Baseline Finite Element Model Research Articles

Evaluation of bridge load capacity using proof-load tests

A proof-load test is often necessary to accurately measure the field behavior of a bridge structure. A new segmental steel bridge has been constructed over the Tisza River in Hungary. The bridge comprises of two independent steel box girders assembled by a welding system. Engineers performed proof load tests before opening the structure to evaluate its load-carrying capacity and deck deflection. This paper presents several aspects of the load testing and evaluation of the bridge structure under static and dynamic loads using a rating factor (RF) approach compared to a baseline finite element model. The load test results helped to calibrate the model and verify the method. The study reveals that the tested bridge has an elastic behavior, a high capacity, and adequate dynamic performance.

Surrogate model development using simulation data to predict weld residual stress: A case study based on the NeT-TG1 benchmark

Surrogate models have been used as a substitute for traditional engineering simulation to get target simulation results faster. These surrogate models usually need sufficient data to fulfill their optimum performance. However, the acquisition of high quality datasets for cases like welding residual stress is both difficult and costly. This work developed a workflow that can rapidly develop machine learning based surrogate models to predict post-weld residual stresses using finite element (FE) simulation data. The workflow comprises five steps: (i) baseline FE model creation, (ii) FE model processing (iii) scripting (iv) data generation and (v) surrogate model development. The workflow presented in the paper automates all the steps involved in generating, calculating, and extracting results from FE simulations, with the aim of reducing the time and cost required for data acquisition. In addition, to minimize the possibility of FE analyses not completing successfully during the automated data generation process and to ensure that the training data can be obtained without any manual intervention, the FE model was simplified without significant loss of accuracy. A single weld bead-on-plate structure, taken from the NeT project Task Group 1, was used as a case study to validate the developed workflow. The overall aim of this work was to validate the feasibility of developing a surrogate model for specific welding conditions with no experimental dataset and with the aid of simulations, and to investigate the predictive performance of an Artificial Neural Network based surrogate model. Four welding parameters, arc advance speed, net energy input rate, arc travel length and position, were considered as the input for the surrogate model to predict the longitudinal stress along the line running across the sample thickness in the mid-length of the specimen. The relative root mean square error of the predictive surrogate model for the test dataset was 0.0024. Residual stress prediction based on the NeT-TG1 benchmark welding case met the R6 validation criteria and the developed model generates predictions that are in line with other methods used by contributors to the NeT-TG1 round robin.

Structural optimisation of the DEMO alternative divertor configurations based on FE and RBF mesh morphing

The DEMO tokamak exhibits extraordinary complexity due to the constraints and requirements pertaining to different fields of physics and engineering. The multidisciplinary nature of the DEMO system makes its design phase extremely challenging since different and often opposite requirements need to be accounted for. Toroidal field (TF) coils generate the toroidal magnetic field required to magnetically confine the plasma particles and support at the same time the poloidal field coils. They must bear tremendous loads deriving from electromagnetic interactions between the coil currents and the generated magnetic field. An efficient tokamak design aims at minimizing the energy stored in its magnetic field and hence at reducing the toroidal volume within the TF coils whose shape would hence ideally mimic co-centrically the shape of the plasma. In order to bear the enormous forces a D-shape is most suitable for the TF coils as it allows them to resist the very large compression on the inner side and to carry the electro-magnetic (EM) pressure mainly by membrane stresses preventing large bending to occur on the outer side. At the same time the divertor structures must fit within the TF coils and this requires adaptations of the TF coil shape in the case of so-called advanced divertor configurations (ADCs), which require larger divertor structures. This article shows the TF coils adapted to ADCs using a structural optimisation procedure applied to the reference shape. The introduced strategy takes as structural optimum the iso-stress profile associated to each coil. A continuous transformation, based on radial basis functions mesh morphing, turns the baseline finite element (FE) model into its iso-stress counterpart, with a series of intermediate configurations available for electromagnetic and structural investigations as output. The adopted strategy allowed to determine, for each of the ADC cases, a candidate shape. Static membrane stress levels during magnetization could be reduced significantly from more than 700 MPa to below 450 MPa.

Damage Detection of FRP Composite Plates from Dynamical Responses using Finite Element Model Updating: Equivalent Material Properties as Parameters

Fibre reinforced plastic (FRP) composite structures are extensively used in weight sensitive applications, such as in aircrafts, ships, etc. Such structures are susceptible to damages during their usual operation or during extreme loading from environment. Due to the anisotropic nature of FRP composite plates, damage detection is difficult for such layered materials particularly when the damage site is inaccessible. The localised loss of stiffness resulting from damage is reflected into the global dynamic responses of such structures. Finite element model updating is a convenient inverse approach in which these changes in stiffness due to damages are estimated from measured dynamical responses using optimization. The equivalent stiffness changes can be expressed in terms of either geometric or material property or both. In most of the cases, changes in geometric parameters physically represent the actual damage scenario with larger sensitivity. On the other hand, material property changes in the damaged area are a very convenient parameter to deal with. In the present work, updating parameters in the finite element model updating procedure are chosen in terms of material property. Detection of local stiffness changes from experimentally measured natural frequencies, mode shapes and/or frequency response functions are investigated. Experimental modal testing is performed on a rectangular FRP composite plate both in its undamaged and damaged state. Baseline finite element model of the composite plate is correlated with experimental model, followed by a sensitivity based finite element model updating algorithm. The results show the rapid convergence and accurate determination of local stiffness change in terms of elastic material parameters alone in all three orthogonal directions. This indicates that material properties like the in-plane Young’s moduli and in-plane Shear modulus within the localised region of damage, can well be used as convenient means for detecting equivalent stiffness loss in damaged structures.

Damage assessment of suspension footbridge using vibration measurement data combined with a hybrid bee-genetic algorithm

Optimization algorithms (OAs) are a vital tool to deal with complex problems, and the improvement of OA is inseparable from practical strategies and mechanisms. Among the OAs, Bee Algorithm (BA) is an intelligent algorithm with a simple mechanism and easy implementation, in which effectiveness has been proven when handling optimization problems. Nevertheless, BA still has some fundamental drawbacks, which can hinder its effectiveness and accuracy. Therefore, this paper proposes a novel approach to tackle the shortcomings of BA by combining it with Genetic Algorithm (GA). The main intention is to combine the strengths of both optimization techniques, which are the exploitative search ability of BA and the robustness with the crossover and mutation capacity of GA. An investigation of a real-life suspension footbridge is considered to validate the effectiveness of the proposed method. A baseline Finite Element model of the bridge is constructed based on vibration measurement data and model updating, which is used to generate different hypothetical damage scenarios. The proposed HBGA is tested against BA, GA, and PSO to showcase its effectiveness in detecting damage for each scenario. The results show that the proposed algorithm is effective in dealing with the damage assessment problems of SHM.

In-situ testing and finite element model updating of a long-span cable-stayed bridge with ballastless track

Ballastless track is widely used in high-speed railways due to its long service life, low maintenance costs, and excellent riding comfort. However, laying a ballastless track on a long-span bridge remains a challenge because of the large deflection and uneven stiffness of the long-span bridge. Limited research has been reported on the experimental behavior of the long-span railway bridge laid with the ballastless track. This study presents the in-situ testing and the finite element model updating (FEMU) of the Ganjiang Bridge, China’s first long-span ballastless railway cable-stayed bridge with a main span that reaches up to 300 m before its opening for operation. The study’s primary purposes include evaluating the mechanical properties of the ballastless railway bridge and establishing a baseline finite element model for subsequent structural health monitoring. The general test plan, sensor placement, and measured responses are described. The static deflection, the stress of the main girder, and the rotation angle at the beam end are used to evaluate the static performance of the bridge. The natural frequencies and mode shapes are used to assess the dynamic performance of the bridge. A FEMU framework that utilizes displacement assurance criterion (DAC) and frequency to construct a single-objective function is proposed to update the initial finite element (FE) model of the bridge. The results show that the deflection to span ratio is 1/1016 (less than1/1000), and the rotation angle at the beam end under live load is 0.032 ‰ rad (<1‰), indicating that the bridge has sufficient vertical stiffness and excellent riding comfort. The stress of the main girder is smaller than the material yield strength, indicating that the bridge has sufficient load-bearing capacity. All the requirements allowing the bridge to start service have been met. The updated FE model shows that the DAC performs better than the displacement and provides more accurate updating results. The updated FE model can well reflect the static and dynamic characteristics of the actual bridge and can be used as a baseline FE model for subsequent studies.

Static and dynamic evaluation of a butterfly-shaped concrete-filled steel tube arch bridge through numerical analysis and field tests

The butterfly-shaped concrete-filled steel tube (CFST) arch bridge is an irregular bridge with unique esthetics. In this paper, this new shape of CFST arch bridge is introduced, and a refined three-dimensional finite element model (FEM) is established to evaluate static and dynamic behavior of the bridge. In order to reduce model errors, the FEM is calibrated according to numerical analysis and field tests. Static calculation results show that the butterfly-shaped bridge has good structural performance. The bending moment and axial force of the arch ribs increase when the camber angle of suspender changing from 15° to 50°. Dynamic test is carried out by ambient vibration testing under traffic and wind-induced excitations. The modal parameters of the bridge were calculated by the stochastic subspace identification method in the time domain. In terms of natural frequencies and mode shapes, the FEM analysis was validated by experimental modal analysis. The updated model thus obtained can be treated as a baseline finite element model, which is suitable for long term monitoring and safety evaluation of the structure in different severe circumstances such as earthquakes and wind loading in future.

Numerical analysis and field load testing of a suspension bridge with a root pile anchorage

The Qiupu River Bridge is the first suspension bridge with the application of a novel anchorage of root pile foundation. The static behaviors of the bridge were studied in this paper. Before the bridge was opened to traffic, the statically loaded field tests of the bridge have been carried out to check its load-carrying capacity. Then, a finite element (FE) model of the bridge was developed and calibrated to the measured initial equilibrium configuration. The efficiency of the FE model has been verified by comparing the calculated results of the model to the measured ones under the live loads, which indicates that calibration of the FE model to the initial equilibrium configuration is crucial to the construction of a baseline FE model. Based on the verified FE model, the influences of anchorage displacements on the bridge loading behavior were studied. Furthermore, a simplified analytical method was proposed to analyze the mechanism of structural responses under the anchorage horizontal displacements. The comparison of analytical results with FE results revealed a good agreement. It is demonstrated that the horizontal displacement of the anchorage of suspension bridges affects the structural responses more obviously than the vertical displacement, while the pylon is sensitive to the anchorage displacement. The deflection of the bridge deck results from the pylon displacement, which is caused by the unbalanced main cable force between the main span and side span. It is reasonable to take the internal force of pylons as the controlling condition of anchorage displacements. Finally, based on the analytical method, the parametric studies reveal that increasing the sag-to-span ratio and side-to-center span ratio can reduce the displacement and internal force of pylons caused by the anchorage displacement.

Targeting the acceleration-time response of vehicle structures under crash impact using equivalent dynamic loads

This work introduces an optimization procedure derived from the targeting force-displacement response (TFDR) method to improve the crashworthiness of full-size vehicle structures. The proposed method aims at targeting the vehicle’s acceleration-time response (ATR) under a crash event using topometry (thickness) optimization. In contrast to the original TFDR method, the proposed targeting method uses a moving coordinate system (MCS) that allows addressing fully dynamic crash models with initial velocity. By setting a proper target ATR curve, the proposed method can improve several crashworthiness indicators including specific energy absorption, maximum deceleration, dynamic penetration, and crash load efficiency. The result of the topometry optimization could be a guideline for the further design. In the proposed method, the nonlinear optimization problem is discretized into a series of analytical subproblems using equivalent dynamic load (EDL). In each iteration, the dynamic response from an explicit dynamic finite element (FE) analysis is utilized to define and solve a subproblem. To demonstrate the proposed iterative method, the baseline FE model of a Dodge Grand Caravan vehicle, obtained from the US National Highway Traffic Safety Administration (NHTSA) website, is optimized. The results show the effectiveness of the algorithm finding the element thickness distribution to make the acceleration-time response of the vehicle’s center of gravity (VCG) gradually approach a target curve. The proposed EDL algorithm finds a converged solution using less than 15 crash simulations. This makes it possible to solve problems involving full-size vehicle FE models.

Application of fibre optic sensing systems to measure rotor blade structural dynamics

This paper compares two fibre optic sensing techniques for vibration characterisation: (a) optical fibre Bragg grating (FBG) strain gauges and (b) a novel direct fibre optic shape sensing (DFOSS) approach based on differential interferometric strain measurements between multiple fibres within the same fibre arrangement. Operational mode shapes and frequency measurements of an Airbus Helicopters H135 bearingless main rotor blade (5.1 m radius) were acquired during a series of ground vibration tests undertaken in a controlled laboratory environment. Data recorded by the fibre optic instrumentation systems were validated using commercially available accelerometers and compared against a baseline finite element model. Both fibre optic sensing systems proved capable of identifying the natural frequencies of the blade in the frequency range of interest (0–100 Hz). The data from the FBG sensors exhibited a dependency on their position relative to the neutral axes of the blade, which meant that full characterisation of the flapping and lagging modes required careful consideration of sensor location in the chordwise direction. The DFOSS system was able to identify all structural dynamics, despite being located on the neutral axis in the lagging direction, due to its sensitivity to angle changes, rather than strain, and its biaxial measurement capability. The DFOSS system also allowed the operational mode shapes of the blade to be determined directly, without the requirement for strain transfer from the blade to the sensor and without the requirement for a model of the underlying structure. The accuracy of obtained natural frequencies and operational mode shapes is assessed, demonstrating the potential of the use of both fibre optic sensing systems for determining blade structural dynamics.

Inverse modeling of damping and soil–structure interface for monopiled offshore wind turbines

There have been many articles contributed to the finite element modeling for the dynamic analysis of monopile offshore wind turbine (OWT) systems. However, the accuracy of the parameter values used in the finite element model has always been a major concern. Mathematically, the design and analysis based on a finite element model is classified as a “forward” problem, while correcting the parameter values of the baseline finite element model based on measured response data is an “inverse” problem. This paper is the first article devoted to the concurrent correction of parameter values of both soil–structure interface and damping of a monpile OWT based on measured response data. While adopting a lumped parameter model (LPM) – which consists of one rotational spring, one horizontal spring and one rotational dashpot – for the soil–structure interface and a Rayleigh damping model for the energy-loss of the tower/substructure, this study develops a novel method for simultaneously updating the Rayleigh damping coefficients and soil–structure interface stiffness/damping parameters based on only a few measured natural frequencies and damping ratios. In the numerical studies, computer simulations with the National Renewable Energy Laboratory 5-MW (NREL 5-MW) reference turbine are carried out to demonstrate the effectiveness of the proposed method.

Structural model updating of the Gageocho Ocean Research Station using mass reallocation method

To study oceanic and meteorological problems related to climate change, Korea has been operating several ocean research stations (ORSs). In 2011, the Gageocho ORS was attacked by Typhoon Muifa, and its structural members and several observation devices were severely damaged. After this event, the Gageocho ORS was rehabilitated with 5 m height to account for 100-yr extreme wave height, and the vibration measurement system was equipped to monitor the structural vibrational characteristics including natural frequencies and modal damping ratios. In this study, a mass reallocation method is presented for structural model updating of the Gageocho ORS based on the experimentally identified natural frequencies. A preliminary finite element (FE) model was constructed based on design drawings, and several of the candidate baseline FE models were manually built, taking into account the different structural conditions such as corroded thickness. Among these candidate baseline FE models, the most reasonable baseline FE model was selected by comparing the differences between the identified and calculated natural frequencies; the most suitable baseline FE model was updated based on the identified modal properties, and by using the pattern search method, which is one of direct search optimization methods. The mass reallocation method is newly proposed as a means to determine the equivalent mass quantities along the height and in a floor. It was found that the natural frequencies calculated based on the updated FE model was very close to the identified natural frequencies. In conclusion, it is expected that these results, which were obtained by updating a baseline FE model, can be useful for establishing the reference database for jacket-type offshore structures, and assessing the structural integrity of the Gageocho ORS.

The Use of Mode Shape Estimated from a Passing Vehicle for Structural Damage Localization and Quantification

Mode shapes estimated from the vehicle responses are normally used to detect bridge damage efficiently for their high spatial resolution. However, an updated baseline finite element model (FEM) is normally required to quantify damages for such an approach. A two-stage damage detection procedure is presented for bridges by utilizing the mode shape estimated from a moving vehicle. Damage locations are first determined through a damage localization index (DLI) defined by regional mode shape curvature (RMSC). Then the relationship between the damage extents and the RMSC changes is investigated by FEM simulation. Finally, an equation set to quantify the single and multiple damages is deduced by combining the RMSCs and the relationship between the damage extents and the RMSC changes established by an un-updated FEM. Numerical and experimental examples are carried out to verify the validity and efficiency of the two-stage method. The results revealed that it can localize and quantify damages with satisfactory precision by using the response measured from one sensor only.

Structural Reliability Estimation with Participatory Sensing and Mobile Cyber-Physical Structural Health Monitoring Systems

With the help of community participants, smartphones can become useful wireless sensor network (WSN) components, form a self-governing structural health monitoring (SHM) system, and merge structural mechanics with participatory sensing and server computing. This paper presents a methodology and framework of such a cyber-physical system (CPS) that generates a bridge finite element model (FEM) integrated with vibration measurements from smartphone WSNs and centralized/distributed computational facilities, then assesses structural reliability based on updated FEMs. Structural vibration data obtained from smartphones are processed on a server to identify modal frequencies of an existing bridge. Without design drawings and supportive documentation but field measurements and observations, FEM of the bridge is drafted with uncertainties in the structural mass, stiffness, and boundary conditions (BCs). Then, 2700 FEMs are autonomously generated, and the baseline FEM is updated by minimizing the error between the crowdsourcing-based modal identification results and the FEM analysis. Furthermore, using 151 strong ground motion records from databases, the bridge response time history simulations are conducted to obtain displacement demand distribution. Finally, based on reference performance criteria, structural reliability of the bridge is estimated. Integrating the cyber (FEM analysis) and the physical (the bridge structure and measured vibration characteristics) worlds, this crowdsourcing-based CPS can provide a powerful tool for supporting rapid, remote, autonomous, and objective infrastructure-related decision-making. This study presents a new example of the emerging fourth industrial revolution from structural engineering and SHM perspective.

Development and validation of a semi-automatic landmark extraction method for mesh morphing

Currently, landmark-based mesh morphing technology is widely used to rapidly obtain meshes with specific geometry, which is suitable to develop parametric human finite element (FE) models. However it takes too much time for landmark extraction to obtain high geometric accuracy. The purpose of this study is to develop and validate a semi-automatic landmark extraction method to reduce the time of manual selection of landmarks without sacrificing the accuracy of identifying landmarks in the process of mesh morphing. A few contour edge landmarks were extracted manually. Mathematical landmarks and pseudo-landmarks were extracted automatically by user-defined algorithm. The radial basis function (RBF) was used to morph the baseline FE model into the target geometry based on these landmarks. The cervical vertebra (C5), rib (R7) and femur were selected as the target geometries to verify the effectiveness of the method. The maximum mean geometric error of the three types of target geometries was less than 1 mm. The mesh quality of the morphed FE model was similar to that of the baseline FE model. Compared to the traditional manual method, 2/3 to 3/4 of the time for landmark extraction was saved by the semi-automatic method.

Safety evaluation method of composite girder cable-stayed bridge based on structural health monitoring system

A comprehensive safety evaluation method which can dynamically reflect the damage changes in operation state is established based on the structural health monitoring (SHM) system of a composite girder cable-stayed bridge. The fuzziness and uncertainties during the evaluation process are considered and the random errors are reduced by using the proposed evaluation method. The normal values and safety limits of monitoring indexes of the Guanhe Bridge are proposed by using numerical simulation and monitoring data statistics of the baseline finite element model, and the index evaluation standard of the related code requirements. The results can be used to complement the lack of online monitoring indexes in the existing regulations, and solve the problem that lacking support for quantitative monitoring data in current bridge management system evaluation module, which can provide theoretical basis for the evaluation, management, maintenance and decision-making of bridge structures.

A Multi-Objective DIRECT Algorithm Toward Structural Damage Identification With Limited Dynamic Response Information

A major challenge in structural health monitoring (SHM) is to accurately identify both the location and severity of damage using the dynamic response information acquired. While in theory the vibration-based and impedance-based methods may facilitate damage identification with the assistance of a credible baseline finite element model, the response information is generally limited, and the measurements may be heterogeneous, making an inverse analysis using sensitivity matrix difficult. Aiming at fundamental advancement, in this research we cast the damage identification problem into an optimization problem where possible changes of finite element properties due to damage occurrence are treated as unknowns. We employ the multiple damage location assurance criterion (MDLAC), which characterizes the relation between measurements and predictions (under sampled elemental property changes), as the vector-form objective function. We then develop an enhanced, multi-objective version of the dividing rectangles (DIRECT) approach to solve the optimization problem. The underlying idea of the multi-objective DIRECT approach is to branch and bound the unknown parametric space to converge to a set of optimal solutions. A new sampling scheme is established, which significantly increases the efficiency in minimizing the error between measurements and predictions. The enhanced DIRECT algorithm is particularly suited to solving for unknowns that are sparse, as in practical situations structural damage affects only a small region. A number of test cases using vibration response information are executed to demonstrate the effectiveness of the new approach.

Prognostic Value of Lordosis Decrease in Radiographic Adjacent Segment Pathology After Anterior Cervical Corpectomy and Fusion

While cervical lordosis alteration is not uncommon after anterior cervical arthrodesis, its influence on radiological adjacent segment pathology (RASP) is still unclear. Biomechanical changes induced by arthrodesis may contribute to ASP onset. To investigate the correlation between cervical lordosis decrease and RASP onset after anterior cervical corpectomy and fusion (ACCF) and to determine its biomechanical effect on adjacent segments after surgery, 80 CSM patients treated with ACCF were retrospectively studied, and a baseline finite element model of the cervical spine as well as post-operation models with normal and decreased lordosis were established and validated. We found that post-operative lordosis decrease was prognostic in predicting RASP onset, with the hazard ratio of 0.45. In the FE models, ROM at the adjacent segment increased after surgery, and the increase was greater in the model with decreased lordosis. Thus, post-operative cervical lordosis change significantly correlated with RASP occurrence, and it may be of prognostic value. The biomechanical changes induced by lordosis change at the adjacent segments after corpectomy may be one of the mechanisms for this phenomenon. Restoring a well lordotic cervical spine after corpectomy may reduce RASP occurrence and be beneficial to long-term surgical outcomes.

From continuous vibration monitoring to FEM-based damage assessment: Application on a stone-masonry tower

The paper presents a damage assessment strategy suitable to historic masonry towers. The methodology is exemplified using the data collected in the continuous dynamic monitoring of the San Vittore bell-tower (Arcisate, Northern Italy). The proposed damage assessment procedure aims not only at detecting the occurrence of structural anomalies, but also at localising the damage in the investigated structure. After a brief description of the tower and past diagnostic survey (including ambient vibration tests and Finite Element modelling), the results of the continuous dynamic monitoring are highlighted and the effect of temperature on automatically identified resonant frequencies is discussed. Subsequently, regression models based on Principal Component Analysis are applied in order to filter out the fluctuations caused by the environmental effects on the identified resonant frequencies. The damage detection and damage localisation issues are then addressed by using novelty analysis tools. The effectiveness of the proposed strategy is demonstrated through the detection and localisation of realistic damage scenarios simulated with the baseline Finite Element model. Specifically, the damage localisation has been tackled by using the “cleaned” modal properties within a continuous Finite Element model updating scheme.

Investigation of Stability Alarming for Retaining Wall Structures with Damage

To warn of the stability of retaining wall structures with damage, a simplified mechanical model and a finite element model of this retaining wall-soil coupling system are established. Via finite element model updating, a baseline finite element model of the wall-soil system is acquired. A damage alarming index ERSD (Energy Ratio Standard Deviation) is proposed via the wavelet packet analysis of a virtual impulse response function of dynamic responses to this baseline finite element model. The internal relationships among the alarming index, earth pressure, and damage stability of the wall are analyzed. Then, a damage stability alarming method for the retaining walls is advanced. To verify the feasibility and validity of this alarming method, vibration tests on the baseline finite element model of a pile plate retaining wall are performed. The ERSD is used as an alarm for the damage stability of the wall. Analysis results show that, with an increase in the ERSD, the stability of the wall changes from a stable state to an unstable one. The wall reaches a critical stable state when the alarming index reaches its threshold value. Thus, the damage stability of this pile plate retaining wall can be alarmed via ERSD.