Coordinate Modal Assurance Criterion Research Articles

Assessment of the rotational stiffness of single-riveted joints in a steel lattice girder by modal analysis

Wrought-iron and mild-steel riveted lattice girders are widespread structural components of the French metallic construction heritage of 1850–1930. Many rafters and purlins of roof structures of train sheds or market halls are made of flat and angle bars assembled with single-riveted joints. The assessment of the mechanical properties of those joints is key to sensitive and targeted retrofitting operations. Despite its influence on the buckling risk of lattice girders, the out-of-plane rotational stiffness of the joints has not been investigated yet. To fill this gap, experimental and numerical investigations based on modal analysis techniques were carried out on a riveted steel lattice girder dating from 1930. The measured natural frequencies and mode shapes were used to update a finite-element model of the girder. The results suggest that the single-riveted joints exhibit a rigid behaviour in the out-of-plane direction. When numerically varying the rotational joint stiffness, two indicators seem to be relevant, one based on the study of mode shapes, and the other one linked to the presence of additional numerical modes compared to the experimental measurements. Furthermore, a numerical study was conducted to assess the potential use of the findings to develop a modal-based damage detection method for riveted joints. With only one measurement point on each lattice web member, an indicator named ΔECOMAC, derived from the enhanced coordinate modal assurance criterion (ECOMAC) proposed in the literature, appears capable of detecting and localising one or several joints presenting a loss of stiffness. Overall, this paper shows that experimental modal analysis can be an efficient tool for assessing single-riveted joints in old steel lattice girders.

Damage identification in RC bridges by confronting two approaches: visual inspection and numerical analysis

The present article aims to summarize the research study that was conducted the efficiency of methods and techniques designed for the detection and localization of faults in civil engineering structures, particularly in bridge structures. The diagnosis of a real reinforced concrete bridge by a visual inspection is presented. Then, three numerical damage detection and localization methods, namely the eigenfrequency change method, the eigenstrain change method (Coordinate Modal Assurance Criterion – CO-MAC), and the strain energy change method, are explicitly presented. Furthermore, the modeling of the bridge, before and after damage, using the Ansys software was carried out in order to identify all possible bridge defects. Afterward, the numerical results are graphically represented using the above mentioned methods. This made it possible to confirm the initial diagnosis and hence assess the damages observed on site and also in other zones.

Structural dynamic response reconstruction using self-attention enhanced generative adversarial networks

In structural health monitoring (SHM) of civil engineering structures, loss of measured structural responses inevitably occurs in practice, especially when structures encounter extreme loads. The loss of measurements severely undermines the completeness of the collected structural information and the reliability of structural condition assessment. Therefore, timely and accurate recovery of lost data is of paramount importance. This paper proposes a novel approach based on a self-attention mechanism enhanced generative adversarial network (SAGAN) for learning the intrinsic correlations between responses and reconstructing the lost data based on the accurately measured ones. SAGAN innovatively embeds the self-attention mechanism in the computational flow to facilitate the extraction of spatial and even temporal correlations among structural responses. In the experimental validations, the reconstructed responses of Guangzhou New Television Tower (GNTT) show great agreement with the true responses in forms of both time sequences and Fourier spectra. SAGAN is also versatile, demonstrating its effectiveness and robustness by reconstructing the responses competently under both ambient and typhoon excitations. In addition, by visualizing and analyzing the internal matrices and feature maps of SAGAN, it is found that the self-attention module benefits the learning of data features and improves the establishment of mappings between responses. The suitability of the proposed approach for SHM related tasks is validated by extremely consistent modal parameters. The identified natural frequencies from the reconstructed and the corresponding true responses are identical, and the Coordinate Modal Assurance Criterion (COMAC) value reaches to 99.98%.

An Effective Crack Identification in Civil Infrastructure with IoT and Improved Convolutional Neural Network

Crack identification of buildings using the Internet of things (IoT) is done by continuously monitoring the building structures that provide an early indication of cracks in buildings. The established IoT system constantly gathers structural information using sensors and stores it on a cloud server. This paper presented an innovative machine learning crack identification methodology for detecting cracks using the sensor data. Initially, the collected sensor data is pre-processed by the cloud server using the data fusion process for further processing. Subsequently, effective damage sensitive features such as mode structure (MS) features such as damage signature, streamlined damage signature index, modal assurance criterion (MAC) and coordinate MAC, improved natural frequency (INF) features, and mode structure curvature (MSC) features with curvature damage factor are extracted from the pre-processed data to differentiate cracks easily. After features are extracted, the feature score-based random projection (FSRP) technique is utilized for dimensionality reduction. Finally, hybridization of improved convolutional neural network with modified whale optimization (ICNN-MWO) detects the cracks in the civil structure utilizing the selected features. These effective classification results might alert the user when a high severity or damage is likely to occur. The implementation platform used in this work is PYTHON. The experimental outcomes of the presented technique proved that the presented work is significantly better in terms of various effective performance measures like accuracy (99.93%), mean squared error (3%), precision (99.91%), recall (99.90%), and F-measure (99.9%). The experimental results of the presented methodology provide improved performance than the existing crack identification techniques.

Bridge identification and damage detection using contact point response difference of moving vehicle

This paper presents the use of a moving vehicle to identify the bridge mode shapes and detect possible damage in the presence of bridge surface roughness. The method utilises the contact point responses at the contact between the wheel and bridge surface, which can be obtained from the vehicle responses and has a direct relation with the bridge responses and surface roughness. A double-pass mass-addition technique is proposed to obtain the contact point response difference using a test vehicle installed with sensors. Then the bridge frequencies can be identified from its spectrum, while the mode shapes can be further obtained by signal filtering and Hilbert transform. Simulation results show that the adverse effect of surface roughness on the contact point acceleration difference is largely reduced. The first three frequencies and mode shapes can be extracted with satisfactory accuracy. Multiple damage locations can be identified by performing wavelet transform on the contact point displacement difference and applying coordinate modal assurance criterion to the mode shapes constructed. The factors that may affect the performance of the proposed method are also investigated, including the distribution of added mass, measurement noise, speed of the test vehicle and co-existing traffic. Experimental validation is conducted on a simply supported aluminium channel beam with artificial roughness carrying a moving model vehicle. The results show that the proposed methodology for bridge identification works in the presence of road surface roughness.

Viability of Image Compression in Vibrothermography

This research focuses on the verification of the viability of image compression in infrared thermography in order to address the problem of data storage. Specifically, images from vibrothermographic tests were utilized due to their special characteristics compared to the results from alternative infrared thermography techniques, which are able to introduce additional uncertainties to the compression process. In this research, an adaptive algorithm based on the lifting discrete wavelet transform and set-partitioning embedded blocks was used for image compression. Five different methods, namely the compression ratio, mean squared error, peak signal-to-noise ratio, structural similarity index and coordinate modal assurance criterion, were applied to evaluate the performance of the compression process while identifying and locating the regions affected more significantly after image compression. Feature extraction through the independent component analysis was then applied to the images to separate the features such as the hot spots so that the influence from the image compression process on each important feature could be evaluated independently. In this article, the theoretical background of the applied data processing techniques is firstly presented. Through two sets of data acquired from vibrothermographic tests on an aerospace-grade composite plate containing delamination, the effects of the image compression process on the relevant hot spots are evaluated, and the effectiveness of the compression process is verified. It is demonstrated that the compression process was able to reduce the size of the images significantly without adversely affecting the quality of the important features indicating the presence of damage. The major characteristics of the key features have been successfully preserved after effective image compression.

Damage Identification in Hemp Fiber (Cannabis sativa) Reinforced Composite Plates Using MAC and COMAC Correlation Methods: Experimental Study

ABSTRACT The use of hemp fiber has increased in recent decade due to the increasing demand for sustainable, recyclable, and biodegradable materials. Hemp fibers are obtained from the stem of a plant for the reinforcement of composites. In this work, experimental modal analysis was performed on a hemp fiber (Cannabis sativa) reinforced plate with a free-free condition. Preliminary results of modal parameter identification of multiple damage detection are presented. To consider multiple damage effects, an undamaged plate including six damaged scenarios are considered. For each scenario, natural frequencies with mode shape were identified with accuracy using accelerometer sensors and impact hammer. Measured the natural frequencies and mode shape for undamaged and damaged plates are compared with each other. To establish the correlation between undamaged and damaged plate, modal assurance criterion (MAC) are considered. In addition, coordinated multiple modal assurance criterion (COMAC) considered that were highly sensitive to the severity of damage scenarios with sufficient mode consideration. It is clearly observed that a COMAC plot results show more sensitive compared to MAC plot results. It reveals that even small level damage present in the specimen can be easily examined through coordinate modal assurance criterion.

An implementation of error localization algorithms for model calibration of dynamical systems

The paper discusses the implementation of three Error Localization Algorithms (ELA), test assessment metrics, and an example of model calibration. During model calibration, users routinely perform sensitivity studies to determine critical parameters for model adjustments. Although this makes engineering sense, sensitivity information only reflects parameter importance and not necessarily model deficiencies. Instead, the task of identifying model deficiencies is best suited for ELA in which measured data is used directly to identify potential problem areas in the model. Three ELA methods are applied in this work: (1) Coordinate Modal Assurance Criterion (CoMAC), (2) Robust Model Error, and (3) Analytical Dynamic Model Improvement (ADMI). To establish credibility of the ELA approaches, data from two analytical examples are used with ELA to identify known problem areas. Of the three ELA approaches implemented, only ADMI correctly identified known problem areas in the model. An example application of the ADMI algorithm is presented to identify problem areas of an isogrid-panel model from experimental data. These identified areas are then used to calibrate a model.

Sensor location in concrete slabs with various layout of opening using modified ‘FEMS-COMAC’ approach

Two-way concrete slabs are widely used around the world for the construction of many types of infrastructures and common buildings. The optimal sensor placement (OSP) in slabs with various opening positions is the most important issue in structural health monitoring (SHM) to increase reliability. In this study, a novel approach of OSP was evaluated to obtain the number and placement of sensors using examination of the closed loop performance. The nonlinear finite element (NFE) was used to discretize the mechanism behavior of slab. Multi-Objective Optimization based on the coordinate modal assurance criterion (COMAC) and cost considerations was considered in the optimization processes. All of the analysis, discretization and optimization process was designed and developed as a novel approach in Matlab by the author under the name ‘FEMS-COMAC’ (FEM analysis of slab with COMAC). The points in the finite element method (FEM) mesh were classified as line by line information along the slab. The OSP in each line was optimized according to the objective function. The slabs with various width, thickness, aspect ratio and opening position were selected as case studies. The results of the OSP using the COMAC algorithm around the slab openings were compared with the novel ‘FEMS-COMAC’ method. The statistical analysis according Mann-Whitney criteria shows that there were significant differences between them in some of the case studies (mean P-value=0.54).

Modal flexibility based damage detection for suspension bridge hangers: A numerical and experimental investigation

This paper addresses the problem of damage detection in suspension bridge hangers, with an emphasis on the modal flexibility method. It aims at evaluating the capability and the accuracy of the modal flexibility method to detect and locate single and multiple damages in suspension bridge hangers, with different level of severity and various locations. The study is conducted numerically and experimentally on a laboratory suspension bridge mock-up. First, the covariance-driven stochastic subspace identification is used to extract the modal parameters of the bridge from experimental data, using only output measurements data from ambient vibration. Then, the method is demonstrated for several damage scenarios and compared against other classical methods, such as: Coordinate Modal Assurance Criterion (COMAC), Enhanced Coordinate Modal Assurance Criterion (ECOMAC), Mode Shape Curvature (MSC) and Modal Strain Energy (MSE). The paper demonstrates the relative merits and shortcomings of these methods which play a significant role in the damage detection of suspension bridges.

Republished Paper. Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms

Damage detection and localization in civil engineering constructions using dynamic analysis has become an important topic in recent years. This paper presents a methodology based on non-destructive detection, localization and quantification of multiple damages in simple and continuous beams, and a more complex structure, namely two-dimensional frame structure. The proposed methodology makes used of Firefly Algorithm and Genetic Algorithm as optimization tools and the Coordinate Modal Assurance Criterion as an objective function. The results show that the proposed combination of Coordinate Modal Assurance Criterion and Firefly Algorithm or Genetic Algorithm can be easily used to identify multiple local structural damages in complex structures. However, the convergence rate becomes slower for the case of multiple damages compared to the case of single damage. The effect of noise on the algorithm is further investigated. It is found that the proposed technique is able to detect the damage location and its severity with high accuracy in the presence of noise, although the convergence rate became slower than in the case when no noise is present. It is also found that the convergence rate of Firefly Algorithm is much faster than that of Genetic Algorithm.

Retraction: Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms

Retraction: Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms

Automated model updating of multiple cracked cantilever beams for damage detection

This paper presents a detailed study on the automated model updating of a cantilever beam with box cross-section including multiple cracks for damage detection. To consider multiple crack effects, a cantilever beam with cracks is considered under six damage scenarios. Finite element models are first constituted in ANSYS software for numerical solution. The results are validated by experimental measurements. For this aim, ambient vibration tests are performed to extract the dynamic characteristics using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. Calculated and measured natural frequencies and corresponding mode shapes for undamaged and damaged beams are compared. For damage detection, automated Model Update is carried out using the modal sensitivity method based on the Bayesian parameter estimation to minimize the difference between the calculated and measured results. Modal Assurance Criterion (MAC) and Coordinate Modal Assurance Criterion (COMAC) factors that show the correlation between the measured and calculated mode shapes are also employed to identify and locate damaged elements within the beam.

Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms

Damage detection and localization in civil engineering constructions using dynamic analysis has become an important topic in recent years. This paper presents a methodology based on non-destructive detection, localization and quantification of multiple damages in simple and continuous beams, and a more complex structure, namely two-dimensional frame structure. The proposed methodology makes used of Firefly Algorithm and Genetic Algorithm as optimization tools and the Coordinate Modal Assurance Criterion as an objective function. The results show that the proposed combination of Coordinate Modal Assurance Criterion and Firefly Algorithm or Genetic Algorithm can be easily used to identify multiple local structural damages in complex structures. However, the convergence rate becomes slower for the case of multiple damages compared to the case of single damage. The effect of noise on the algorithm is further investigated. It is found that the proposed technique is able to detect the damage location and its severity with high accuracy in the presence of noise, although the convergence rate became slower than in the case when no noise is present. It is also found that the convergence rate of Firefly Algorithm is much faster than that of Genetic Algorithm.

Assessment of shear damaged and NSM CFRP retrofitted reinforced concrete beams based on modal analysis

Near Surface Mounted (NSM) Carbon Fiber Reinforced Polymer (CFRP) has shown to be a very effective technique for shear strengthening of reinforced concrete beams. Previous work showed important strength increases due to application of NSM CFRP in undamaged beams. However, few results were found in the literature to show the effectiveness of the technique for retrofitting damaged beams, especially those subjected to shear. On the other hand, several studies have shown the applicability of damage identification techniques based on modal analysis in different types of structures. No studies were found on the application of such techniques to identify damage generated by shear, which causes a cracking pattern significantly differently from flexural cracking. The purpose of this investigation is therefore to identify damages generated by shear in reinforced concrete beams through modal analysis techniques. In the same way, for retrofitted beams, to verify the changes of dynamic properties during application of NSM CFRP technique. For this purpose, reinforced concrete beams were produced and some of them were subjected to pre-loads corresponding to 40% and 70% of beam strength. These beams were then retrofitted by NSM CFRP to identify experimentally the efficiency of the procedure. Prior and after any phase of damage and retrofitting, modal analysis were performed allowing comparisons of dynamic properties. Comparisons of natural frequencies, vibration modes, Modal Assurance Criterion, Coordinate Modal Assurance Criterion, modal curvatures and damage index allowed damage identification and localization in most cases. However, it was not possible to identify significant changes of dynamic properties when the beams were retrofitted, although the important increases in strength. In light of these results it is believed that the NSM CFRP technique could not improve significantly the stiffness of the structural element while increased their strength.

A Correlation Improvement Technique for Model Updating of Structures

This study proposes a new correlation improvement technique for the optimum node removal location to get improved modal assurance criterion (MAC) matrix. The technique is applied to updating of the finite element model (FEM) of a structure. The developed routine is tried on a utility helicopter. It is proven that it is capable of showing better performance than the coordinate MAC (coMAC), commonly used in such analyses. Commercial software is utilized for the finite element analysis of the helicopter fuselage and tail. Experimental modal analyses are also performed for updating the model for tail of the helicopter to demonstrate the effectiveness of the new technique.

Vibration-based damage detection for a composite helicopter main rotor blade

This work presents experimental results of two damage detection techniques based on modal properties, with the application on a full-size composite helicopter main rotor blade. The damage detection methods used in this study are the coordinate modal assurance criterion (COMAC) and the modal strain energy method, which are respectively based on the comparison of vibration modes and on the comparison of the modal strain energy of a beam. Modal parameters were obtained with experimental modal analysis and damage was introduced artificially on the blade by attaching a small mass to it, changing its global properties in this way. Finally, experimental results for the damage detection technique are shown for both methodologies, and remarks concerning sensitivity and robustness of the methods are discussed.

Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection

We perform nonlinear system identification (NSI) on the acceleration signals that were experimentally measured at ten, almost evenly spaced positions along a cantilever beam undergoing vibro-impacts between two rigid stops with clearances. Our goal is to characterize the nonlinear dynamics due to vibro-impacts with a view toward structural health monitoring (SHM) and damage detection (DD). The NSI methodology is based on the correspondence between analytical and empirical slow-flow dynamics, with the first step requiring empirical mode decomposition (EMD) analysis of the measured time series leading to sets of intrinsic modal oscillators (IMOs) governing the vibro-impact dynamics at different time scales. By comparing the spatiotemporal variations of the nonlinear modal interactions (and hence the IMOs), we examine how vibro-impacts influence the low- and high-frequency modes in global and local senses. In applications of the NSI results to SHM/DD, we calculate typical measures such as the modal assurance criterion (MAC) and the coordinate modal assurance criterion (COMAC) by extracting information about the mode shape functions from the spatiotemporal IMO solutions. Whereas the MAC provides a global aspect of damage occurrence (i.e., which modes are more affected by induced defects), the COMAC can narrow down the damage locations (i.e., where in the structure defects exist that yield low correlation values in specific modes).

Propagation of mode shape errors in structural identification

It is of interest to the modal testing and health monitoring community to quantify how an error in any identified mode shape propagates to the identified flexibility matrix. Here this problem is investigated in a probabilistic framework. The approach followed involves deriving analytical expressions to track how errors, due to random deviations between identified and “true” mode shapes, propagate to the Modal Assurance Criterion (MAC) and the Coordinate Modal Assurance Criterion (COMAC) values as well as the estimated flexibility matrix. The comparison of the expected values and variances of these errors identifies the inconsistency between the magnitude of errors in the MAC and COMAC values and the identified flexibility matrix. The analytical results are further validated via Monte Carlo simulations. Finally, two mode shape comparison criteria, termed as the Flexibility Proportional Modal Assurance Criterion (FPMAC) and the Flexibility Proportional Coordinate Modal Assurance Criterion (FPCOMAC), are proposed. These new criteria aim to mimic the expected error in the predicted flexibility matrix in a direct comparison of the identified and “true” mode shapes, and hence they can be used to complement MAC and COMAC in interpreting the analysis results.

Locating damaged storeys in a shear building based on its sub-structural natural frequencies

Vibration-based damage detection methods are simple and conventionally adopted to monitor the structural health of buildings. This work proposes a simple and efficient approach to locating the storeys whose properties (stiffness and mass) change in the life cycle of a shear building. The storeys that may be damaged are determined by comparing the natural frequencies of sub-structures in different stages in the life cycle of a building. An appropriate ARX (autoregressive with exogenous input) model of a sub-structure of a shear building is established from the sub-structural dynamic responses in terms of acceleration or velocity. The parameters in an ARX model of a sub-structure are identified through the continuous wavelet transform, and the natural frequency and damping ratio of the sub-structure are estimated directly through these identified parameters. The effectiveness of the proposed procedure is verified using the numerically simulated earthquake acceleration responses and ambient vibration responses of a six-storey shear building that is damaged at one or two storeys with different damage levels. The effect of noise on the accuracy of the proposed approach is also examined. The proposed scheme is demonstrated to be superior to COMAC (Coordinate Modal Assurance Criterion) and the frequency response function curvature method in identifying damaged storeys. The proposed method is also applied to process the dynamic responses of three five-storey steel frames, which are not shear buildings, in shaking table tests. The differences in the floor mass or storey stiffness among these frames are accurately reflected in the sub-structural natural frequencies that are obtained by the proposed approach.