Uncertainties In Material Properties Research Articles

Centrifugal Test Replicated Numerical Model Updating for 3D Strutted Deep Excavation with the Response-Surface Method

Centrifugal tests provide an efficacious experimental process to predict the behavior of deep excavations, and numerical models are indispensable for demonstrating the test results and analyzing the engineering demand parameters. Uncertainty in material properties can cause simulations to differ from tests; therefore, updating the model becomes inevitable. This study presents a response-surface-based model updating technique for the nonlinear three-dimensional simulation of the centrifugal testing model of strutted deep excavation in sand. An overview of the fundamentals of the response-surface model is provided, including selecting uncertain parameters as input factors, creating a design order for training the model, building a second-order polynomial surface, and updating the input factors through targeted centrifugal results. The bending strains of diaphragm wall panels at multiple points along the depth are used to form the multiobjective function. Response-surface model predictions were well-matched with actual numerical responses, with less than a 0.5% difference. Parametric analyses could be conducted utilizing this updated strutted deep excavation model.

Dimensional stability and moisture-induced strains in spruce cross-laminated timber (CLT) under sorption/desorption isotherms

The paper presents a comprehensive experimental–numerical study on dimensional stability of spruce CLT panels and provides new insights into understanding the effect of mechanical properties of wood layers on moisture-induced strains. Deformations in Norway spruce CLT as well as their wood layers were studied in two orthogonal planes under sorption and desorption cycles. Coefficients of Moisture Expansion (CME), Coefficient of Moisture Contraction (CMC), as well as Coefficient of Thermal Expansion (CTE) were determined using dimensional measurements at 15° and 50℃. A 3-D nonlinear finite element (FE) model was developed to better understand the effect of glue and wood mechanical properties, as well as their CME and CTE on two CLT cross-sections. Unlike previous studies, the glue layers have been modelled as thin physical layers bonding wood layers. Hence, the effect of glue lines on the performance of CLT panels can be elucidated quantitatively. Results demonstrated good agreement between the FE model predictions of moisture-induced strains and the experimental data under both sorption and desorption isotherms when the wood moisture content is below fibre saturation point (FSB). Discrepancies between experiments and the model were noted at moisture contents above FSB. Such discrepancies may be attributed to measurement inaccuracies at small scale, the annual ring patterns, uncertainties in material properties, glue penetration into wood cell walls, as well as imperfect bonding at the glue lines. Results highlighted the significant effect of the mismatch between CTE and CME (or CMC) of wood in different directions on the development of stresses and consequently delamination, and perpendicular to grain failure in CLT panels subjected to extreme humidity levels.

Probabilistic approach to assess URM walls with openings using discrete rigid block analysis (D-RBA)

This study aims to improve our current understanding of the seismic assessment of load-bearing unreinforced masonry (URM) systems by proposing a probabilistic computational modeling framework using the discrete element method (DEM). The main objective is to predict the structural behavior and capacity of URM walls with openings subjected to lateral loading, considering uncertainties in material properties. The proposed modeling strategy represents masonry as an assembly of rigid blocks interacting along their boundaries by adopting the point-contact hypothesis. Fracture energy-based softening contact models are implemented into a commercial discrete element code (3DEC) to better simulate both the pre- and post-peak behavior of masonry. The results highlight the influence of material properties on the force capacity, displacement capacity (drift limits), and collapse mechanisms of walls with openings. Based on the applied non-spatial probabilistic analyses, the most commonly observed failure mechanisms are further assessed using a simplified macro-block formulation. As a result, practical, yet necessary, inferences are made, providing valuable contributions. Furthermore, the validated discontinuum analysis framework is demonstrated as an accurate structural analysis strategy and a useful approach to simulating the potential collapse mechanism of load-bearing URM structures.

Probabilistic safety assessment of nuclear containment vessel under internal pressure considering spatial variability of material properties

It is well known that ensuring the safety of the nuclear containment vessels (NCVs) is very important. The assessment should be performed in a probability method considering various uncertainties. However, most of investigations focus on the deterministic analysis or only regard the uncertainty as random variables. The widely existing spatial uncertainty is ignored for nearly all studies on the NCV. In this paper, we conducted a probabilistic safety assessment of a typical NCV considering the spatial uncertainty of material properties. The spatial variability is modeled with the random field generated by the geodesic-based decomposition method. Accompanied with a high-fidelity finite element (FE) procedure and Monte Carlo simulation, 800 FE models considering spatial varying concrete properties are analyzed to investigate the stochastic performance of the NCV. It is demonstrated that when the spatial variability of concrete properties is considered, the results are very different from the deterministic and the random variables-based results, including the deformation curves, the failure point distributions, the internal pressure capacity distribution, and the failure probability. Moreover, the common variables-based analysis will overestimate the actual reliability of the NCV. Consequently, it is necessary to consider the spatial variability in the safety assessment of the pressured NCVs, and this type of safety assessment can be conducted by the procedure proposed in the paper.

Uncertainty Quantification of Input Parameters in a 2-D Finite-Element Model for Broken Rotor Bar in an Induction Machine

In this article, a forward uncertainty propagation method is presented for a 2-D finite-element (FE) model in an induction machine. This method is applied to quantify the uncertainty of input parameters, for example, dimensions and material properties, and demonstrate their variability effect on harmonics related to the broken rotor bar (BRB) faults. To show the most influential input parameters in the case of BRB harmonics, a global sensitivity analysis is performed from the polynomial chaos expansion (PCE) approximation of the FE model. The results of this study indicate that BRB harmonics are highly sensitive to stator inner diameter, rotor outer diameter, rotor bar conductivity, and core materials. Moreover, the combined variability of these sensitive input parameters can attenuate the amplitude of the BRB harmonics 30%–90% compared to the simulation results at nominal values of input parameters and closely match with measurement results.

An elitist multi-objective particle swarm optimization algorithm for composite structures design

Optimization is an important area of research in Engineering, usually due to the potentiality of saving costs and improving structural safety. Composite structures are typically complex, and the Finite Element Method is frequently required to evaluate such structures. From another perspective, Robust Design Optimization (RDO) is an approach that aims to consider the variability of the composite structures response due to uncertainty in design variables or material properties. Under these conditions, the problem of maximizing the robustness is added to the optimality problem related to minimizing the structure's weight. This work combines the advantages of Particle Swarm Optimization (PSO), such as simplicity and greater exploration and exploitation capabilities, with fitness assignment methodologies and elitist strategies commonly applied to Genetic Algorithms. The purpose is to achieve a more perceptible Pareto front and faster. The development is applied to the RDO bi-objective optimization problem in composite structures. Results for optimal design variables, critical displacements and stresses are discussed. The results show that elitist-based PSO approaches lead to a Pareto front with a larger number of optimal solutions, with more robust and lighter solutions when compared to other methodologies.

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region.We use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. We show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Furthermore, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

This paper emphasized the size-dependent thermo-elastic vibration characteristics of uncertain functionally graded (FG) porous nano-beams by employing the first-order perturbation theory (FOPT) with the finite element method. An isoparametric quadratic beam element having three nodes is used for the finite element analysis of the nano-beams with variation in degree of uncertainty in material properties, geometric configuration, and thermal environment. The power-law model is employed to obtain the effective material properties of the considered beams. The governing equations are presented according to Eringen’s elasticity theory and Reddy’s beam theory using the minimum potential energy. The computed FOPT results for the vibration statistics are assessed with the help of Monte Carlo simulation (MCS) and a well agreement is found. Further, results are presented by analyzing the effects of degree of source uncertainty, size-dependent parameter, volume fraction indices, porosity distribution, porosity index, thermal environment, and aspect ratios on the fundamental frequency of the FGM nano-beams. The numerical results revealed the significant influence of thermal environment and porosity on the vibration statistics of the nano-beams and provided guidance for the precise and reliable design of nano-devices for the application in thermal environment.

FEM-Bayesian Kriging method for deformation field estimation of earth dams with limited monitoring data

The health monitoring and operation behavior assessment of earth dams are research focuses in geotechnical engineering. Due to the limited monitoring data and the uncertainty of material properties, existing monitoring data-based interpolation methods and mechanism-based finite element method (FEM) can not accurately estimate the dam deformation field. Therefore, studying an accurate estimation method of the deformation field is important to guarantee the serviceability of earth dams. In this paper, a FEM-Bayesian kriging (FBK) method is proposed, in which the FEM is introduced into the Bayesian kriging framework as the source of soft data, taking the FEM results as a trend surface of the deformation field, the spatial distribution of the random residual is determined by the exact monitoring data, thereby the FEM results are corrected. In this method, data-rich but low-precision FEM results and limited but high-precision monitoring data are coupled to approach the real deformation field. A numerical experiment is designed to verify the accuracy of the proposed method, and the estimation error of the FBK is reduced by about 80% compared with traditional methods. The case study of an actual earth dam also shows that the proposed method can effectively characterize the deformation behavior of earth dams.

System reliability-based design of steel-concrete composite frames with CFST columns and composite beams

This paper presents an effective reliability analysis procedure and proposes the system resistance factors for the system design of steel-concrete composite frames that comprise of concrete-filled steel tubular (CFST) columns and composite beams. Advanced analysis is employed to predict the ultimate resistance of frames using fibre beam-column elements in OpenSees. The obtained predictions of the load-carrying capacity of frames compare well with experimental results with the mean value of the test-to-prediction ratio around 1.027 and the coefficient of variation (CoV) of 8.4%. Both Monte Carlo (MC) and subset simulations are used in the reliability analysis. The uncertainties of model error, geometric and material properties, and external loads are included to predict the system reliability index. Five different frame configurations are considered. The results of the reliability analysis show that the system resistance factors for both US and AS codes are quite similar. In the case of gravity load, the system resistance factor is from 0.78 to 0.90, whilst this value for the case of combined wind and gravity load is from 0.8 to 0.95. The resistance factors suggested herein become valuable reference information for the system design of composite frames.

Effects of spatial variability and correlation in stochastic discontinuum analysis of unreinforced masonry walls

This study investigates the influence of the uncertainty in material properties on the in-plane lateral behavior and capacity of stone masonry walls via a stochastic discontinuum analysis framework. The framework is demonstrated via the 3D numerical assessment of an unreinforced masonry (URM) wall using a stochastic analysis in the form of Monte Carlo simulations. The random parameters considered in this study are the prism compressive strength of masonry, the tensile strength of the masonry units and joints, and the friction angle for joints and units. Novel research is conducted using a fast and accurate DEM model to determine whether the spatial variability of the material properties should be taken into account. In addition, the effects of joint-to-joint correlation of modeling parameters are examined to identify if such a correlation exists. A total of 1200 stochastic discontinuum analyses for 12 different cases are carried out. The results call attention to considering the spatial variability of the modeling parameters in the stochastic analysis, as they significantly reduce the variation in the wall's strength and displacement capacity. Results also demonstrate the influence of the correlation between bed-joint parameters on the strength and failure mode of the walls. Ultimately, propagation of the uncertainty in the joint friction angle into the strength and displacement capacity of the walls is quantified.

Lightweight design process considering assembly connection and non-probabilistic uncertainty with its application to machine structural design

Owing to the complexity of machines, lightweight structural design needs to consider the influence of assembly connection and non-probabilistic uncertainty in material properties. This study suggests a novel lightweight design process that incorporates these two factors. In this process, the assembly connection was modelled with the finite element model and validated by experiments. The non-probabilistic uncertainty was described using the multidimensional parallelepiped model, and then the corresponding non-probabilistic reliability-based design optimization method was applied to ensure the safety of structures. The proposed design process was applied to the structural design of the upper beam of a forming machine. The results showed that ignoring the assembly connection and non-probabilistic uncertainty may lead to an unsafe structural design, and thus they should be considered in the lightweight structural design of machines. Moreover, the weight reduction by 30.43% for the upper beam achieved using the proposed method demonstrated its effectiveness.

Coupling machine learning and stochastic finite element to evaluate heterogeneous concrete infrastructure

Probabilistic analyses facilitate the incorporation of inherent uncertainties in dam safety evaluation. Their application is limited due to the high computational burden, especially for the complex transient analyses and the cases in which the random field theory is applied to account for spatial uncertainty in material properties. In this work, uncertainty in the heterogeneous concrete is modeled by a series of probabilistic seismic finite element simulations. The outcome of stochastic models is fed into a random forests model for further post-processing and sensitivity analysis. The challenging aspect of this research lies in the fact that the initial number of finite element realizations is relatively small (due to computational time) regarding the random variables. Despite such an unfavorable setting, the meta-model showed reasonable accuracy for predicting the maximum displacement at the crest and the maximum stress at the base. A comprehensive discussion is provided on the variable importance and the partial effect of the inputs: the areas in the dam body with the highest impact in the response are identified, and the spatial distribution of input material properties is appropriately captured. These results show the possibilities of random forests in high-dimensional problems for predicting and interpreting dam behavior.

Probabilistic demand models and performance-based fragility estimates for concrete protective structures subjected to missile impact

The manifold missile attacks upon structures and deficiency of codal provisions motivated the current study to develop probabilistic demand models for protective structures subjected to hard missile impact. These energy-based models are estimated using a defined performance-based design framework (PBD) with three performance levels associated with four damage states, i.e. from minor damage to total collapse. The evaluation of unknown model parameters is constructed using the Bayesian approach. The current and upcoming range of structural variables is chosen for numerical experimental design. LS-DYNA, a finite element (FE) numerical method, is used to generate necessary probabilistic data of Reinforced Concrete (RC) & Prestressed Concrete (PC) panels subject to a hard missile. Novel formulations for local damages of a target, such as perforation limit of RC panel & Ballistic limit of the missile for RC & PC panels, are estimated. The developed demand models are used to assess the fragility estimation of either panel under chosen performance levels for a containment structure located in Tarapur, Palghar, India. An accurate fragility plot and comparative study shows the consistency of probabilistic models with test results. These models consider aleatory and epistemic uncertainties in modeling, material & geometrical properties, strain rate & inertia effect, and complex interaction involved in an impact scenario.

Structural uncertainty quantification with partial information

Quantifying the impact of uncertainty in material properties and ground motion records on the structural response is essential in implementing the performance-based earthquake engineering framework. Within the finite element approach with implicit limit states, a large number of nonlinear transient simulations are typically required to quantify the impact of potential epistemic and aleatory random variables (RVs). This paper’s contribution is twofold: First, we discuss how to develop a series of matrices that combine various realizations of hybrid epistemic-aleatory RVs. For this purpose, we modify the classical Cloud analysis (CLA) method (with only aleatory variability) to “Extended CLA” (which incorporates the epistemic uncertainties) and “Scaled CLA” (which uses higher scale factor) methods.Second, multiple matrix completion methods are proposed and applied to the generated dataset. The matrix completion is a means to estimate the simulation results for the entire set of input parameters by analyzing only a small subset of data. Our proposed algorithm includes both sampling techniques (for choosing a subset of representative simulations using unsupervised machine learning) and further refinement using regression analysis techniques, such as neural networks. The proposed algorithm is applied to a complex tower, and the structural responses (i.e., displacements and base shear) are estimated. Results show that the proposed algorithm can effectively estimate the response from a full set of nonlinear simulations. Further recommendations on choosing the optimal percentage of initial simulations are provided to develop fragility functions.

Bayesian inference of dense structural response using vision-based measurements

As-built structures typically behave differently than their analytical models because of uncertainties in material properties, boundary conditions, loading scenarios, or other modeling assumptions. Therefore, to perform structural health monitoring effectively, analytical models need to be calibrated or updated to match the measured responses from as-built structures. Bayesian model updating provides a rigorous framework to integrate data and parameter uncertainty and has been applied successfully in numerous application settings employing traditional sensors that are often sparsely distributed. Computer vision has shown tremendous success for the measurement of static and dynamic displacements of structures. Vision-based measurements have the potential to be transformative for model updating of large-scale civil infrastructure, as measurements can be obtained for dense array of points within the camera frame using a single device. However, model updating using vision-based measurements to date has been limited to the use of a few points selected manually, leading to the investigation of simple structures or their global behaviors (e.g. first few modal responses); developing a systematic and highly automated procedure for estimating structural displacement and its uncertainty densely, registering the measured data to the finite element model, and then updating the model based on all the available data remains a challenge. This study proposes Bayesian inference using dense vision-based measurements to estimate the localized response of the entire structure. Finite element models are incorporated into the three-dimensional displacement measurement and registration process (model-informed approach), and then the Markov chain Monte Carlo method is applied to enable the Bayesian inference for large and complex civil infrastructure. The proposed method is applied to a laboratory-scale three-dimensional steel truss to perform inference of the overall system response based on the a posteriori knowledge. The results demonstrate the adequacy of performing Bayesian inference of structural response using vision-based measurements.

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.

Stochastic finite element analysis of composite cycloidal propeller blade during crash-stop ship maneuver

This article quantifies uncertainty in the dynamic responses of marine cycloidal propeller (MCP) blade by Stochastic Finite Element Method (SFEM) during crash-stop ship maneuver. Stopping a ship in an emergency is known as crash-stop astern maneuver. A MCP contains a horizontal circular metallic disc on which six aerofoil blades are hung vertically. All blades are made up of carbon fiber-reinforced composite laminates. Uncertainty in ship speed and composite material properties are propagated to find out the statistical response of natural frequencies, displacement, and stresses on the blade. SFEM is a combination of Stochastic Response Surface Method (SRSM) and Finite Element Method (FEM). SRSM is a collocation-based non-intrusive polynomial chaos expansion to transform any random distribution into a stochastic response surface equation (surrogate model). During ship maneuvering motion, the whole unit rotates about a vertical axis at the centre. For each rotation of the disc, all blades undergo periodic oscillations. The SRSM for uncertainty propagation is computationally more efficient than the standard Monte Carlo Simulation (MCS) technique without compromising the accuracy of the results. It is observed that uncertainty in vibration responses of MCP blade is significant and worth study.

Reliability based failure assessment of deteriorated cast iron pipes lined with polymeric liners

Defects may appear or further develop in cast iron pipes lined with polymeric liners in the form of surface corrosion pits/patches, through-wall holes, gaps, longitudinal cracks, circumferential cracks and/or failed joints etc. This paper examines the performance of deteriorated cast iron pipes lined with polymeric liners using probabilistic analysis. The deterioration of lined cast iron pipes includes corrosion of cast iron pipes together with creep and creep rupture of polymeric liners. Various potential failure modes of lined pipes and the uncertainties of key physical parameters, including geometries, deterioration models and material properties of the pipe and liner, dimensions of the defects in the pipe and loading conditions etc., in probabilistic failure assessment of lined pipes are considered. The probability of failure of each lined pipe is calculated over its lifetime and a sensitivity analysis is also conducted to identify the most influential parameters on the failure probability of the lined pipe. It is found that the coefficients for the rupture strength and the creep retention factors of the liners are most influential on the probability of failure of the lined pipes.

Advanced Reliability Analysis of Mechatronic Packagings coupling ANSYS©and R

The complexity challenges of mechatronic systems justify the need of numerical simulation to efficiently assess their reliability. In the case of solder joints in electronic packages, finite element methods (FEM) are commonly used to evaluate their fatigue response under thermal loading. Nevertheless, Experience shows that the prediction quality is always affected by the variability of the design variables. This paper aims to benefit from the statistical power of the R software and the efficiency of the finite element software ANSYS©, to develop a probabilistic approach to predicting the solder joint reliability in Mechatronic Packaging taking into account the uncertainties in material properties. The coupling of the two software proved an effective evaluation of the reliability of the T-CSP using the proposed method.