Modal Strain Energy Change Research Articles

Two-Stage Damage Identification Based on Modal Strain Energy and Revised Particle Swarm Optimization

This paper presents a novel two-stage damage detection method by integrating modal strain energy and revised particle swarm optimization (RPSO). In the first stage, the modal strain energy change ratio (MSECR) is used to roughly identify the locations of damaged elements via an appropriate MSECR threshold which is determined through parameter estimation. In the second stage, RPSO that integrates evolutionary theory with general PSO is used to precisely locate and quantify the damage with the gravity position of the selected excellent particles in the current entire population taken into consideration. Two numerical simulations and a seven-story steel frame experiment in laboratory conditions are performed to validate the proposed method, and a comparison is made between the proposed approach and existing methods. The results show that: (1) the proposed method can not only effectively locate damage, but also accurately evaluate the extent of damage. Meanwhile, it also enjoys good noise-tolerance and adaptability; (2) the damage threshold of the MSECR presented in this paper can be determined by the parameter estimation and reliability index, and then used to reduce the number of elements to be analyzed and to improve the computation efficiency in the second stage; and (3) compared with general PSO algorithm, RPSO is more efficient and robust for damage detection with a better noise-tolerance. This study shows that the proposed method can provide a reliable and fast tool to accurately identify, locate and quantify single- and multi-damage of complex engineering structures.

A multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy

The use of damage indicators based on changes of the systems’ dynamic properties before and after the occurrence of damage, generally represents a good tool in detecting the presence, the position and also the severity of the damage itself. However, signal noises, difficulties to excite systems for identifying the significant modes of vibrations, particularly the ones more sensible to the damage scenarios and also the presence of multiple damage locations can particularly affect the efficiency of these indicators. In recent years, new algorithms and innovative techniques devoted to improve the efficiency of the classical damage indicators have been carried out in many studies. In this context, the paper presents an approach for damage identification of linear systems developed by combining the use of classical damage indicators based on the modal strain energy (MSE) with a multi-stage data-fusion procedure. In particular, modal strain energy change ratios (MSECR) are evaluated by accounting different sets of modes of vibration. Then, the obtained MSECRs are converted in local decisions and involved in a multi-stage data-fusion process which provides indices able to detect the damage location and its extent. The approach provides a significant improvement of the efficiency of the damage indicators particularly in the presence of noises and multiple damages as shown by the numerical applications reported in the paper.

Damage Identification of a Beam-Like Structure Using Element Modal Strain Energies and Natural Frequencies

A two-step damage identification method based on elemental modal strain energies and natural frequencies has been presented for a beam-like structure. In the first stage, this method makes use of the change of elemental modal strain energy before and after damage to locate the potential damage regions. And in the second stage, a damage identification algorithm based on the frequency changes is developed to calculate the damage extent and further determine the actual damage locations. The performance of the proposed method is numerically demonstrated by a simply supported beam with two damage cases. Results indicate that the method can identify the damage location and quantify the damage severity accurately in a beam-like structure.

Structural Damage Localization Using D-S Evidence Theory

Damage localization is a key issue in the Structural Health Monitoring (SHM). In order to enhance the accuracy of damage localization, an approach based on D-S evidence theory is studied in this paper. First, damage results obtained from the modal strain energy change ratio (MSECR) method and the multiple damage location assurance criterion (MDLAC) method are regarded as two independent information sources, respectively. And then, the D-S evidence theory-based information fusion technique is employed to integrate these two results and make a final decision. To compare the damage identification results under different methods, a practical damage evaluation indicator is presented. Numerical study on a cantilever beam is carried out to verify the proposed method. Results indicate that the damage evaluation indicators calculated by D-S evidence theory are superior to the single method. That is to say, structural damage identification method based on D-S evidence theory performs very well in determining the damage locations.

Damage detection in truss bridges using vibration based multi-criteria approach

This paper uses dynamic computer simulation techniques to develop and apply a multi-criteria procedure using non-destructive vibration-based parameters for damage assessment in truss bridges. In addition to changes in natural frequencies, this procedure incorporates two parameters, namely the modal flexibility and the modal strain energy. Using the numerically simulated modal data obtained through finite element analysis of the healthy and damaged bridge models, algorithms based on modal flexibility and modal strain energy changes before and after damage are obtained and used as the indices for the assessment of structural health state. The application of the two proposed parameters to truss-type structures is limited in the literature. The proposed multi-criteria based damage assessment procedure is therefore developed and applied to truss bridges. The application of the approach is demonstrated through numerical simulation studies of a single-span simply supported truss bridge with eight damage scenarios corresponding to different types of deck and truss damage. Results show that the proposed multi-criteria method is effective in damage assessment in this type of bridge superstructure.

Two-Stage Multi-damage Detection Method Based on Energy Balance Equation

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on energy balance equation and evidence fusion is presented. First, a Frequency Change Identification (FCI) method and Modal Strain Energy Dissipation Ratio (MSEDR) method are utilized to preliminarily identify structural damage locations, and then a Fusion Damage Localization (FDL) method based on evidence theory is proposed to precisely detect damage locations. The FDL method mainly utilizes evidence theory to combine both the FCI localization information and the MSEDR localization information. Thus, more precise damage localization information can be acquired. After the damaged locations are determined, an Energy Balance Equation (EBE) index is presented to identify structural damage extent. Considering that strain energy dissipation should be equal to the change of modal strain energy, a quartic EBE equation is deduced, and structural damage extent can be obtained through the solution of the equation. An average quantification index is also proposed to improve identification precision. The simulation results demonstrate that the FDL method can perfectly detect structural damage locations, and the EBE index and average index can identify structural damage extent.

Structural Damage Detection Based on Strain Energy and Evidence Theory

In order to solve the damage detection problem, a damage detection method based on strain energy and evidence theory is presented in this paper. First, an evidence theory method is proposed to identify structural damage locations. Then, structural modal strain energy is utilized to quantify structural damage extents. In general, structural strain energy dissipation should be equal to the change of modal strain energy, according to this theory, a new energy equation is deduced, and structural damage extent can be obtained through the solution of the equation. The simulation results show that the method can perfectly identify damage locations and extents. Therefore, the proposed method is effective for the structural damage identification.

Application of the damage index method for plate-like structures to timber bridges

The paper presents a research recently completed by the authors utilizing a method of damage evaluation for identifying damage in timber bridges, numerically and experimentally. The method utilizes changes in modal strain energy between the undamaged and damaged states of plate-like structures. A finite element model of a laboratory timber bridge was developed to investigate the capabilities and limitations of the method to detect damage. A simple four-girder bridge was fabricated and tested in a laboratory to verify the method. The numerical studies showed that the method can correctly identify single and multiple damage locations within the bridge. The experimental studies also showed promising results for detecting severe damage, but less effective for light and medium damage. Copyright © 2009 John Wiley & Sons, Ltd.

Damage detection in jacket type offshore platforms using modal strain energy

Structural damage detection, damage localization and severity estimation of jacket platforms, based on calculating modal strain energy is presented in this paper. In the structure, damage often causes a loss of stiffness in some elements, so modal parameters; mode shapes and natural frequencies, in the damaged structure are different from the undamaged state. Geometrical location of damage is detected by computing modal strain energy change ratio (MSECR) for each structural element, which elements with higher MSECR are suspected to be damaged. For each suspected damaged element, by computing cross-modal strain energy (CMSE), damage severity as the stiffness reduction factor -that represented the ratios between the element stiffness changes to the undamaged element stiffness- is estimated. Numerical studies are demonstrated for a three dimensional, single bay, four stories frame of the existing jacket platform, based on the synthetic data that generated from finite element model. It is observed that this method can be used for damage detection of this kind of structures.

Simulation study on damage localization of a beam using evidence theory

Structural damage localization plays an important role in structural damage identification. An cumulative structural damage localization method based on evidence theory is studied in this paper. An algorithm for cumulative fusion of primary localization information is presented. In the numerical study, a fixed-end beam is inspected. Two damage cases are studied, one with single damage and the other with multiple damages. White noises are added to the beam mode shapes of the first five orders to simulate the measurement noises. First, Modal Strain Energy Change Ratio (MSECR) method is used to localize the damage elements using the noise-contaminated mode shapes. Then, the locations determined by MSECR are taken as primary information and fused cumulatively. In both the single-damage-case and the multiple-damage-case, the fused results show that damaged elements are accurately identified. Furthermore, the damage elements are distinguished much more clearly than those identified from MSECR.

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.

Condition Assessment of Structures Under Ambient White Noise Excitation

This paper proposes a damage detection method based on the wavelet packet energy of covariance of measured acceleration responses of structures under ambient excitation. It is a model-based method comparing the measured acceleration responses before and after damage occurrence. The ambient excitation is assumed to be white noise. A damage index based on the change of modal strain energy is used for damage localization. The damage quantification is performed using the sensitivity of the wavelet packet energy of the covariance function. A cantilever five-bay truss structure is used to demonstrate the efficiency of the method with three damage scenarios. The combined two-stage approach is shown capable of locating and accurately quantifying local damages in the presence of measurement noise. A nine-bay three-dimensional truss structure is also assessed in the laboratory with the proposed method, and the whole process of damage detection with incomplete and noisy measurement, initial model error, etc., is demonstrated to be successful for identifying, with good accuracy, local damages in members.

Application of the modified damage index method to timber beams

In this paper the use of two existing algorithms developed for global nondestructive evaluation to locate and evaluate localised damage in timber beams is investigated using a finite element model. These damage localisation algorithms were found, through this investigation, not to be effective in locating multiple damage scenarios and unable to evaluate the severity of damage. Hence, modifications on damage index algorithms as well as a hybrid algorithm are proposed to overcome the problems. In this study, experimental modal analysis (EMA) was used as a tool to extract mode shapes for calculating the damage index in the proposed method which utilises changes in modal strain energy between the undamaged and the damaged timber beam model. The modified damage index (MDI) method normalises the mode shape curvature and the hybrid algorithm combines the modified damage index and changes in flexibility algorithms which reflect the changes of natural frequency and mode shape. Analytical evaluations were performed to compare and verify the ability of original and modified damage localisation algorithms in locating single and multiple damage in timber beams. The modified damage index (MDI) algorithm and the hybrid damage algorithm are also used in the experimental studies to validate the effectiveness of the methods to locate and evaluate damage within timber beams by laboratory experiments.

Vibration-based damage detection in beams using genetic algorithm

In this paper, an improved GA-based damage detection algorithm using a set of combined modal features is proposed. Firstly, a new GA-based damage detection algorithm is formulated for beam-type structures. A schematic of the GA-based damage detection algorithm is designed and objective functions using several modal features are selected for the algorithm. Secondly, experimental modal tests are performed on free-free beams. Modal features such as natural frequency, mode shape, and modal strain energy are experimentally measured before and after damage in the test beams. Finally, damage detection exercises are performed on the test beam to evaluate the feasibility of the proposed method. Experimental results show that the damage detection is the most accurate when frequency changes combined with modal strain-energy changes are used as the modal features for the proposed method.

Damage localisation and severity evaluation of a beam-like timber structure based on modal strain energy and flexibility approaches

Timber bridges are often exposed to harsh environmental conditions, which, over time, can lead to deterioration resulting from decay, insect attack, weathering, and mechanical damage. In turn, this deterioration may lead to a loss of structural integrity that is detrimental to the structure and its users. Non-destructive evaluation (NDE) techniques provide effective means for assessment of current structural integrity status of given structures. As a global NDE technique, vibration-based damage identification techniques have received increasing attention for structural damage evaluation. Among them, there is a popular and promising damage identification method called the damage index method based on calculating the change of modal strain energy before and after damage. Despite its popularity, however, a systematic investigation on its capability and limitations in locating and quantifying damage is yet to be reported, especially for structures suffering multiple damage. In this paper, after reviewing the current NDE methods, the focus was set on the vibration-based NDE methods, in particular the damage index method. The investigation was based on finite element analysis (FEA) results of a timber beam by which the capability and limitation of the damage index was fully explored. As a result of the investigation, a new hybrid algorithm combining modified damage index (MDI) and change in flexibility algorithms is proposed for damage localisation and severity evaluation. The numerical results indicate that the proposed hybrid algorithms based on MDI method and flexibility have clear advantages in detecting damage locations and evaluating damage severities, especially for multiple damage cases.

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.

Damage identification in beam-type structures: frequency-based method vs mode-shape-based method

This paper presents a methodology to nondestructively locate and estimate the size of damage in structures for which a few natural frequencies or a few mode shapes are available. First, a frequency-based damage detection (FBDD) method is outlined. A damage-localization algorithm to locate damage from changes in natural frequencies and a damage-sizing algorithm to estimate crack-size from natural frequency perturbation are formulated. Next, a mode-shape-based damage detection (MBDD) method is outlined. A damage index algorithm to localize and estimate the severity of damage from monitoring changes in modal strain energy is formulated. The FBDD method and the MBDD method are evaluated for several damage scenarios by locating and sizing damage in numerically simulated prestressed concrete beams for which two natural frequencies and mode shapes are generated from finite element models. The result of the analyses indicates that the FBDD method and the MBDD method correctly localize the damage and accurately estimate the sizes of the cracks simulated in the test beam.

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 include...

Closure to “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Closure to “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Discussion of “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang

Discussion of “Structural Damage Detection from Modal Strain Energy Change” by Z. Y. Shi, S. S. Law, and L. M. Zhang