Uncertainties In Material Properties Research Articles

Characterizing the cyclic behavior of piping T-joint connections

Failures in piping systems during earthquakes have resulted in operational disruptions and financial losses for critical facilities, such as nuclear power plants and hospital infrastructure. Past earthquake events have shown that failures in piping systems occur primarily at discontinuities, such as T-joints, elbows, and nozzles. Therefore, it is important to understand the behavior of piping joints under cyclic loading to mitigate the impact of such failures. This manuscript investigates the behavior of piping T-joints under cyclic loading. The behavior of these joints under cyclic loading is greatly influenced by the material properties of the piping components. Any variation in material properties can alter the responses of the piping joints, eventually affecting the seismic fragility of the piping system. This manuscript uses data from laboratory experiments to characterize and quantify uncertainties in material properties that influence the seismic fragility of piping systems. Additionally, this manuscript uses the data from laboratory experiments to validate a new limit state for characterizing the failure of piping joints under cyclic loading. In addition, it explores the effects of uncertainties in material properties on the performance function used to characterize the new limit state for failures at T-joint connections. In summary, this study provides insights into the influence of uncertainty in material properties on the seismic fragility of a piping system with an intent to improve the resiliency of piping systems in critical infrastructure facilities.

Distributed-collaborative surrogate modeling approach for creep-fatigue reliability assessment of turbine blades considering multi-source uncertainty

This paper proposes a substructure-based distributed-collaborative surrogate modeling approach for improving the accuracy and efficiency in the estimation of the creep-fatigue reliability of gas turbine blades with the integration of the Least Absolute Shrinkage and Selection Operator (LASSO), kriging, Distributed Collaborative (DC) strategy and substructure simulation method, called as the substructure-based DCLKM. Further, the creep-fatigue reliability assessment framework is set by combining the proposed substructure-based DCLKM with some theoretical models, which takes into account the uncertainties of structural sizes, applied loads and material properties and the nonlinearity of creep/fatigue damage interaction. Firstly, the total strain range, mean stress, absolute temperature and maximum stress at the critical location are regarded as the first-level output responses, and their required samples are predicted through the fitted surrogate models. Secondly, the creep life and Low-Cycle Fatigue (LCF) life are regarded as the second-level output responses and predicted. Finally, the creep-fatigue damage and reliability assessment are performed for several given applied cycles, respectively. The proposed substructure-based DCLKM is validated on a case study. The results show that the proposed substructure-based DCLKM is feasible with high accuracy and efficiency in the creep-fatigue reliability assessment of turbine blades.

Efficient reliability-based concurrent topology optimization method under PID-driven sequential decoupling framework

The continuous improvement of advanced equipment performance has promoted the development of detailed structural design. The detailed design of the structure should meet many requirements such as high reliability, strong robustness, lightweight, and high efficiency. This paper proposes a proportional-integral-derivative-driven efficient reliability-based concurrent topology optimization strategy under the sequential framework. Considering the uncertainty of load position, load direction, load amplitude, and material properties, an efficient reliability-based concurrent topology optimization model is constructed based on the sequential strategy. Based on effectively quantifying the nonlinear characteristics brought by multi-source uncertainty, a constraint refinement movement strategy based on the proportional-integral-derivative controller is proposed, which to some extent overcomes the tedious calculation of uncertainty quantification. This paper provides sensitivity information on macroscopic and microscopic level set functions under displacement constraints. Four numerical examples demonstrate the effectiveness, efficiency, and generalization ability of the proposed method.

Investigating the Impact of Blunt Force Trauma: A Probabilistic Study of Behind Armor Blunt Trauma Risk.

Evaluating Behind Armor Blunt Trauma (BABT) is a critical step in preventing non-penetrating injuries in military personnel, which can result from the transfer of kinetic energy from projectiles impacting body armor. While the current NIJ Standard-0101.06 standard focuses on preventing excessive armor backface deformation, this standard does not account for the variability in impact location, thorax organ and tissue material properties, and injury thresholds in order to assess potential injury. To address this gap, Finite Element (FE) human body models (HBMs) have been employed to investigate variability in BABT impact conditions by recreating specific cases from survivor databases and generating injury risk curves. However, these deterministic analyses predominantly use models representing the 50th percentile male and do not investigate the uncertainty and variability inherent within the system, thus limiting the generalizability of investigating injury risk over a diverse military population. The DoD-funded I-PREDICT Future Naval Capability (FNC) introduces a probabilistic HBM, which considers uncertainty and variability in tissue material and failure properties, anthropometry, and external loading conditions. This study utilizes the I-PREDICT HBM for BABT simulations for three thoracic impact locations-liver, heart, and lower abdomen. A probabilistic analysis of tissue-level strains resulting from a BABT event is used to determine the probability of achieving a Military Combat Incapacitation Scale (MCIS) for organ-level injuries and the New Injury Severity Score (NISS) is employed for whole-body injury risk evaluations. Organ-level MCIS metrics show that impact at the heart can cause severe injuries to the heart and spleen, whereas impact to the liver can cause rib fractures and major lacerations in the liver. Impact at the lower abdomen can cause lacerations in the spleen. Simulation results indicate that, under current protection standards, the whole-body risk of injury varies between 6 and 98% based on impact location, with the impact at the heart being the most severe, followed by impact at the liver and the lower abdomen. These results suggest that the current body armor protection standards might result in severe injuries in specific locations, but no injuries in others.

An intelligent computational iBCMO-DNN algorithm for stochastic thermal buckling analysis of functionally graded porous microplates using modified strain gradient theory

The authors propose an intelligent computational method using the deep feedforward neural network integrated with an improved balance composite motion optimization algorithm to formulate a so-called iBCMO-DNN for solving the stochastic thermal buckling problems of functionally graded porous microplates. In the present approach, the deterministic behaviors of the functionally graded porous microplates were firstly analyzed by the combination of a unified higher-order shear deformation theory, modified strain gradient theory, and Ritz-type series solutions, and then stochastic responses under uncertainty of material properties are obtained by the iBCMO-DNN algorithm. The deep neural network with the long short-term memory model is used as a surrogate method to replace the time-consuming computational model, while the improved balance composite motion optimization is used to search for the optimal solutions. The obtained numerical results for various boundary conditions, uncertainty parameters, and three types of temperature distribution indicated that the proposed method achieves its accuracy and effectiveness in predicting stochastic thermal buckling of the functionally graded porous microplates. The improved balance composite motion optimization algorithm demonstrates a computational time ∼1.7 times faster than its predecessor. Furthermore, integrating a deep neural network into the improved algorithm reduces computational time to about 2/5 compared to the method without it.

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.

Research on optimal design method of dynamic stress parameters of helical gear based on orthogonal experimental design

Aiming at the reliability optimization design problem of two-grade helical cylindrical gear transmission system, the UG parameterized model based on expression and ADAMS dynamic simulation model under real working conditions are integrated in ISIGHT platform, and the distribution law of peak contact force on the tooth surface of helical gear pair in the transmission system at different meshing times is obtained. Considering the uncertainty of material properties, load conditions and geometric parameters, the sample set was generated according to the orthogonal experimental design method, and the Kriging approximation model was established. On this basis, the contact strength reliability of helical gear was analyzed. The mathematical model of meshing efficiency reliability optimization of helical gear pair was established and solved by Hooke-Jeeves Direct Search method. The results show that the meshing efficiency and reliability of the optimized helical gear pair are improved, and the peak value of the contact force is obviously reduced.

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.

Probabilistic Assessment of Ballooning of Pressure Tube under Severe Accident Conditions

For postulated accident scenario of loss of coolant accident coupled with the failure of emergency core cooling system, the pressure tube will deform due to presence of decay heat. The pressure tube deforms due to creep and this shall ultimately result in a contact with the calandria tube. In this work, the time for this contact to happen is calculated considering the uncertainties in mechanical and thermal material properties of the material. Finite element analysis of temperature distribution in the pressure tube has been carried out considering heat dissipation by conduction, convection and radiation. The source is heat generation due to decay heat of fuel bundles inside pressure tube. The ballooning of the pressure tube material is modelled using the Norton’s creep law. The finite element model is validated using experimental results from literature. As the finite element model is very complex and time intensive, it is difficult to employ the traditional uncertainty propagation methods like Monte Carlo simulations. The uncertainty analysis in this work is performed using Wilk’s method. The time duration when the contact of pressure tube and Calandria tube would happen and the temperature of the pressure tube at that instant is estimated. The results are presented in terms of the 95 percentile values with a confidence of 95 percent. The analysis gives an upper bound to the contact time between pressure tube and Calandria tube during loss of coolant accident condition subject to unavailability of emergency core cooling system.

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.