Updated Finite Element Model Research Articles

Stiffness identification of deteriorated PC bridges by a FEMU method based on the LM-assisted PSO-Kriging model

Stiffness identification from measured responses is an important part of structural health monitoring, in which finite element model updating (FEMU) is a widely studied method. However, the practicability of this method still needs to be improved when applied to large deteriorated civil structures. In this paper, a new FEMU strategy based on the PSO (particle swarm optimization)-Kriging model assisted by the Levenberg–Marquardt (LM) algorithm is proposed for the stiffness identification of deteriorated long-span prestressed concrete (PC) continuous girder bridges. The strategy is implemented in two phases: global stiffness identification based on the LM algorithm is adopted in phase I to determine the sampling interval of the identification parameters; then, in phase Ⅱ, the girder is divided into segments, and the accurate value of each segment stiffness is determined. The PSO-Kriging model is employed to facilitate the high accuracy and efficiency of the method. The effectiveness of the proposed method is demonstrated through comparison studies in an existing experiment and a full-scale test, and the parameter selection of the method is also discussed.

Analysis of the Recorded Response of a School Building Heavily Damaged by the 2016 Central Italy Earthquake

The OSS (acronym of the Italian “Osservatorio Sismico delle Strutture”) is a network of permanent seismic monitoring systems installed on about 150 buildings in Italy. Each system consists of a number of sensors sufficient to completely describe the dynamic response of the structure. Structural typologies have been selected according to their representativeness of the public building stock and to their importance for emergency management. Data available for each building include: structural survey and in situ tests on materials, experimental modal analysis, finite element models and model updating. In the above framework, a school building located in Amatrice, a small town in the meizoseismal area heavily impacted by the 2016 Central Italy earthquake, is one of the buildings instrumented by the OSS; thus, its monitored dynamic response, including that under the main shock, is available. The building showed diffused huge damage with partial collapses. Firstly, a linear finite element model is used in the interpretation of small amplitude vibrations in order to give a reliable dynamic characterization of the initial conditions of the structure. Some relevant quantities of the recorded structural motion under seismic excitation are used to describe the experimental dynamic behaviour. The recorded displacements are then applied to a nonlinear finite element model, and the numerical results are compared with the experimental evidence. The main aim is to discuss the capability of the combined use of experimental response and computational tools in quantifying damage suffered by a structure on the basis of the measured response to an earthquake.

Real-Time Structural Health Monitoring and Damage Identification Using Frequency Response Functions along with Finite Element Model Updating Technique.

Throughout service, damage can arise in the structure of buildings; hence, their dynamic testing becomes essential to verify that such buildings possess sufficient strength to withstand disturbances, particularly in the event of an earthquake. Dynamic testing, being uneconomical, requires proof of concept; for this, a model of a structure can be dynamically tested, and the results are used to update its finite element model. This can be used for damage detection in the prototype and aids in predicting its behavior during an earthquake. In this instance, a wireless MEMS accelerometer was used, which can measure the vibration signals emanating from the building and transfer these signals to a remote workstation. The base of the structure is excited using a shaking table to induce an earthquake-like situation. Four natural frequencies have been considered and six different types of damage conditions have been identified in this work. For each damage condition, the experimental responses are measured and the finite element model is updated using the Berman and Nagy method. It is seen that the updated models can predict the dynamic responses of the building accurately. Thus, depending on these responses, the damage condition can be identified by using the updated finite element models.

Finite Element Model Updating Approach for Structural Health Monitoring of Lightweight Structures Using Response Surface Optimization

Mechanical defects in the structure changes it’s vibration response. There is a wide variety of methods that examine changes in measured vibration response to detect, locate, and characterize damage in structural and mechanical systems. One method to evaluate the structural changes and to analyse their causes is the Finite Element Model Updating (FEMU). The objective of this research is to investigate the FEMU procedure for mechanical damage identification and to propose an experimental-computational SHM method for lightweight structures. The structural dynamic response to impact excitation of a structure with and without defects are collected from transient and modal analysis using Ansys FE software. Afterwards, FEMU algorithm using Ansys Surface Response Optimization is investigated for its applicability to damage identification. Obtained results revealed the possibility to use this algorithm with having minimum discrepancy between parameters obtained from experiments and finite element modelling.

On the inverse identification methods for forming plasticity models using full-field measurements

The simulation of deep drawing processes and its quality is intrinsically dependent on the accuracy of the constitutive model in reproducing the mechanical behaviour of the sheet metal material. Today, the calibration of elastoplastic models – correspondent to the inverse identification of the material parameters – often uses full-field measurements, through Digital Image Correlation (DIC) techniques, to capture non-homogeneous strain fields and states, coupled with non-straightforward numerical inverse methodologies. In the last decade, new parameter identification methodologies, such as the Finite Element Model Updating (FEMU), the Constitutive Equation Gap (CEG) method, the Equilibrium Gap Method (EGM) and the Virtual Fields Method (VFM) have been developed and have proven to be effective for non-linear plasticity models. Nonetheless, the FEMU and the VFM have distinguished themselves from the others. More recently, supervised Machine Learning (ML) techniques have been also used as an inverse identification method. These artificial intelligence-based methods use large datasets of numerical tests to train an inverse model in which the input is the history of the strain field and loads during the test, and the output are directly the material parameters.The goal of this paper is to analyse, compare and discuss these inverse identification methods, with particular focus on the FEMU, VFM, and ML methodologies. A heterogeneous tensile-load test is considered to compare in detail the FEMU, VFM, and ML strategies.

Stress prediction of bridges using ANSYS soft and general regression neural network

Bridge managers are often eager to identify the carrying capacities and service performance characteristics of bridge structures. In view of the massive number of bridges managed and maintained in China, providing a quick evaluation of bridge performance bridges has become an urgent challenge for bridge engineering. Aiming at many adverse problems of bridge load tests, such as their high costs, long time consumption, low efficiency, impact on traffic, and damage to bridge structures, a new method for bridge static behavior prediction is proposed herein, based on dynamic load test data. The method adopts a generalized regression neural network algorithm with fast convergence and a nonlinear approximation, determines the sensitive parameters based on a full-bridge sensitivity analysis, forms training samples using a uniform design sampling method, and establishes intelligent agent model. The initial finite element analysis model of the bridge structure is updated using the proposed proxy model and dynamic load test data, and the static behavior of the existing bridge structure is accurately predicted based on the updated finite element model. To verify the correctness of the proposed method, a practical bridge is considered as the research object, and the static response of the bridge structure is predicted. The predicted results are consistent with the static load test results for the bridge, verifying the correctness of the proposed method. The results show that the maximum error between the theoretical calculation result and measured value is only 4.34% and the minimum error is only 3.52%. The strain prediction results are consistent with the measured results, and the modified theoretical analysis model provides high accuracy for strain prediction results under different working conditions. The application in practical engineering shows that the prediction results under different load conditions are adaptable and highly accurate.

Optimal sensor placement and model updating applied to the operational modal analysis of a nonuniform wind turbine tower

Abstract. Test planning is a crucial step in the operational modal analysis (OMA) of wind turbines (WT), and it is an essential part of choosing the best positions for installing the sensors of the structures. On the other hand, updating the finite element model (FEM) with the OMA results implies a better prediction of the real structure's dynamic and vibrational behavior. This paper aims to show how the OMA of a nonuniform and two-section wind turbine tower can be performed more effectively, using the required test planning and optimal sensor placement. Then, accordingly, the OMA is used in operating and parked conditions to find the objective bending mode characteristics. Moreover, the updating of the applicable FEM of the multi-sectional wind turbine tower will be described. The tailor-made genetic algorithm (GA) is used to find the MEMS (micro electro-mechanical system) sensors' optimal positions of the WT under study. The OMA was performed and the acquired data analyzed using the stochastic subspace identification (SSI) method. Based on the OMA results, the FEM is updated by applying the sensitivity method. The results show that a tailor-made GA is a practical and quick approach to finding the optimal position of the sensors to obtain the best results for the objective modes of the WT. The OMA results, under operating and parked conditions, prove some modal characteristics of WTs. Based on the sensitivity analysis and engineering judgment, the modulus of elasticity was selected as a parameter for updating. Finally, we found that the updated FEM had less than 1 % error compared to the obtained frequencies from the test.

2D Local identification of the elasticity parameters of heterogeneous materials by the finite element model updating method

Abstract This work is subjected to an identification of elasticity properties which are the Young’s modulus E and the Poisson’s ratio v of a heterogeneous material. We have created the experimental displacements by solving the direct problem. A re-calibration of the experimental and the simulated displacements is done based on the principle of the finite element model updating (FEMU). The minimization of the cost function obtained by the FEMU method in the inverse problem is done by Newton type algorithms. A complete study has been done by studying the sensitivity of the identified values with respect to the refinement of the mesh and with respect to the level of disturbance.

Model Updating of a Prestressed Concrete Rigid Frame Bridge Using Multiple Markov Chain Monte Carlo Method and Differential Evolution

Model updating is a widely adopted method to minimize the error between test results from the real structure and outcomes from the finite element (FE) model for obtaining an accurate and reliable FE model of the target structure. However, uncertainties from the environment, excitation and measurement variability can reduce the accuracy of predictions of the updated FE model. The Bayesian model updating method using multiple Markov chains based on differential evolution adaptive metropolis (DREAM) algorithm is explored, which runs multiple chains simultaneously for a global exploration, and it automatically tunes the scale and orientation of the proposal distribution during the evolution of the posterior distribution. The performance of the proposed method is illustrated numerically with a beam model and a three-span rigid frame bridge. Results show that the DREAM algorithm is capable for updating the FE model in civil engineering. It extends the Bayesian model updating method to multiple Markov chains scenario, which provides higher accuracy than single chain algorithm such as the delayed rejection adaptive metropolis-hastings (DRAM) method. Moreover, results from both examples indicate that the proposed method is insensitive to values of initial parameters, which avoid errors resulting from inappropriate prior knowledge of parameters in the FE model updating.

A computer vision-based method for bridge model updating using displacement influence lines

This paper presents a new computer vision-based method that simultaneously provides the moving vehicle’s tire loads, the location of the loads on a bridge, and the bridge’s response displacements, based on which the bridge’s influence lines can be constructed. The method employs computer vision techniques to measure the displacement influence lines of the bridge at different target positions, which is then later used to perform model updating of the finite element models of the monitored structural system.The method is enabled by a novel computer vision-based vehicle weigh-in-motion method which the co-authors recently introduced. A correlation discriminating filter tracker is used to estimate the displacements at target points and the location of single or multiple moving loads, while a low-cost, non-contact weigh-in-motion technique evaluates the magnitude of the moving vehicle loads.The method described in this paper is tested and validated using a laboratory bridge model. The system was loaded with a vehicle with pressurized tires and equipped with a monitoring system consisting of laser displacement sensors, accelerometers, and cameras. Both artificial and natural targets were considered in the experimental tests to track the displacements with the cameras and yielded robust results consistent with the laser displacement measurements.The extracted normalized displacement influence lines were then successfully used to perform model updating of the structure. The laser displacement sensors were used to validate the accuracy of the proposed computer vision-based approach in deriving the displacement measurements, while the accelerometers were used to derive the system’s modal properties employed to validate the updated finite element model. As a result, the updated finite element model correctly predicted the bridge’s displacements measured during the tests. Furthermore, the modal parameters estimated by the updated finite element model agreed well with those extracted from the experimental modal analysis carried out on the bridge model.The method described in this paper offers a low-cost non-contact monitoring tool that can be efficiently used without disrupting traffic for bridges in model updating analysis or long-term structural health monitoring.

Simultaneous extraction of the elastic-plastic properties of a thin film and its substrate from an identifiability-based design of depth-sensing nanoindentation testing

This work presents an approach to simultaneously identify reliable elasto-plastic properties of a 100 nm amorphous alumina film and plastic properties of its silicon substrate by the Finite Element Model Updating (FEMU) method, using exclusively nanoindentation P−h curves. A 2D axisymmetric finite element model simulates the nanoindentation tests, and the Young's modulus E, the initial yield stress σy and the hardening modulus Hp of the thin film, as well as the yield stress of silicon σys are the parameters to identify. This work relies on a numerical design of experiments carried prior to the identification process. It uses the sensitivity of the nanoindentation force to a variation of the parameters to define an identifiability indicator (I-index) based on the conditioning of the inverse problem. It reflects the stability of the potential solution of the inverse problem. I-index minimisation below a certain value allows to ensure a reliable identification by designing the best combination of experiments in terms of relevant information. I-index analyses values demonstrate that combining Berkovich and cube corner nanoindentation tests at two different indentation depths brings sufficient information to well-conditioned the inverse problem. Indeed, the increased penetration and the varied indenter tip shape induce differentiating factors which activates the substrate effect, or anvil effect, and allow the dissociation of the thin film plasticity from that of the substrate, and thus its identification. The identification procedure of the four parameters carried out with the designed dual nanoindentation test from several starting points reveals that the FEMU method converged to a unique solution. Lastly, the identified parameters are validated by confronting experimental and numerical (i) P−h curves of a Berkovich test on a bulk silicon sample and (ii) residual topographies using a 3D FEM of a Berkovich test on the composite system thin film – substrate.

Approximation Method for Stress–Strain Using Metamodel Parameter Updating

The properties of the material applied to the finite element (FE) simulation can be expressed by constitutive models, and simple constitutive and complex constitutive models can be used to show the actual phenomenon. The technology to improve the accuracy of the constitutive model applied to FE simulation is the inverse method. The inverse method is a method to curve fit the FE simulation result to the test data by utilizing finite element model updating (FEMU). Inverse methods are general approaches to update material properties. The inverse method can iteratively run many FE simulations for constitutive model optimization and consider metamodel-based simulation optimization (MBSO) to reduce this resource waste. With MBSO, one can obtain significant results with fewer resources. However, the MBSO algorithm has the problem in that the optimization performance deteriorates as the number of parameters increases. The typical process of the inverse method is to adjust these factor values individually. If there are many factors in the constitutive model, the optimization result may deteriorate owing to the performance limit of the MBSO when the structural method is used. This paper proposes a method of fitting a stress–strain constitutive model with a scaling factor to improve the efficiency of the inversion method using MBSO. For this purpose, a process was performed to determine the curve characteristics during the pretreatment stage. The results show that the proposed method significantly improved the prediction efficiency of the combination function. Thus, we conclude that initializing the combination function and setting the parameters of the inverse method by applying the proposed approach improves the efficiency of large deformation analyses.

FEM updating for damage modeling of composite cylinders under radial compression considering the winding pattern

This work aims at developing a strategy to obtain damage evolution parameters of wound cylinders to verify the influence of the winding pattern on them. First, a detailed description of the pattern generation is presented. Then, a finite element (FE) model is developed, in which the cylinders are constructed with winding patterns (WP) of 1/1, 2/1, and 3/1 and subjected to radial compressive loading. Since the cylinder-to-plate contact is considered, the variation of radial stiffness with respect to the parallel plate position is also analyzed. In addition, a damage model is used to predict the progressive failure of those cylinders. A finite element model updating (FEMU) routine is then developed to find the damage input parameters that best simulate experimental force–displacement curves. Key results show that the FEMU algorithm is strongly dependent on the initial guesses producing, however, an excellent correlation with experimental data. The predicted force versus displacement curves for all winding patterns are within the experimental standard deviation, except for the cases in which the winding pattern is not taken into consideration. The computational framework proposed is validated both quantitatively and qualitatively through post-mortem analysis of the specimens. The winding pattern affects the failure and damage mechanisms of the cylinders and, consequently conventional FE models that disregard the pattern cannot capture these mechanisms.

Model updating of a masonry tower based on operational modal analysis: The role of soil-structure interaction

Vibration-based finite element model (FEM) updating of cultural heritage assets is gaining so much attraction these days since destructive tests are usually not allowed to be performed. In this study, a framework for developing three-dimensional (3D) FEMs is proposed using 3D laser scanners and applied on Slottsfjell tower, a stone masonry tower in Tønsberg, Norway. Operational modal analysis (OMA) was done based on the ambient vibration testing (AVT) data to define the frequency values and corresponding mode shapes of the tower. Mechanical properties of the tønsbergite stone were utilized to derive the base values of the material properties of the homogenized masonry for performing sensitivity analysis and FEM updating. To investigate the effect of the soil-structure interaction (SSI) on the FEM updating results, three FEMs are developed. The fixed-base model is the FEM without considering the SSI effects, and two other FEMs are developed using the substructure and direct methods for simulating the SSI effects. Sensitivity analysis was performed to investigate the effective parameters on the dynamic characteristics of the models. FEM updating was conducted on the three FEMs, and results are compared to each other to show the role of the SSI on the FEM updating results. The resonance effect can cause damages to buildings located even in low seismicity zones. For this aim, the risk of resonance effect has been evaluated for the tower. Finally, linear dynamic analysis was performed on the three calibrated models, and the results were compared to each other.

Bridge Digital Twinning Using an Output-Only Bayesian Model Updating Method and Recorded Seismic Measurements.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The described process is a practice of digital twinning and the updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.

Inverse Identification of Residual Stress Distribution in Aluminium Alloy Components Based on Deep Learning

Residual stress within a structural component can significantly affect the mechanical performance and stability of a structure. Therefore, it is crucial to find a way to determine the residual stress distribution to maintain the normal working of structures. Conventional methods for residual stress determination primarily include experimental testing, finite element simulations and inverse identification. However, these methods suffer from disadvantages of high testing costs, long calculation time and low inverse efficiency. To avoid these shortcomings, this study developed a high-performance method based on a deep learning technique. In this method, an artificial neural network was used to replace the finite element calculation in the finite element model updating (FEMU) technique and the residual stress distribution of structural components was inversely obtained based on the measured residual stresses of a finite number of measuring points. Compared with the conventional FEMU technique, the calculation efficiency of the proposed method was considerably improved. Furthermore, the accuracy and efficiency of the method were verified by simulated four-point bending experiments considering an elastic-plastic material.

FEMU based identification of the creep behavior of Zircaloy-4 claddings under simulated RIA thermo-mechanical conditions

This study aims to identify the creep behavior of Zircaloy-4 fuel claddings under simulated reactivity initiated accident (RIA) thermo-mechanical conditions. In a previous work ballooning creep tests performed in simulated RIA conditions were described. A challenge to overcome when analyzing these experiments is that ballooning tests imply structural effects during the deformation of the specimen that have to be taken into account to identify the creep behavior of the material. In this paper a FEMU (finite element model updating) based identification is proposed to identify the creep law of the cladding, weakly coupled to the phase transformation of the material at high temperatures. Since the loading conditions are solely known in the part of the optical field of the cameras used for stereocorrelation, only this region is modeled using a Love-Kirchhoff assumption to impose the boundary conditions through the sample thickness. A Norton creep law, whose parameters are expressed as a function of the β phase fraction in the material, is identified and reproduces the first 10 s of the experiments with mean errors on the radial displacement rates of about 10%. Finally, an extension to higher time scale is proposed in Norton’s law to model the non linearity in the material response by taking into account the grain growth contribution.

Swarm intelligence-based technique to enhance performance of ANN in structural damage detection

Artificial neural network (ANN), a powerful technique, has been used widely over the last decades in many scientific fields including engineering problems. However, the backpropagation algorithm in ANN is based on a gradient descent approach. Therefore, ANN shows high potential in local stagnancy. Besides, choosing the right architecture of ANN for a specific issue is not an easy task to deal with. This paper introduces a simple, effective hybrid approach between an optimization algorithm and a traditional ANN for damage detection. The global search-ability of a heuristic optimization algorithm, namely grey wolf optimizer (GWO), can solve the drawbacks of ANN and also improve the performance of ANN. Firstly, the grey wolf optimizer is used to update the finite element (FE) model of a laboratory steel beam based on the vibration measurement. The updated FE model of the tested beam then is used to generate data for network training. For an effective training process, GWO is utilized to identify the optimal parameters for ANN, such as the number of the hidden nodes, the proportion of dataset for training, validation, test, and the training function. The optimization process provides an optimal structure of ANN that can be used to predict the damages in the beam. The obtained results confirm the accuracy, effectiveness, and reliability of the proposed approach in (1) alleviating the differences between measurement and simulation and (2) damage identification including damage location and severity, in the tested beam considering noise effects. For both applications, dynamic characteristics like natural frequencies and mode shapes of the beam derived from the updated FE model, are collected to calculate the objective function

Identification of Orthotropic Elastic Properties of Wood by a Synthetic Image Approach Based on Digital Image Correlation.

This work aims to determine the orthotropic linear elastic constitutive parameters of Pinus pinaster Ait. wood from a single uniaxial compressive experimental test, under quasi-static loading conditions, based on two different specimen configurations: (a) on-axis rectangular specimens oriented on the radial-tangential plane, (b) off-axis specimens with a grain angle of about 60° (radial-tangential plane). Using digital image correlation (DIC), full-field displacement and strain maps are obtained and used to identify the four orthotropic elastic parameters using the finite element model updating (FEMU) technique. Based on the FE data, a synthetic image reconstruction approach is proposed by coupling the inverse identification method with synthetically deformed images, which are then processed by DIC and compared with the experimental results. The proposed methodology is first validated by employing a DIC-levelled FEA reference in the identification procedure. The impact of the DIC setting parameters on the identification results is systematically investigated. This influence appears to be stronger when the parameter is less sensitive to the experimental setup used. When using on-axis specimen configuration, three orthotropic parameters of Pinus pinaster (, and ) are correctly identified, while the shear modulus () is robustly identified when using off-axis specimen configuration.

Operational modal analysis and finite element model updating of a 230 m tall tower

Dynamic response levels are critical for tall and slender civil structures. Studying the dynamic behavior of large civil structures with finite element modeling techniques requires detailed and accurate modeling of structural geometry, material properties, member fixities, connection types, and accompanying assumptions. Still, the finite element model results are approximations that could be away from representing the actual structural behavior. Structures are dynamically tested at their operational conditions to validate the finite element model results. This paper presents Operational Modal Analysis (OMA) and finite element model updating of a tall structure located in the West Bay area of Doha (Qatar). The structure is a reinforced concrete building with shear wall cores situated towards the center of the building plan, which was constructed between 2012 and 2016. With 53 stories above the ground and two stories below ground, the 230 m (755 ft) tall building is being used for residential and hotel purposes. For the finite element model updating and calibration tasks presented in this paper, the authors intentionally introduced drastic model changes for the first two model updates so that the results from the first two attempts guide how to proceed with a more reasonable update for the third calibration of the finite element model. While this is a non-standard technique that represents a specific condition where the initial attempts on the finite element model are very crude approximations, it is a systematized demonstration of how to operate when the structural parameters are sparse or uncertain for modeling purposes. While in theory, the finite element model updates can always be fine-tuned in a way to further decrease the error between the measured and predicted OMA results, in this paper, the authors predominantly focused on the presentation of three finite element model updates to demonstrate the way they have improved the modal assurance criteria plots and lowered the average absolute errors by visiting two drastic and then one moderate finite element model updates. The material presented here in this paper is arguably the first published work on large-scale dynamic testing of a civil structure in the State of Qatar.