Dynamic parametric modeling-based model updating strategy of aeroengine casings

Hierarchical model updating strategy of complex assembled structures with uncorrelated dynamic modes

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

The main objective of this work is to present a vibration-based damage estimation framework for structural systems by integrating vibration experimental measurements in a high-fidelity, large-scale, finite element (FE) model. Using the measured responses of a healthy structural system under operational vibrations, a parameterized FE model could be tuned using state-of-the-art FE model updating techniques in order to develop a high-fidelity model of the structural system, representing the healthy reference model. These methods provide much more comprehensive information about the condition of the monitored system than the analysis of raw data. The diagnosed degradation state, along with its identified uncertainties, can be incorporated into robust reliability tools for updating predictions on the residual useful lifetime of structural components and safety against various failure modes, taking into account stochastic models of future loading characteristics. A fault or damage would cause a sudden change in the operational responses of the structure. Incorporating the unhealthy response under measured operational excitations, a series of FE model updating runs of incrementally reparameterized FE models could be automated. The sensitivity of the unhealthy response to the parameter change pertains to the sensitive parts of the FE model, where damage or fault is located. A recursive reparameterization of those sensitive parts, followed by an FE model updating, leads toward both the detection localization and the type and magnitude of the fault or damage. The proposed framework is applied on a small-scale laboratory steel truss bridge.KeywordsFE model updateTransmittance functionsDamage identification

The vibrational effect is one of the primary considerations during construction due to the ambient excitation from the surrounding environment. Thus, it is necessary to find the most dependable Finite Element (FE) model for the actual structure to improve its quality and life span on site. In this context, the study included a 3-story building model that was analyzed using finite element analysis to determine its dynamic properties such as natural frequency and mode shape to avoid the resonance effect. It is due to the importance of obtaining a reliable and accurate model by verifying with the results of the Operational Modal Analysis (OMA). In general, the goal of this study is to update the FE model so that it is close to the actual scaled model based on the previous OMA study. As a result, an initial linear FE model of the 3-story building scaled model was created using CAD software based on actual geometry to describe the structure's physical properties. The FE model was then imported into CAE software, where the boundary condition and estimated material properties were assigned to determine the effect of random vibration. Through the pairing of Finite Element Analysis results and previous studies, 9 natural frequencies and 9 mode shapes were extracted. The Modal Assurance Criterion (MAC) was used to compare the mode shape of FE results against the OMA to determine the degree of consistency between paired mode shapes. A model updating process was carried out to reduce the discrepancy between the methods. The uncertainties arising from the initial conditions have been discussed in terms of the stiffness of the material used. The updated model allows for an evaluation of the structure's current actions as well as the development of models for a wide range of potential future research scenarios.

Finite element analysis model is the discretion and simplification of actual structure. Due to some uncertain factors in the process of modeling, such as element type, material properties, geometric shape, the uncertainty of boundary conditions and so on, the finite element analysis model tends to have certain error, which will affect the accuracy of the analysis results. Therefore, model updating and validation are needed to improve the accuracy and reliability of the model. Model updating method based on the first-order optimization was employed to update finite element models referring to experimental modal parameters in the paper. Taking an aero-engine simulation casing as the research object, modal test was carried out to obtain experimental modes. Then the finite element software was used to calculate the corresponding modal parameters. The calculated modal parameters were compared with the experimental ones. As the calculated results obtained by the finite element method may be not so accurate, the test modal data was utilized to update the finite element model, and the modal parameters were selected as references for optimization. With the correction of elastic moduli in each part of the finite element model, modal parameters of the updated finite element model were obtained, and modes of the revised model were in good agreement with the experimental modal parameters. The modal frequency differences between the calculated and experimental results were significantly reduced and the modal shapes of them were identical. The results demonstrated that model updating method based on the correction of elastic modulus is feasible and suitable for the accurate finite element modeling of large and complex structures in engineering.

Updating model parameters from frequency domain data via reduced order models

In various applications it is important to determine dynamically equivalent spatial finite element (FE) model of complex structures. For instance, obtaining the FE model of an existing aerospace structure is a major requirement for reliable aeroelastic analysis. In such applications a reliable FE model may not be always available, and when this is so a dynamically equivalent FE model derived from modal test will be very useful. This paper presents a noble method to determine spatial FE model of a structure by using experimentally measured modal data along with the connectivity information of measurement points. The method is based on the mass and stiffness orthogonality equations written using experimentally determined mode shapes and natural frequencies. These equations are solved for geometric and material properties constituting global spatial mass and stiffness matrices of an initial FE model. Starting from this initial FE model, mass and stiffness orthogonality equations are updated iteratively employing experimentally obtained natural frequencies and corresponding eigenvectors from the FE model. Iterations are continued until eigensolution of the updated FE model closely correlates with experimentally measured modal data. A simulated case study on GARTEUR scaled aircraft model is presented in order to demonstrate the applicability of the method.

Finite element analysis is a powerful tool in the biomechanical study to analyse whole body vibration. The objective of this work is to develop a biomechanical model of human trunk-neck-head (above the pelvis level) and analyse its mode shape characteristics using finite element analysis (FEA). A parametric finite element model is developed using solid-works and analysed using ANSYS software. The natural frequencies were obtained for the developed human trunk-neck-head model using free vibration modal analysis, and compared with the results obtained in the past literatures. Mode shapes and deflection due to whole body vibration in all resonance frequency ranges are numerically obtained and interpreted. A total of ten vibration modes were obtained from the finite element model. The principal resonance at 5.11 Hz consisted of a half body mode, in which the head and spinal column move almost rigidly, with axial and shear deformation lower than L5 occurring in the fourth mode at 18.35 Hz. A bending mode of the entire spine was found in the eighth mode at 33 Hz, which was making a minor contribution to the principal resonance. As in the experimental results, a neck rotation was found in both the ninth mode at 35.26 Hz and in the tenth mode 43.24 Hz.

In this paper, a finite element model updating (FEMU) method is proposed based on the response surface model (RSM) and genetic algorithm (GA) to establish a high-precision finite element (FE) model of space station scientific experiment racks. First, the fine solid and mixed FE models are established, respectively, and a comparison of the modal test results is conducted. Then, an orthogonal experimental design is used to analyze the significance of the parameters, and the variables to be modified are determined. The design parameters are sampled via the Latin hyperbolic method and are substituted into the FE model to obtain the modal parameters of the scientific experiment rack. The mapping relationship between the design and modal parameters is fitted by constructing the Kriging function, and the RSM is established. The design parameters of the scientific experiment rack are optimized via GA, and the initial FE model is updated, which has the advantage of improving the computing efficiency. Finally, the updated FE model of the experiment rack is verified by frequency sweep and random vibration tests. The experimental results show that the proposed approach has high precision and computing efficiency, and compared with the test results, the modal frequency errors of the updated model are within 5%, and the vibration response errors under random excitation of the updated model are within 7%.

Finite element model updating from full-field vibration measurement using digital image correlation

Uncertainties in finite element (FE) model updating arise from two main sources: measurement noise and modeling errors. The latter includes model parameter uncertainty and model uncertainty itself. Among these sources of uncertainty, model uncertainty has been proven to be the most influential source of error in FE model updating, which is particularly important when using the updated model for damage identification (DID) purposes. This paper investigates the effects of model uncertainty when updating mechanics-based nonlinear FE models of building structures subjected to earthquake excitation. To solve the parameter estimation problem, the unscented Kalman filter is used as parameter estimation tool. Numerically simulated response data of two state-of-the-art nonlinear FE models of building structures designed according to modern design codes are used as application examples. A two-dimensional steel building and a three-dimensional reinforced concrete building, both subjected to seismic base excitation, are analyzed for different types and levels of model uncertainty. The results show that model uncertainty may have significant detrimental effects when using the updated FE model for DID, chiefly in the case of large modeling uncertainty. Although a good match between the measured (observed) and FE predicted responses is usually achieved, unobserved responses at global and local levels often show significant errors.

ABSTRACTObjective: The goal of this study was to explore a framework for developing injury risk functions (IRFs) in a bottom-up approach based on responses of parametrically variable finite element (FE) models representing exemplar populations.Methods: First, a parametric femur modeling tool was developed and validated using a subject-specific (SS)-FE modeling approach. Second, principal component analysis and regression were used to identify parametric geometric descriptors of the human femur and the distribution of those factors for 3 target occupant sizes (5th, 50th, and 95th percentile males). Third, distributions of material parameters of cortical bone were obtained from the literature for 3 target occupant ages (25, 50, and 75 years) using regression analysis. A Monte Carlo method was then implemented to generate populations of FE models of the femur for target occupants, using a parametric femur modeling tool. Simulations were conducted with each of these models under 3-point dynamic bending. Finally, model-based IRFs were developed using logistic regression analysis, based on the moment at fracture observed in the FE simulation. In total, 100 femur FE models incorporating the variation in the population of interest were generated, and 500,000 moments at fracture were observed (applying 5,000 ultimate strains for each synthesized 100 femur FE models) for each target occupant characteristics.Results: Using the proposed framework on this study, the model-based IRFs for 3 target male occupant sizes (5th, 50th, and 95th percentiles) and ages (25, 50, and 75 years) were developed. The model-based IRF was located in the 95% confidence interval of the test-based IRF for the range of 15 to 70% injury risks. The 95% confidence interval of the developed IRF was almost in line with the mean curve due to a large number of data points.Conclusions: The framework proposed in this study would be beneficial for developing the IRFs in a bottom-up manner, whose range of variabilities is informed by the population-based FE model responses. Specifically, this method mitigates the uncertainties in applying empirical scaling and may improve IRF fidelity when a limited number of experimental specimens are available.

Parameterized meso-scale modeling and experimental study on the tensile damage evolution and strength of 3D five-directional braided composites

An efficient method for constructing multiple candidate finite element (FE) models which are consistent with the measured dynamic properties of a civil structure is presented. A parameterised sensitivity-based FE model updating method was developed to permit a feasible FE model set for the target structure to be produced. In this method, an aggregated multi-objective function, which is defined by the weighted sum of the error functions, is parameterised by its relative weighting factors. By introducing multiple parameter sets for the weighting factors, a number of optimal updated FE models are produced that permit both the natural frequency errors and mode shape errors to be simultaneously minimised. The effectiveness of the proposed method is illustrated by an example using an existing cable-stayed bridge. The findings show that error-minimised, well-distributed FE models can be obtained in terms of modal frequency errors and mode shape errors. The high quality of the candidate model sets is also verified by observations showing that the distributions of the structural parameters are consistent through each updated FE models, and the characteristic features of the target structure such as non-symmetric mode shapes are relatively well captured.

Parametric finite element model of lower cervical spine (C3–C7) in sagital plane