Uncertainties In Material Properties Research Articles

Seismic analysis of gravity dam-foundation systems using stochastic spectral finite element method

Seismic analysis of dam-foundation systems is inherently complex due to uncertainties in material properties. This study investigates the effects of material randomness and heterogeneity on the seismic response of gravity dam-foundation systems using the stochastic spectral finite element method (SSFEM) based on the Karhunen Loève expansion and the polynomial chaos expansion. The Pine Plane dam is taken as an analysis example. First, the appropriate Karhunen Loève expansion modes and polynomial chaos order are determined for SSFEM by comparing them with the Monte-Carlo simulations. Subsequently, the seismic response of the dam is analyzed in the stochastic and deterministic models, respectively. Results indicate that material randomness and heterogeneity may reduce the seismic response of gravity dams, and the deterministic model may overestimate dynamic responses. Subsequently, the parametric analysis of the correlation length, which measures the spatial correlation between variables in different positions and indicates the size of heterogeneity material patches, is conducted. It is demonstrated that the correlation length would not significantly affect the mean responses, but a larger correlation length leads to greater dispersions in responses. Finally, the effects of randomness in the foundation are investigated. The heterogeneities in the foundation affect the response of the dam in the high-frequency range. Therefore, the uncertainty in material properties should be fully considered in a structural assessment and risk analysis.

A two-loop RBDO approach for steel frame structures using EVPS, GWO, and Monte Carlo simulation

This paper evaluates Enhanced Vibrating Particle System (EVPS) and Grey Wolf Optimizer (GWO) algorithms for Reliability-based Design Optimization (RBDO) of steel frames. The two-loop RBDO method minimizes frame weight while satisfying strength, drift, and reliability constraints, considering uncertainties in material properties and loads. Both EVPS and GWO effectively reduce structure weight and ensure required reliability levels, demonstrating their applicability in sustainable steel frame design.

Stochastic assessment of 3‐D tunnels in near‐fault ground motion using modified domain reduction method

AbstractA robust assessment of tunnels due to uncertainties present in soil and ground motion properties can affect the dynamic response of these structures. In this paper, a stochastic analysis considering an aleatory variability in shear velocity Vs by performing Monte Carlo simulations and assessing its influence on underground tunnels. To numerically assess the response of the soil‐tunnel system to near‐fault earthquake ground motion, the required computational domain usually spans multiple kilometers including both earthquake fault and the structure. Thus, these simulations are computationally expensive. An efficient alternative method, that is, the Domain Reduction Method (DRM), in which a modular two‐step methodology for reducing the computational costs in the large domain analysis is employed. A 3‐D soil‐tunnel structure interaction is modeled to simulate the response of tunnel subjected to an inclined earthquake fault. The numerical simulation of the soil‐tunnel‐fault system is conducted in an open‐source FE package called Multi‐hazard Analysis for STOchastic time DOmaiN phenomena (MASTODON) based on MOOSE framework. The interactive analyses are carried out for three distinct types of soils based on National Earthquake Hazards Reduction Program (NEHRP) provision, that is, soft, medium, and hard, by generating 130 realizations. The results provide many insights into the influence of local site effects, that is, frequency shift for the peak response and the importance of input ground motion characteristics that govern the response of underground structures. The dynamic response of the structure is very sensitive to the uncertainty in rock material properties, especially, the stiffness of the rock sample and the shear wave velocity.

A Pushover analysis approach considering structural and loading uncertainties for seismic performance assessment

This paper proposes an approach for evaluating the seismic performance of buildings. By considering the uncertainties in material and geometrical properties of the structural elements as well as those related to the seismic loading, this method aims to delimit the performance zone of the structure rather than focusing on a single performance point commonly used in pushover analysis. This zone makes it possible to identify the probable levels of performance of the building linked to uncertainties and to indicate the most severe level of damage. Reasoning by performance points leads to an answer that gives a single state of damage. The performance zone is defined by capacity curves and response spectrum representing the mean values plus and minus standard deviation obtained by Monte Carlo simulations. These simulations consider the stiffnesses of the structural elements, the natural periods, and the damping ratio of the response spectrum as random variables. The application of the procedure to a case of a building made it possible to identify the upper limit of damage corresponding to the most unfavourable scenario of uncertainties, as well as the situation of the response value of the studied structure in the performance zone, indicating a less critical level of damage (minor damage) to the building. The calculation of the performance point revealed a level of damage oscillating between Immediate Occupancy (IO) and Life Safety (LS). Considering the uncertainties in the material and geometric properties of the structural elements as well as those linked to the response spectrum, the probable extreme damage state is between the LS and CP levels (severe damage).

A comprehensive study on seismic dynamic responses of stochastic structures using sparse grid-based polynomial chaos expansion

The seismic response is a critical aspect of structural engineering, as it directly influences the design and safety evaluation of such systems. Structural seismic response becomes more complicated when unavoidable uncertainties in the structure are considered. Therefore, solving and analyzing the stochastic dynamic response of structures efficiently and accurately is of great significance. Various uncertainty quantification methods such as the stochastic finite element method, Monte Carlo method, and polynomial chaos expansion method have made significant progress in this field. However, these methods do not provide a comprehensive study of the seismic response of stochastic structures and efficiency problems rapidly emerge as the number of random variables increases. This paper delivers a comprehensive study of the seismic dynamic response of space truss and reticulated shell structure considering uncertainties in material properties, geometry, and loading. To this end, the finite element model of the structure was first modeled and the deterministic solutions were obtained. Then, polynomial surrogates are modeled for the natural frequency, mode participation factor, mode superposition response, and transient response of the structure under stochastic uncertainties. The sparse grid technique is used to select sparse quadrature points, which overcomes the curse of dimensionality caused by full grid integration. The results demonstrate that the sparse grid-based polynomial chaos expansion is more efficient. Uncertainty quantification reveals the uncertainty of modal analysis, response spectrum analysis, and transient response analysis of space truss and reticulated shell under seismic excitation. In summary, this study provides valuable insights and an efficient and accurate uncertainty quantification tool for the seismic dynamic analysis of stochastic structures, ultimately contributing to safer and more robust structural designs.

Probabilistic Design Method for Aircraft Thermal Protective Layers Based on Surrogate Models

In this study, a probabilistic method was proposed for an aircraft’s thermal protective layers. The uncertainties of material properties, geometric dimensions, and incoming flow environments were considered for the design inputs. To accelerate the design efficiency, Latin hypercube sampling and surrogate models were built based on finite element method calculations to enhance the simulation efficiency. Thus, the Monte Carlo method can be implemented with such a fast simulation method and produce a massive number of samples for the uncertainty quantification and sensitivity analysis, exploring their impact on the back temperature of the thermal protection layer. Compared to the deterministic method with the extreme deviation design, the probabilistic design yields a weight reduction of 15.61%. This indicates that probabilistic design is an efficient approach to enhance the performance of aircraft and reduce the overall weight of the aircraft. The general goal of this study is to provide a new design method for the coating film of thermal protection systems by considering multiple sources of uncertainties.

Study on the Stresses Released in a Notched, Postensioned Concrete Beam

Structural prestressed concrete elements (SPCE) face uncertainties in accurately assessing the actual prestressing force. Over time, the initial prestressing force decreases due to several factors. Incorrect estimation of prestress losses can lead to design inefficiencies or structural issues. Monitoring the prestressing force can be achieved through instrumentation during casting, but existing SPCE lack such devices, necessitating indirect methods to determine prestressing force variations. This study focuses on analyzing stresses released in a notched post-tensioned concrete beam using the saw-cutting technique. Surface notches induce local decompression, allowing for strain measurements in the isolated concrete block. These measurements, considering uncertainties in initial prestress and material properties, are analyzed through backward calculations. The findings enhance understanding of saw-cutting and enable future applications to determine effective prestressing force in unmonitored SPCE. Further experimental studies are required to explore prestressing force consistency under monitored conditions. This research provides valuable insights into the potential of the saw-cutting technique as a non-destructive testing method for assessing prestressing force in unmonitored SPCE. Accurately determining the prestressing force is crucial for evaluating existing SPCE and ensuring their structural integrity. Keywords: prestressed concrete, beam, test, saw-cut, notch

Generic fully coupled framework for reliability assessment of offshore wind turbines under typical limit states

Offshore wind turbines (OWTs) generally experience harsh marine environments with uncertainties in marine loads, soil properties, and material properties; therefore, the structural integrity assessment of OWTs is a challenging task. Most of the previously proposed methods for reliability assessment are time-consuming and neglect the coupling effects of aerodynamics, hydrodynamics, and OWT structural dynamics under complex environmental loads. In this study, a fully coupled framework for the reliability assessment of OWTs is proposed, in which a dynamic simulation tool in the time domain is combined with surrogate models. The established Kriging, multivariate regression, and support vector regression surrogate models are compared to determine the most feasible model. Furthermore, the influence of different solving methods, such as first-order reliability method (FORM), importance sampling (IS), and subset simulation (SS), on the estimation of structural reliability indexes are discussed. The superiority of the estimated reliability indexes in the safety assessment of OWTs is proved using the SS method based on the Kriging surrogate model. Subsequently, the potential failure modes of an OWT under different operational states are revealed, indicating that excessive tower vibrations must be eliminated for stable power production from OWTs. Furthermore, the SS method is found to be feasible as it ensures the estimation accuracy of the reliability indexes of the parked OWT based on Kriging and the other surrogate models. Finally, the significance of soil–structure interactions in the reliability index estimation is investigated, and the equivalent coupled spring boundary is proposed from the perspectives of structural safety and simulation accuracy.

Uncertainty quantification in multiaxial fatigue life prediction using Bayesian neural networks

In practical engineering scenarios, unforeseen failures may result in significant costs and risks. Assessing the uncertainty related to multiaxial fatigue life prediction is crucial for engineering applications. However, establishing a reliable multiaxial fatigue life prediction model remains challenging due to uncertainties in physical models, material properties, and measurement data. This paper proposes an effective Bayesian Neural Network (BNN) model for quantifying the uncertainty in multiaxial fatigue life prediction. Fatigue parameters in the multiaxial fatigue life prediction model are used as inputs for the BNN. The BNN method utilizes No-U-turn Sampler (NUTS) and Automatic Differentiation Variational Inference (ADVI) to address the inference problem in the model and perform life predictions for unknown non-proportional loading paths and different materials. Validation using experimental data from six different materials confirms the effectiveness of the BNN model. Experiments show that the performance of BNN models is beneficial in most cases compared to classical ML models, assessed through different error standards, statistical tests, Taylor diagrams, uncertainty analysis, and scatter index analysis. The proposed method provides a clear understanding of the uncertainty in multiaxial fatigue life prediction, offering a promising approach for simulating fatigue life under multiaxial loading in engineering applications.

Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

A modified interval perturbation statistical energy analysis method for structural reliability analysis of vibro-acoustic systems with interval uncertain parameters

Structural reliability analysis has become a critical aspect of engineering design for vibro-acoustic systems. With the increasing complexity and uncertainty of design parameters, it is essential to develop methods and tools that can accurately account for all the sources of uncertainty. This paper presents a novel approach for structural reliability analysis of vibro-acoustic systems with interval parameters within the framework of Statistical Energy Analysis (SEA). By introducing the Sherman-Morrison-Woodbury formula and the sub-interval technique, a modified interval perturbation statistical energy analysis is proposed to predict the interval bounds of energy and stress response. Then, the non-probabilistic structural reliability is assessed by using the volume ratio theory. Case studies of a plate-cavity system and a launch fairing model, in which the interval uncertainties in external loads and material properties are considered, are presented to demonstrate the effectiveness of the proposed approach. The results show that the proposed method can effectively handle uncertainties and provide accurate estimates of the probability of failure.

Development of a health monitoring framework: Application to a supercritical pulverized coal-fired boiler

This work details the development of a physics-based equipment health monitoring framework for a supercritical boiler, using first-principles models to estimate the remaining useful life (RUL) of its components. The framework accounts for fatigue and creep life consumption, generating spatio-temporal variations in mechanical and thermal stress. Analysis of the stress profile throughout the boiler highlights the finishing superheater inlet steam header as a vulnerable location susceptible to damage from cycling operation. The framework also yields quantified uncertainty in the RUL projection for specific locations, accounting for uncertainties in material properties and boiler operation. Results indicate that operational uncertainties (e.g., seasonal variation and operational strategy) and material properties (e.g., rupture time coefficients, Young's modulus, yield strength, and coefficient of thermal expansion) significantly impact the RUL of the finishing superheater inlet steam header. Additionally, case studies demonstrate the use of the health monitoring framework as a predictive tool for operational planning under uncertainty, including scenarios with and without updates on the operation of the boiler.

Stochastic critical buckling speed analysis of rim-driven rotating composite plate using NURBS-based isogeometric approach and HSDT

This article is the first attempt in the open literature to investigate the impact of uncertainty in material properties on the critical buckling speed of rim-driven rotating laminated plates. The formulations are constructed using the isogeometric approach (IGA) and higher-order shear deformation theory (HSDT). Coriolis and centrifugal forces resulting from rotation are taken into consideration. The results of the current formulation are compared to the previous results and validated. The accuracy and flexibility of the RBFN-based surrogate model, designed for uncertainty analysis, is verified by comparing the result with Monte Carlo simulation (MCS). Through a variety of parametric experiments, the critical buckling speed of rotating laminates driven by a rim is stochastically analyzed. Variance-based sensitivity analysis is employed to identify the influence of individual material properties on the critical buckling speed. Further, the impact of sensitive properties on the probability of structural failure is estimated. This research can be used to forecast the probability of failure of a structure at various levels of material uncertainty associated with it.

Deterministic and stochastic flexural behaviors of laminated composite thin-walled I-beams using a sinusoidal higher-order shear deformation theory

In this study, a novel sinusoidal higher-order shear deformation thin-walled beam theory is presented to examine the effects of material properties and external load uncertainty on static responses of laminated composite thin-walled beams with open sections. The solution for the deterministic flexural analysis is based on Hamilton’s principle and Ritz-type exponential shape function series. Several mechanical parameters of laminated composite materials are randomized and plugged into the beam solver to investigate the thin-walled beam’s stochastic flexural behaviors. The computational cost and accuracy of the polynomial chaos expansion (PCE) method with both projection and linear regression approaches are presented and evaluated by comparing its results with crude Monte Carlo simulation (MCS). This comparison allows for a thorough assessment of the PCE method’s performance. Additionally, a sensitivity analysis is conducted to compare the relative significance of the uncertainty in material properties and loads on the stochastic responses. The supervised training of the artificial neural network based on the MCS beam data is also conducted and compared to the PCE and MCS methods. The findings about the stochastic outputs are introduced in various statistical metrics and illustrations to demonstrate the influences of material properties’ randomness on different laminated composite thin-walled beam configurations.

Hygrothermal Modelling of one-dimensional Wall Assemblies: inter-model Validation between WUFI and DELPHIN

Various Heat-Air-and-Moisture models may give divergent results for the same case, due to differences in assumptions, simplifications, or approximations. Inter-model comparisons have been used as ‘peer review’, but common limitations and/or mistakes may remain concealed. Recent validation efforts, confronting simulations with measured datasets, use limited materials, configurations, and boundary conditions. A thorough and stepwise assessment is still lacking. In this study, dedicated hygrothermal experiments on four wall assemblies (comprising calcium silicate board, mineral wool, wood fiber board and vapor barrier in different configurations) are conducted in a hot box-cold box at KU Leuven, Belgium as a benchmark. Temperatures, relative humidity, heat fluxes and moisture mass are monitored while the thermal and hygric properties of the materials from the same batch are measured. One dimensional simulations in WUFI and DELPHIN are employed to reproduce the experiments in three stages: (1) “similar” materials (with the closest properties) from respective databases provide realistic trends but also significant deviations; (2) “same” materials (attained by mathematical translation) give better agreement but uncertainties in material properties and simplifications still have great influence; (3) monitored datasets are employed to compare with simulated results using measured material properties, based on which a collaborative inter-model blind-box validation has been initiated.

Holistic estimation and sensitivity-based experiment design method of composite laminate first-ply failure models using statistical approaches

In this paper, a probabilistic approach is presented to simultaneously evaluate all strength and additional fitting parameters of a pre-selected composite first-ply failure model using known uniaxial and multiaxial failure stress states. The method processes all available mechanical test results in terms of failure stress states as one batch of data. For parameter fitting it implements the Maximum Likelihood Method and controlled numerical sampling techniques. The present work introduces the theoretical background as well as investigates the effect of the selection of the underlying strength distribution function type. The biggest benefit of this approach is the simultaneous handling of all available test data as well as the generality in terms of assumed strength distribution function and failure model type. In addition, the automatic evaluation of the uncertainty of all strength parameters enables introduction of a safety factor quantification related to uncertainty in material properties as one of the main contributors to scatter sources. A local sensitivity-based stress-state determination process is also introduced to design a set of input failure stresses that guarantee the identifiability of all parameters thus, ensuring robustness of the fitted constants. The entire methodology is demonstrated through the example of the Tsai-Wu model by processing experimental data and by comparing the results against the literature.

Damage description, material characterization, retrofitting, and dynamic identification of a complex neoclassical monument affected by the 2015 Gorkha, Nepal earthquake

Neoclassical monuments with multiple courtyards are complex brick masonry constructions of the 19th century. They are vulnerable to seismic ground shaking. The 2015 Gorkha earthquake in Nepal damaged several such structures in Kathmandu Valley. Seismic capacity and/or vulnerability of such structures is associated with large uncertainties. Numerical modeling of such structures is challenging due to underlying uncertainties in their material properties and lack of construction details at the time of their construction. Retrofitting of such structures when damaged by earthquakes, although important for the preservation of their historical and cultural values, is challenging on many fronts. This paper presents a case study of a neoclassical monument in Nepal. A detailed description of the damage caused by the 2015 Gorkha earthquake is presented. Then retrofitting measures used to restore and enhance the structure of the monument are discussed in detail. In-situ and laboratory tests conducted to characterize material properties of the monument are also presented. Numerical models of the monument are then created to estimate its modal vibration properties. Dynamic identification of vibration frequencies of the monument before and after retrofitting is shown as a viable means to reduce uncertainties in the numerical model, a large part of which is due to inherent uncertainties in material properties of such monuments. The results show a significant increase in the stiffness of the structure after retrofitting it with measures that are compliant with the preservation of historical monuments.

Stochastic nonlinear inelastic analysis for steel frame structure using Monte Carlo sampling

This work comprehensively investigates the realistic ultimate resistance of steel frame structures based on the probability study model of input random variables due to uncertainty of material properties and geometric parameters. Four independent parameters and thirteen of their dependent components vary randomly in a variational range and seven scenarios of random combination are investigated by the probabilistic modeling, which incorporates the advanced inelastic analysis with direct Monte Carlo simulation. The analysis results for a typical example shows that the stochastic analysis result of steel frame's realistic ultimate resistance is lower than its deterministic analysis result, indicating that a stochastic analysis is needed to comprehensively qualify the safety of the structure. Moreover, a spectrum response, which is produced based on stochastic analysis, provides a better scientific solution.

Self-optimization wavelet-learning method for predicting nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations

In the present work, we propose a self-optimization wavelet-learning method (SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations. The randomly structural heterogeneity, temperature-dependent nonlinearity and material property uncertainty of heterogeneous materials are considered within the proposed self-optimization wavelet-learning framework. Firstly, meso- and micro-structural modeling of random heterogeneous materials are achieved by the proposed computer representation method, whose simulated hierarchical configurations have relatively high volume ratio of material inclusions. Moreover, temperature-dependent nonlinearity and material property uncertainties of random heterogeneous materials are modeled by a polynomial nonlinear model and Weibull probabilistic model, which can closely resemble actual material properties of heterogeneous materials. Secondly, an innovative stochastic three-scale homogenized method (STSHM) is developed to compute the macroscopic nonlinear thermal conductivity of random heterogeneous materials. Background meshing and filling techniques are devised to extract geometry and material features of random heterogeneous materials for establishing material databases. Thirdly, high-dimensional and highly nonlinear material features of material databases are preprocessed and reduced by wavelet decomposition technique. The neural networks are further employed to excavate the predictive models from dimension-reduced low-dimensional data. At the same time, advanced intelligent optimization algorithms are utilized to self-search the optimal network structure and learning rate for obtaining the optimal predictive models. Finally, the computational accuracy and efficiency of the presented approach are validated via various numerical experiments on realistic random composites.

Modeling of frontal polymerization of carbon fiber and dicyclopentadiene woven composites with stochastic material uncertainty

A novel finite element modeling framework is proposed for simulating dicyclopentadiene (DCPD) frontal polymerization in carbon fiber (CF) woven composites. A mesoscale CF/DCPD representative volume element (RVE) model was developed with two triggering directions, resulting in out-of-plane and in-plane DCPD polymerization. The Arrhenius equation coupled with a modified Prout-Tompkins autocatalytic model was used to evaluate the dynamic DCPD polymerization process. The rate and degree of DCPD cure were calculated by the material property uncertainties of DCPD with and without random void inclusions (3 % used as a reference in this work). The DCPD frontal polymerization in CF/DCPD composite was strongly influenced by the triggering direction. In the RVE model considered in this work, DCPD frontal polymerization was slightly faster in the in-plane (warp/weft yarn) directions than the out-of-plane (thickness) direction; polymerization occurs first in DCPD resin and is followed by CF/DCPD interface. Material property uncertainty and void inclusion had significant effects on both out-of-plane and in-plane DCPD polymerization. A large variation in DCPD material properties and the presence of void inclusions significantly delayed the rate and degree of DCPD frontal polymerization. This work provides the preliminary estimation of the frontal polymerization of DCPD-based composites and guides the structural applications of these materials.