Stochastic Finite Element Model Research Articles

Experimental and numerical study on lateral stability of temporary structures

This paper investigates the lateral performance of temporary structures, which consist of slender members and corresponding joints, under both vertical and horizontal loads. The ultimate bearing capacity, failure modes and the strain distribution of members are illustrated. Experimental results indicate that the lateral stability of the temporary structures is weaker than the vertical stability. Diagonal bracings are the main load-bearing members which resist horizontal loads while the horizontal bars are used to keep stress low. Based on the joint mechanical parameters and the probabilistic models of initial geometric imperfection, the stochastic finite element models (SFEMs) using the Monte Carlo method have been established. The models can consider the semi-rigid performances of joints and initial geometric imperfection. The numerical results demonstrate consistency with structural tests data. Moreover, the influences of structural layers and spans are analysed based on the SFEM. Multiple factors, including spans, layers and upper vertical loads, should be considered when the lateral capacity of temporary structures is calculated. A rapid prediction formula of the lateral stability of temporary structure has been obtained.

Effect of delamination on the stochastic natural frequencies of composite laminates

The coupled effect of manufacturing uncertainty and a critical service-life damage condition (delamination) is investigated on the natural frequencies of laminated composite plates. In general, delamination is an unavoidable phenomenon in composite materials encountered often in real-life operating conditions. We have focused on the characterization of dynamic responses of composite plates considering source-uncertainty in the material and geometric properties along with various single and multiple delamination scenarios. A hybrid high dimensional model representation based uncertainty propagation algorithm coupled with layer-wise stochastic finite element model of composites is developed to achieve computational efficiency. The finite element formulation is based on Mindlin's theory considering transverse shear deformation. Numerical results are presented for the stochastic natural frequencies of delaminated composites along with a comprehensive deterministic analysis. Further, an inevitable effect of noise is induced in the surrogate based analysis to explore the effect of various errors and epistemic uncertainties involved with the system.

Sensitivity analysis of structural health risk in operational tunnels

Abstract During the operation of metro tunnels, structural performance could inevitably degrade due to the combined effects of the stochastic and disadvantageous environment. In order to reduce the randomness and uncertainty underlying the structural safety risk analysis in operational tunnels, this paper develops a novel hybrid approach to perform global sensitivity analysis. The deterministic and stochastic finite element (FE) model is used to develop the approximate relationship between input and output parameters with a high level of accuracy. Based on the simulated data from an FE model, a meta-model is constructed by a built Particle Swarm Optimization-Least Square Support Vector Machine (PSO-LSSVM) model. In this research, 10,000 groups of data are generated by the built PSO-LSSVM model, which provides data support for the global sensitivity analysis through Extended Fourier Amplitude Sensitivity Test (EFAST). The input variables with a high global sensitivity are identified as crucial variables which should be well controlled and managed during tunnel operation. A Hankou-Fanhu (H-F) tunnel section in the Wuhan metro system is utilized as a case study to verify the applicability of the proposed approach. Global sensitivity analysis enables the reduction of the epistemic uncertainty in tunnel structural safety management, providing insight into a better understanding of (1) the input-output causal relationships of the structural safety risk in operational tunnels, (2) the reduction of the epistemic uncertainty in project safety management of operational tunnels.

Uncertainty Quantification for Junction Temperature of Automotive LED With Die-Attach Layer Microstructure

Junction temperature is a critical metric for reliability evaluation of light-emitting diodes (LEDs) as light sources for automotive lamps. While numerous researchers have quantified the junction temperature accurately, uncertainty factors including electrical–thermal–mechanical boundary conditions and the die-attach layer (DAL) microstructure in automotive LEDs have not been addressed; the propagation of these variables degrades the precision of the junction temperature quantification. In this paper, a junction temperature uncertainty quantification framework involving finite element modeling, the evolution separation spectrum, and Monte Carlo simulation is introduced to build 3-D stochastic finite element models for automotive LEDs with stochastic DAL microstructures. Evolution of the statistical junction temperature probability for three types of automotive LEDs subjected to electrical–thermal–mechanical loadings is discussed and the failure risk is predicted. The results show that the temperature-mechanical displacement coupling of the DAL plays a major role in the junction temperature with regard to automotive boundary loadings, and the thermal power load is more likely to cause junction temperature deterioration of LED with DALs having voids. The automotive LED failure rate is dependent upon the boundary conditions, the DAL microstructures, and the LED numbers. The failure rate for LED modules with DALs having voids is higher than that for modules with uniform DALs; the failure rate is higher in aged LED modules; the failure risk at the given junction temperature threshold increases with increasing LED numbers in the module; and when operating at lower junction temperatures, the voids in LED DALs may not increase the module failure risk.

Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties

This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen–Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.

Probabilistic structural damage detection approaches based on structural dynamic response moments

Because of the inevitable uncertainties such as structural parameters, external excitations and measurement noises, the effects of uncertainties should be taken into consideration in structural damage detection. In this paper, two probabilistic structural damage detection approaches are proposed to account for the underlying uncertainties in structural parameters and external excitation. The first approach adopts the statistical moment-based structural damage detection (SMBDD) algorithm together with the sensitivity analysis of the damage vector to the uncertain parameters. The approach takes the advantage of the strength SMBDD, so it is robust to measurement noise. However, it requests the number of measured responses is not less than that of unknown structural parameters. To reduce the number of measurements requested by the SMBDD algorithm, another probabilistic structural damage detection approach is proposed. It is based on the integration of structural damage detection using temporal moments in each time segment of measured response time history with the sensitivity analysis of the damage vector to the uncertain parameters. In both approaches, probability distribution of damage vector is estimated from those of uncertain parameters based on stochastic finite element model updating and probabilistic propagation. By comparing the two probability distribution characteristics for the undamaged and damaged models, probability of damage existence and damage extent at structural element level can be detected. Some numerical examples are used to demonstrate the performances of the two proposed approaches, respectively.

Structural failure investigations through probabilistic nonlinear finite element analysis: Methodology and application

Abstract Structural failure investigations can be strongly influenced by high levels of uncertainty in modelling parameters, particularly in the case of historical constructions. This suggests forensic analysts to perform probabilistic simulations, allowing a risk-informed diagnosis and prognosis of structural failures. In this study, a failure investigation methodology including uncertainty characterisation, modelling and propagation is presented and applied to a historic piperno stone balcony, the collapse of which caused four casualties. High uncertainty in physical and mechanical properties of piperno stone, which has been widely used for a long time in the architectural heritage of Naples and Southern Italy, motivated stochastic finite element (SFE) simulations to account for spatial variability of material properties throughout the balcony. Based on field inspections, laboratory surveys and experimental testing, a three-dimensional finite element (FE) model with four alternative restraint conditions was developed and material properties were statistically characterised. Experimental data were found to be in agreement with those available in the literature for similar piperno stones. Deterministic nonlinear FE simulations with mean material properties showed a major influence of restraint conditions, providing an initial identification of the most realistic model that was able to reproduce the observed damage. Then, SFE simulations were performed on structural models having random fields of material properties. It is shown that the selected SFE model of the balcony had a mean load capacity very close to the total load expected at the time of collapse, allowing the lowest uncertainty level in the output of forensic analysis.

Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates

This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C0 stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.

Probabilistic Baseline of Finite Element Model of Bridges under Environmental Temperature Changes

AbstractThe material properties and structural stiffness of actual bridges fluctuate with variations in environmental temperature; therefore, it is not appropriate to use a determined finite element model (FEM) as the baseline model for localizing the structural damage of bridges. To address this issue, we proposed the concept of the probabilistic baseline of FEM of bridges under variable environmental temperature, that is, we established reasonable probability distributions of the physical parameters of bridges that are suitable for damage localization with varying environmental temperature. First, a method is presented to obtain the probabilistic baseline of FEM of bridges, which imports cluster analysis into stochastic FEM updating. Unlike the conventional methods, the measured natural frequencies first are classified into different clusters using the Gaussian mixture method (GMM), with each cluster consisting of measured data that satisfy the same Gaussian distribution. Then, the conventional methods of stochastic FEM updating can be conveniently implemented to obtain the probabilistic baseline of FEM for each cluster. Second, for each cluster, the mean values and covariance of the updating parameters are updated in two sequential steps, and a new approach is proposed for determining the initial covariance of the updating parameters. The results of an actual example show that predetermining a reasonable initial covariance for the updating parameters can accurately and efficiently obtain the updated results. Finally, the effectiveness of the presented method is verified through the monitoring data of an actual bridge.

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

A stochastic finite element-based methodology is developed for creep damage assessment in pipings carrying high-temperature fluids. The material properties are assumed to be spatially randomly inhomogeneous and are modelled as 3-D non-Gaussian fields. A spectral-based approach for random field discretization that preserves exactly the non-Gaussian characteristics is used in developing the stochastic finite element model. The meshing used in random field discretization is distinct from FE meshing, depends on the correlation characteristics of the random fields and is computationally efficient. The methodology enables estimating the failure probability and the most likely regions of failure in a section of a circular pipe.

Surface Defect Inspection of Pressure Equipment Based on Indentation and Numerical Simulation

Surface defects caused by damage or corrosion are major factor in petrochemical pressure vessels and line pipes failure. The characteristic size of typical surface defect is from micron to submillimeter which belongs to mesoscopic scale, leading to difficulties for inspection and evaluation. The instrumented indentation method has widely used in the characterization of micro-zone mechanical behavior which could be effective in surface defects analysis. This paper aims at investigating the correspondence between indentation experimental results and distribution characteristics of surface defects. Mechanical properties of pressure vessel steel with surface defects are measured by indentation, and corresponding finite element models are established. Finite element simulation results of equivalent mechanical properties under indentation and three dimensional deformations are compared, and the applicability of finite element models for indentation test of steel with surface defects is analyzed. The effect of randomized surface defects on measuring result is studied subsequently using stochastic finite element models. The relation of equivalent mechanical properties and description of surface defects is proposed. The achievement could used to estimate the degree of damage or corrosion by miniature indentation testing techniques for safety assessment.

Deterministic and Stochastic Model Order Reduction for Vibration Analyses of Structures With Uncertainties

To reduce the computational effort using polynomial chaos expansion to predict the dynamic characteristics of structures with several uncertain parameters, hybrid techniques combining stochastic finite element analysis with either deterministic or stochastic model order reduction (MOR) are developed. For the deterministic MOR, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. For the stochastic MOR, a stochastic reduced basis method is implemented in which the structural modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. To demonstrate the computational efficiency of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate randomized by uncertain geometrical and material parameters is examined. Results are compared with both Monte Carlo (MC) simulations and nonreduced stochastic models. Using the reduced models, the effects of the individual uncertain parameters as well as the combined uncertainties on the dynamic characteristics of the plate are examined.

Natural frequencies-based stochastic finite element model updating using equal weighting factors

Natural frequencies-based stochastic finite element model updating using equal weighting factors

Natural frequencies-based stochastic finite element model updating using equal weighting factors

Though traditional deterministic finite element model updating (FEMU) methods are being used in the industry with good results, however, these methods do not include the small variations in uncertainties. These uncertainties arise due to unknown experimental errors or variability in nominally identical dynamic systems. It is necessary to resort to the stochastic finite element model updating (SFEMU) methods to deal with these problems. Although any modal parameter can be used to update a dynamic system, this paper explores the possibility of updating a dynamic system using only natural frequencies, because natural frequencies can be obtained more accurately with lesser computational cost than obtaining any other modal parameters. In this paper, stochastic finite element model updating procedure has been proposed which uses natural frequencies with equal weighting factors to perform the stochastic finite element model updating. The effectiveness of the proposed stochastic finite element model updating procedure is demonstrated by two numerical examples and one experimental example. The results show that the stochastic finite element model updating procedure using only natural frequencies with equal weighting factors can be used for accurate quantification of uncertainties in the dynamic systems.

Effects of cross-correlated multiple spatially random soil properties on wave-induced oscillatory seabed response

The evaluation of seabed response under wave loading is important for prediction of stability of foundations of offshore structures. In this study, a stochastic finite element model which integrates the Karhunen-Loève expansion random field simulation and finite element modeling of wave-induced seabed response is established. The wave-induced oscillatory response in a spatially random heterogeneous porous seabed considering cross-correlated multiple soil properties is investigated. The effects of multiple spatial random soil properties, correlation length and the trend function (the relation of the mean value versus depth) on oscillatory pore water pressure and momentary liquefaction are discussed. The stochastic analyses show that the uncertainty bounds of oscillatory pore water pressure are wider for the case with multiple spatially random soil properties compared with those with the single random soil property. The mean pore water pressure of the stochastic analysis is greater than the one obtained by the deterministic analysis. Therefore, the average momentary liquefaction zone in the stochastic analysis is shallower than the deterministic one. The median of momentary liquefaction depth generally decreases with the increase of vertical correlation length. When the slope of the trend function increases, the uncertainty of pore water pressure is greatly reduced at deeper depth of the seabed. Without considering the trend of soil properties, the wave-induced momentary liquefaction potential may be underestimated.

Stochastic finite element model calibration based on frequency responses and bootstrap sampling

A new stochastic finite element model calibration framework for estimation of the uncertainty in model parameters and predictions from the measured frequency responses is proposed in this paper. It combines the principles of bootstrapping with the technique of FE model calibration with damping equalization. The challenge for the calibration problem is to find an initial estimate of the parameters that is reasonably close to the global minimum of the deviation between model predictions and measurement data. The idea of model calibration with damping equalization is to formulate the calibration metric as the deviation between the logarithm of the frequency responses of FE model and a test data model found from measurement where the same level of modal damping is imposed on all modes. This formulation gives a smooth metric with a large radius of convergence to the global minimum. In this study, practical suggestions are made to improve the performance of this calibration procedure in dealing with noisy measurements. A dedicated frequency sampling strategy is suggested for measurement of frequency responses in order to improve the estimate of a test data model. The deviation metric at each frequency line is weighted using the signal-to-noise ratio of the measured frequency responses. The solution to the improved calibration procedure with damping equalization is viewed as a starting value for the optimization procedure used for uncertainty quantification. The experimental data is then resampled using the bootstrapping approach and the FE model calibration problem, initiating from the estimated starting value, is solved on each individual resampled dataset to produce uncertainty bounds on the model parameters and predictions. The proposed stochastic model calibration framework is demonstrated on a six degree-of-freedom spring-mass system prior to being applied to a general purpose satellite structure.

A computational stochastic multiscale methodology for MEMS structures involving adhesive contact

This work aims at developing a computational stochastic multiscale methodology to quantify the uncertainties of the adhesive contact problems due to capillary effects and van der Waals forces in MEMS. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the involved structural behaviors suffer from a scatter. To numerically predict the probabilistic behaviors of structures involving adhesion, the proposed method introduces stochastic meso-scale random apparent contact forces which can be integrated into a stochastic finite element model. Because the evaluation of their realizations is expensive, a generator for the random apparent contact force using the polynomial chaos expansion is constructed in an efficient way.

Stochastic finite element method for free vibration characteristics of random FGM beams

The stochastic free vibration characteristics of a functionally graded material (FGM) beam with material properties graded across spatial position are examined in this paper, in which both physical parameters of each constituent material and volume fraction index denoting material distribution are treated as random variables with low variability. Integrating random variables into modelling by using the first-order perturbation technique, a stochastic finite element model is developed for the FGM beam and the direct relationship is derived between the first-derivatives of structural modal frequencies and mode shapes with respect to random variables and those of the FGM effective material properties with respect to random variables. The material graduation in FGMs is represented by power-law function. Comparing with the Monte-Carlo simulation, the influence of constituent material properties, material distribution and slenderness ratio on the statistics of free vibration characteristics for the FGM beam is systemically examined. The results show that the randomness coming from constituent material physical properties contributes much more to the scatterings of modal parameters than the randomness from material distribution while material distribution plays an important role in the stochastic study of the structure, and the slenderness ratio has significant effect on the mean values of both modal frequencies and mode shapes.

Development and validation of a generic finite element vehicle buck model for the analysis of driver rib fractures in real life nearside oblique frontal crashes

ObjectiveFrontal crashes still account for approximately half of all fatalities in passenger cars, despite several decades of crash-related research. For serious injuries in this crash mode, several authors have listed the thorax as the most important. Computer simulation provides an effective tool to study crashes and evaluate injury mechanisms, and using stochastic input data, whole populations of crashes can be studied. The aim of this study was to develop a generic buck model and to validate this model on a population of real-life frontal crashes in terms of the risk of rib fracture. MethodThe study was conducted in four phases. In the first phase, real-life validation data were derived by analyzing NASS/CDS data to find the relationship between injury risk and crash parameters. In addition, available statistical distributions for the parameters were collected. In the second phase, a generic parameterized finite element (FE) model of a vehicle interior was developed based on laser scans from the A2MAC1 database. In the third phase, model parameters that could not be found in the literature were estimated using reverse engineering based on NCAP tests. Finally, in the fourth phase, the stochastic FE model was used to simulate a population of real-life crashes, and the result was compared to the validation data from phase one. ResultsThe stochastic FE simulation model overestimates the risk of rib fracture, more for young occupants and less for senior occupants. However, if the effect of underestimation of rib fractures in the NASS/CDS material is accounted for using statistical simulations, the risk of rib fracture based on the stochastic FE model matches the risk based on the NASS/CDS data for senior occupants. ConclusionThe current version of the stochastic model can be used to evaluate new safety measures using a population of frontal crashes for senior occupants.

Assessment of stochastically updated finite element models using reliability indicator

Finite element (FE) model updating techniques have been a viable approach to correcting an initial mathematical model based on test data. Validation of the updated FE models is usually conducted by comparing model predictions with independent test data that have not been used for model updating. This approach of model validation cannot be readily applied in the case of a stochastically updated FE model. In recognizing that structural reliability is a major decision factor throughout the lifecycle of a structure, this study investigates the use of structural reliability as a measure for assessing the quality of stochastically updated FE models. A recently developed perturbation method for stochastic FE model updating is first applied to attain the stochastically updated models by using the measured modal parameters with uncertainty. The reliability index and failure probability for predefined limit states are computed for the initial and the stochastically updated models, respectively, and are compared with those obtained from the ‘true’ model to assess the quality of the two models. Numerical simulation of a truss bridge is provided as an example. The simulated modal parameters involving different uncertainty magnitudes are used to update an initial model of the bridge. It is shown that the reliability index obtained from the updated model is much closer to true reliability index than that obtained from the initial model in the case of small uncertainty magnitude; in the case of large uncertainty magnitude, the reliability index computed from the initial model rather than from the updated model is closer to the true value. The present study confirms the usefulness of measurement-calibrated FE models and at the same time also highlights the importance of the uncertainty reduction in test data for reliable model updating and reliability evaluation.