitivity concept to identify a baseline model that represents the target structure. Thirdly, the proposed prestress-force monitoring method and the multi-phase SID scheme are evaluated from controlled experiments on a lab-scaled PSC girder. On the PSC girder, a few natural frequencies and mode shapes are experimentally measured for various prestress forces. System parameters of a baseline finite element (FE) model are identified by the proposed multi-phase SID scheme for various prestress forces. The corresponding modal parameters are estimated for the model-update procedure. As a result, prestress-losses are predicted by using the measured natural frequencies and the identified zero-prestress state model.

Approximate analytical method for damage detection in free–free beam by measurement of axial vibrations

Nowadays, sophisticated structures and machinery parts are constructed by using metallic beams. Beams are widely used as structural element in civil, mechanical, naval, and aeronautical engineering. In structures and machinery, one undesirable phenomenon is crack initiation in which the impact cannot be seen overnight. Cracks develop gradually through time that lead finally to catastrophic failure. Therefore, crack should be monitored regularly with more care. This will lead to more effective preventive measure and ensure continuous operation of the structure and machine. Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters, that is, modal frequencies. Thus, vibration technique can be suitably used as a nondestructive test for crack detection of component to be tested. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole structure component. In this paper, efforts are made to develop suitable methods that can serve as the basis to detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure and also indeed, the advantage in modeling complexity. In theoretical analysis, the relationship between the natural frequencies, crack location, and crack size has been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Uncertainty Quantification for Stochastic Damage Localization for Mechanical Systems

Mechanical systems under vibration excitation are prime candidate for being modeled by linear time invariant systems. Damage detection in such systems relates to the monitoring of the changes in the eigenstructure of the corresponding linear system, and thus reflects changes in modal parameters (frequencies, damping, mode shapes) and finally in the finite element model of the structure. Damage localization using both finite element information and modal parameters estimated from ambient vibration data collected from sensors is possible by the Stochastic Dynamic Damage Location Vector (SDDLV) approach. Damage is related to some residual derived from the kernel of the difference between transfer matrices in both reference and damage states and a model of the reference state. Deciding that this residual is zero is up to now done using some empirically defined threshold. In this paper, we show how the derivation of the uncertainty of the state space system can be used to derive uncertainty on the damage localization residuals and help to decide about the damage location.

Approximate Analytical Method for Damage Detection in Beam

Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters i.e., modal frequencies. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole component. Thus vibration technique can be suitably used as a nondestructive test for testing crack detection of component. In this article efforts are made to develop a suitable method that can serve as a basis for detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent axial spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam and crack location. Also the relationship between the natural frequencies, crack location, and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Intelligent-based Structural Damage Detection Model

This article presents the application of a novel artificial neural network (ANN) model for the diagnosis of structural damage. The ANN model, denoted as the GRNNFA, is a hybrid model combining the general regression neural network model (GRNN) and the fuzzy ART (FA) model. It not only retains the important features of the GRNN and FA models (i.e., fast and stable network training and incremental growth of network structure) but also facilitates the removal of the noise embedded in the training samples. Structural damage alters the stiffness distribution of the structure and so as to change the natural frequencies and mode shapes of the system. The measured modal parameter changes due to a particular damage are treated as patterns for that damage. The proposed GRNNFA model was trained to learn those patterns in order to detect the possible damage location of the structure. Simulated data is employed to verify and illustrate the procedures of the proposed ANN-based damage diagnosis methodology. The results of this study have demonstrated the feasibility of applying the GRNNFA model to structural damage diagnosis even when the training samples were noise contaminated.

Study on the Relations between the Structural Parameters and the Dynamics Properties

The general rule that the modal parameters of linear system change with the structural parameters was discussed. The calculational method of the change of modal parameters was given on the basis of the current modal parameters and the change pattern variation of structural parameters. An example indicated that this method can greatly save computational time than repeated modal analysis. Withal, the qualitative conclusions of the change of modal parameters can be expediently gained. These results are important to amelioration and optimization design of systems.

Wavelet-Based Analysis of Power System Low-Frequency Electromechanical Oscillations

This paper addresses the use of the continuous wavelet transform (CWT) in the study of power system low-frequency electromechanical oscillations (LFEOs). Based on a modified complex Morlet mother-wavelet function, an approach is proposed to exploit the relationship between system low-frequency oscillation features and the Morlet CWT of a system ringdown signal for detection of modal parameter changes as well as for modal frequency and damping computation. Also, several guidelines for selecting the center frequency and bandwidth parameters, the scaling factor and the translation factor, are proposed in order to provide reliable modal identification estimates. The efficiency of the proposed approach is confirmed by applying it to synthetic, simulated and measured signals.