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Typically, the parameters entering a physical simulation model carry some kind of uncertainty, e.g., due to the intrinsic approximations in a higher fidelity theory from which they have been obtained. Global sensitivity analysis (GSA) targets quantifying which parameter uncertainties impact the accuracy of the simulation results, e.g., to identify which parameters need to be determined more accurately. We present a GSA approach based on the Cramérs–von Mises distance. Unlike prevalent approaches, it combines the following properties: (i) it is equally suited for deterministic as well as stochastic model outputs, (ii) it does not require gradients, and (iii) it can be estimated from numerical quadrature without further numerical approximations. Using quasi-Monte Carlo for numerical integration and a first-principles kinetic Monte Carlo model for the CO oxidation on RuO2(110), we examine the performance of the approach. We find that the results agree very well with what is known in the literature about the sensitivity of this model and that the approach converges in a modest number of quadrature points. Furthermore, it appears to be robust against even extreme relative noise. All these properties make the method particularly suited for expensive (kinetic) Monte Carlo models because we can reduce the number of simulations as well as the target variance of each of these. [ABSTRACT FROM AUTHOR]

The inherent spatial variability of rock mass strength has been explicitly considered in reliability analyses of slopes governed by the Hoek–Brown(HB) criterion. However, previous studies have primarily focused on extensive slopes where plane strain analysis is applicable, neglecting rock slopes constrained by boundaries that exhibit significant 'end effects' and are unsuitable for two-dimensional(2D) analysis. To bridge this gap, this research presents a novel three-dimensional(3D) reliability framework designed specifically for width-limited slopes in spatially variable rock masses. Considering the efficiency limitation of previously widely adopted numerical simulations, which struggle to accommodate extensive computation task, this study constructs the deterministic model using upper bound limit analysis (UBLA). A discretized mechanism is developed to determine the safety factor of spatially variable HB slopes. The integration of accelerated search strategies enables the determination of a solution to safety factor within a mere 5 min, mitigating the computational burden associated with high-dimensional stochastic problems or scenarios with a low probability of failure. Probabilistic analysis is conducted using a metamodel Sparse Polynomial Chaos Expansion (SPCE) in conjunction with Monte Carlo Simulation (MCS). Parametric analysis is employed to investigate the influence of various factors on slope reliability, including the autocorrelation length, coefficient of variation of strength, and correlation coefficient. This research presents a novel, computationally efficient deterministic model for slopes characterized by spatial variability in HB strength parameters. Furthermore, the employed principles show promising applicability in adjacent fields, such as tunneling and foundation engineering. Highlights: Develops a novel 3D reliability framework for width-limited slopes in spatially variable rock masses governed by the Hoek-Brown criterion. Develops an efficient UBLA-based deterministic model with a 3D spatial discretized technique and accelerated search strategies, reducing Fs computing time to within 5 mins. Integrates SPCE metamodel and MCS for probabilistic analysis, enabling investigation of various factors on slope reliability. The employed principles demonstrate promising applicability in adjacent fields, such as tunneling and foundation engineering. [ABSTRACT FROM AUTHOR]

Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications. This is all the more important when elements composed of brittle materials are exposed to dynamic environments, resulting in catastrophic fatigue failures. The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables. Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading. Crack growth is modelled using a phase-field approach within a finite element framework. For modelling fatigue, fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function. Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties. Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method. This proposed approach can accurately predict results typically obtained through 10 5 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs. The independent random variables' sensitivity to the system response is determined using Sobol' indices. The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace, nuclear and biomedical engineering. The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing. [ABSTRACT FROM AUTHOR]

In this paper, methodological approaches for distribution functions of nonlinear stochastic differential equations (SDEs) with uncertain parameters are elaborated. The stationary and nonstationary Fokker–Planck–Kolmogorov (FPK) equations associated with the considered random equations are investigated. A semi-analytical approach based on the extended exponential closure handling the parameters uncertainty effects is presented. A new numerical method coupling the polynomial chaos with the differential quadrature method (DQM) is elaborated for the stationary case. A compact matrix formulation is established allowing considering a large number of generalized polynomial chaos. For nonstationary random FPK equations, the polynomial chaos is coupled with the quadrature discretization. A symmetric discretization of the main Fokker–Planck operator using a tensor product of the Hilbert state space and the Hilbert probabilistic space has resulted. The obtained eigenvalues and random eigenfunctions are used for a spectral decomposition. The time solution is obtained by the spectral expansion as well as by the random Euler stochastic method. The accuracy, effectiveness and advantages of the developed procedure in analyzing the stationary and nonstationary probabilistic solutions of nonlinear stochastic dynamical systems with uncertain parameters excited by a Gaussian white noise are demonstrated. [ABSTRACT FROM AUTHOR]

ABSTRACT Experimental studies on the cellular uptake of nanoparticles (NPs), useful for the investigation of NP‐based drug delivery systems, are often difficult to interpret due to the large number of parameters that can contribute to the phenomenon. It is therefore of great interest to identify insignificant parameters to reduce the number of variables used for the design of experiments. In this work, a model of the wrapping of elliptical NPs by the cell membrane is used to compare the influence of the aspect ratio of the NP, the membrane tension, the NP–membrane adhesion, and its variation during the interaction with the NP on the equilibrium state of the wrapping process. Several surrogate models, such as Kriging, Polynomial Chaos Expansion (PCE), and artificial neural networks (ANN) have been built and compared to emulate the computationally expensive model. Only the ANN‐based model outperformed the other approaches by providing much better predictivity metrics and could therefore be used to compute the sensitivity indices. Our results showed that the NP's aspect ratio, the initial NP–membrane adhesion, the membrane tension, and the delay for the increase of the NP–membrane adhesion after receptor dynamics are the main contributors to the cellular internalization of the NP, while the influence of other parameters is negligible. [ABSTRACT FROM AUTHOR]

We propose a set of equations for preliminary risk‐targeted seismic design of structures base‐isolated using single friction pendulum (SFP) bearings. The equations offer statistical estimates of the maximum displacement of the superstructure relative to the base and the maximum displacement of the isolated base response quantities of interest (RQIs), given ground motion intensity measures and the essential dynamic properties of the SFP bearing base‐isolated structure. The set of proposed equations enables preliminary seismic design of SFP base‐isolated structures using the mean annual frequency of exceeding displacement‐defined limit states related to the two RQIs. To develop the design equations, we define and use a two‐degree‐of‐freedom (2DOF) surrogate model that features a few essential dynamic parameters of the SFP bearing base‐isolated structure. We first verify that the 2DOF surrogate model is accurate enough to represent the base and superstructure displacements compared to the complete multiple‐degree‐of‐freedom model of the prototype SFP bearing base‐isolated structure. Next, we perform more than 5 million non‐linear dynamical analyses of 4900 distinct 2DOF surrogates subjected to 210 different recorded ground motions scaled five times. We fit the response data of each 2DOF surrogate to a linear model and use two different modeling techniques to derive the design equations. One model is based on Polynomial Chaos Expansion (PCE), and the other model is based on Linear Regression (LR). The PCE model is more accurate than the LR model, with the trade‐off regarding its simplicity. Nevertheless, both the PCE and the LR models are accurate enough to estimate the design quantities of interest of the SFP bearing base‐isolated structure for preliminary design purposes. Lastly, we exemplify the use of the proposed design equations and we show that the estimate of base displacement is conservative in the cases when the superstructure of the SPF bearing base‐isolated structure yields. [ABSTRACT FROM AUTHOR]

The authors address the problem of observability analysis and enhancement for missiles equipped with strapdown seekers, especially considering the line‐of‐sight angle‐only measurements and the constraints on impact angle and terminal acceleration. First, based on the generalised polynomial chaos expansion, a novel data‐driven observability analysis method is proposed to quantitatively analyse the observability of the radome aberration estimation system in real time, including the observability condition, the observability degree of each state and the effect of stochastic noises. The results show that under conventional proportional navigation guidance, the radome aberration estimation system is weakly observable with line‐of‐sight angle‐only measurements. To address this problem, a novel manoeuvre algorithm, the observability‐enhanced guidance law, is introduced to enhance the system observability within specified constraints, thereby improving the estimation performance. This guidance law incorporates a bias term to meet terminal constraints, and optimises the navigation gain using the proposed observability indices. Simulations are conducted to verify the performance of the proposed guidance law in conjunction with a target state estimator. [ABSTRACT FROM AUTHOR]

The uncertain factors in wind tunnel experiments, especially the interference effects, will cause the flow around the test model to differ from that under the free flow condition. The wind tunnel wall interference effects are challenging to be eliminated, especially in transonic flow regions where classical linear correction methods are ineffective. To address this issue, an efficient wind tunnel wall interference correction framework based on data assimilation is proposed for steady and shock buffet flows around the airfoils in the transonic region in this work. The ensemble Kalman filter (EnKF) is used to find the combination of inflow conditions, which minimizes the differences between the pressure coefficients measured in the wind tunnel experiment and those estimated by computational fluid dynamics (CFD). The polynomial chaos expansion method is used to propagate uncertainty in the forecast step of the EnKF in order to improve efficiency. Typical wind tunnel wall interference correction problems are studied, including two steady cases: the transonic flow around the Royal Aircraft Establishment 2822 (RAE2822) and the National Aerospace Laboratory 7301 (NLR7301) airfoils, and one unsteady case: the transonic shock buffet on the National Aeronautics and Space Administration supercritical (phase 2)-0714 (NASA SC(2)-0714) airfoil. It is demonstrated that with the corrected Mach number and angle of attack, the estimated CFD results are in better agreement with the measured experimental data than traditional linear methods and the computational efficiency is improved compared to the original EnKF. [ABSTRACT FROM AUTHOR]

This research investigates the statistics in terms of mean and coefficient of variance of thermal buckling temperature of shape memory alloy (SMA) fiber-reinforced composite laminated plate using polynomial chaos (PC). The basic mathematical formulation is adopted based on Co finite element method (FEM) in conjunction with secant function-based shear deformation theory. The uncertain input system properties in material and geometrical parameters are modeled as random variables. The effects of SMA fiber and location, pre-strain, loading, modes, temperature distribution, modulus ratio, fiber orientation, length-to-thickness ratio, aspect ratio, and various boundary conditions on the statistics of critical temperature are analyzed. The small amount of random change in input system parameters significantly affects the variance and reliability of SMA fiber-reinforced composite laminated plate thermal buckling temperature under uniform and non-uniform temperature variations. The present PC simulation's results are compared with independent Monte Carlo simulation and those existing in the literature. [ABSTRACT FROM AUTHOR]

This work develops a novel multi-objective optimization for a robust attitude determination method using the narrow bound theory, which is more appropriate to the limited uncertain samplings. The classical Wahba problem for determining attitude is expanded into the framework of the interval uncertainty theory to comply with the complex environment of actual space. Since on-orbit data samples are limited and it is inconvenient to quantify uncertainty using probabilistic and statistical methods, this paper quantifies various incomplete information of the attitude determination system into unknown-but-bounded (UBB) numbers. As long as the limited ranges of uncertainties or errors are identifiable, these uncertainties will be precisely quantified in the overall attitude determination. To overcome the overestimation defect caused by interval perturbation analysis theory, this study designed a narrow bound theory originated from polynomial chaos expansions, that is, the boundary determined by interval dimension-wise analysis (IDWA) with accurate estimated bounds of attitude determination. An advanced multi-objective optimization algorithm (SPEA/R) is used to address the minimum nominal value and minimum fluctuation of the uncertain attitude determination problem, and the efficiency of this method is validated through a numerical example. [ABSTRACT FROM AUTHOR]

The approximation of complex engineering problems and mathematical regressions serves as the authentic inspiration behind the artificial intelligence metamodeling methods. Among these methods, polynomial chaos expansion, along with artificial neural networks, has emerged at the forefront and become the most practical technique. Previous studies have highlighted their robust capabilities in solving complex problems and their wide utilization across numerous applications, particularly in structural analysis, optimization design problems, and predictive models of uncertainty outcomes. The aim of this article is to present a methodology that introduces their implementation of for structural engineering, primarily focusing on reinforced concrete bridges. The proposed approach consists of demonstrating the applicability of the polynomial chaos to evaluate the dynamic behavior of two-span reinforced concrete bridges through a predictive model of natural vibration properties for eigenvalues modal analysis. Subsequently, response spectral method is conducted according to the Moroccan guide for bridge seismic design and the prescription of the EUROCODE 8 within the context of reliability assessment using Monte Carlo simulation. The efficacy of the proposed approach is illustrated by a comparison between the predicted vibration properties and the resulting values obtained through finite element modal analysis and artificial neural networks. The polynomial chaos process is based on a collected dataset of multiple reinforced concrete bridges sourced from technical studies offices and the Regional Administration of the East, affiliated with the Moroccan Ministry of Equipment and Water. Finally, this work contributes to the field by enhancing predictive modeling and reliability evaluation for bridge engineering using artificial intelligence metamodels. [ABSTRACT FROM AUTHOR]

Geometric deviations arising from manufacturing and assembly processes can significantly impact the aerodynamic stability of scramjet inlets. This study aims to quantify the uncertainty and sensitivity of the inlet aerodynamics caused by geometric deviations. Specifically, three representative operating modes are considered: start, half-start, and unstart. Five geometric parameters are extracted as random uncertain variables, including the first and second ramp angle (α1, α2), the horizontal and vertical distance between the lip point and the throat point (dh, dv), and the inner angle of the cowl lip (α3). To achieve the quantification objective, the non-intrusive polynomial chaos method is employed for uncertainty quantification. Sobol indices are utilized to assess the impact of each geometric parameter on the uncertainty of quantities of interest. Results indicate that geometric deviations for only ±1% can have a significant impact on the aerodynamic performance of the inlet. Specifically, the pressure uncertainty in the shock region is more than four times that of the non-shock region, exceeding 40%. With respect to the performance parameters, the mass capture ratio demonstrates a high sensitivity to geometric deviations, with the uncertainty for 6.76%. Sensitivity analysis indicates that the three primary factors affecting the aerodynamic stability within the isolator are dv, α2, and dh. Therefore, deviations in their manufacturing and assembly should be strictly controlled. [ABSTRACT FROM AUTHOR]

Advancements have been achieved in the optimization of waverider designs with the aid of machine learning to expedite the design process. However, these approaches are hampered by the need for extensive sample sizes and susceptibility to becoming ensnared in local optima. This study undertakes a parametric design based on the wedge-derived, power-law-shaped waverider, increasing configuration diversity and creating a dataset with limited samples by calculating waverider geometry and aerodynamic parameters. At a Mach number of 10, a multi-objective optimization design is implemented using the Young's double-slit experiment-least squares support vector regression (YDSE-LSSVR) surrogate model in conjunction with improved congestion distance multi-objective particle swarm optimization algorithm, focusing on maximizing the lift-to-drag ratio and volumetric efficiency as much as possible. The results indicated that, under conditions of limited samples, the YDSE-LSSVR model outperforms standard models such as support vector regression, LSSVR, Kriging, and Polynomial Chaos Expansions-Kriging regarding prediction accuracy. The Pareto solutions for both concave and convex waveriders, obtained through multi-objective optimization, improve the lift-to-drag ratio by 17.36% and 21.70%, respectively, and increase the volumetric efficiency by 88.89% and 105.56%, in comparison to baseline configurations. In addition, the research examines the impact of various design parameters on the Pareto solutions. Finally, the study applies the K-means method to conduct a cluster analysis of the Pareto solutions, generating three-dimensional waverider configurations based on distinguished solutions from different clusters. [ABSTRACT FROM AUTHOR]

This paper presents the delamination impact over the dynamic response of the variable angle tow (VAT) composite plates. The VAT plates with various fiber angles are constrained to different boundary conditions for parametric investigation, while delamination is made to present over two different locations with varying sizes. A comparative stochastic vibration study is performed to evaluate the contribution of composite properties to delaminated and intact plates. The randomness in the material properties is modeled with the efficient Latin hypercube sampling method. The polynomial neural network-based surrogate model, considered an efficient substitute for computationally expensive Monte Carlo simulation, is employed in the present work to examine the stochastic behavior of VAT plates. The contribution of the composite properties on the uncertain vibration characteristics is evaluated. It is observed from the investigations that the sensitivity of the composite properties varies significantly with the delamination. Lastly, a failure probability estimation is carried out with a developed polynomial neural network-based surrogate model to provide safe design estimation for various cases. [ABSTRACT FROM AUTHOR]

The assessment of casualty risks associated with re-entry necessitates a comprehensive analysis of trajectories and the examination of pertinent safety-related quantities such as the ground impact area and ground reaching velocity. In practical scenarios, the presence of uncertainty in input conditions introduces variability in safety-related quantities. Consequently, employing stochastic re-entry trajectory analysis becomes crucial in overcoming the limitations of conventional deterministic analyses. Conducting sensitivity assessments during the break-up phase is imperative to gain more insights into how to manage the variability of safety-related measures. Therefore, this paper conducted a surrogate-based global sensitivity analysis and employed explainability machine learning techniques to unveil the complexities of the relationship between input uncertainty conditions and three key measures: ground-reaching velocity, falling range, and falling time, with the object of interest being the Apollo-type capsule. A three-step polynomial chaos expansion-based strategy was devised to efficiently approximate the discontinuous relationships. The results show that the relationship is characterized by severe discontinuity that separates two modes: low- and high-ground reaching velocity caused by the presence of two distinct trim points, with precautionary measures that should be taken to prevent the occurrence of the latter. From this set of procedures, three key input conditions that significantly affect the safety-related measures were identified, namely, the altitude, pitch rate, and path angle of the capsule during the breakup. Subsequently, explainability techniques were utilized to give suggestions on how to control the input variability and avoid the high ground reaching velocity mode, aiming to achieve more dependable predictions for the three safety parameters mentioned earlier. • Performed surrogate-based sensitivity analysis for stochastic re-entry trajectory. • Utilized explainability machine learning techniques to decipher relationships. • Identified key input conditions influencing safety measures for Apollo-type capsules. • Contributed insights to minimize hazardous re-entry modes and mitigate risks. • Uncovered complex discontinuity in response surface with explainable surrogate models. [ABSTRACT FROM AUTHOR]

Designing underwater vehicles considering uncertainties in mechanical properties of composites is computationally expensive. In this paper, inexpensive-to-evaluate sparse polynomial chaos expansion (PCE) based on small data is employed to alleviate computational burden arising in uncertainty analysis. Experiments and finite element analysis for buckling are performed. Relative contribution of mechanical properties to critical buckling pressure is quantified. Distribution function histogram and risk of structral failure are obtained by performing Monte Carlo simulation (MCS) on inexpensive-to-evaluate sparse PCE. Mean of critical buckling pressure is 8.27 MPa, with coefficient of variation 8.59%. 95% confidence interval is 6.86 MPa–9.65 MPa. [ABSTRACT FROM AUTHOR]

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An aeroengine faces multi-source uncertainty consisting of aeroengine epistemic uncertainty and the control system stochastic uncertainty during operation. This paper investigates actuator fault estimation under multi-source uncertainty to enhance the fault diagnosis capability of aero-engine control systems in complex environments. With the polynomial chaos expansion-based discrete stochastic model quantification, the optimal filter under multi-source uncertainty, the Hyperelliptic Kalman Filter, is proposed. Meanwhile, by treating actuator fault as unknown input, the Two-stage Hyperelliptic Kalman Filter (TSHeKF) is also proposed to achieve optimal fault estimation under multi-source uncertainty. However, considering that the biases of the model are often fixed for the individual, the TSHeKF-based fault estimation is robust and leads to inevitable conservativeness. By adding the additional estimation of the unknown deviation in state function caused by probabilistic system parameters, the hybrid fault observer (HFO) is proposed based on the TSHeKF and realizes conservativeness-reduced estimation for actuator fault under multi-source uncertainty. Numerical simulations show the effectiveness and optimality of the proposed HFO in state estimation, output prediction, and fault estimation for both single and multi-fault modes, when considering multi-source uncertainty. Furthermore, Monte Carlo experiments have demonstrated that the HFO-based optimal fault estimation is less conservative and more accurate than the Two-stage Kalman Filter and TSHeKF, providing better safety and more reliable aeroengine operation assurance. [ABSTRACT FROM AUTHOR]

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. These calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency. [ABSTRACT FROM AUTHOR]

The suspension system is an important part of a vehicle and directly affects the vehicle's comfort and stability during driving. There are various nonlinearities and uncertainties in the vehicle suspension system, and even small changes can have a significant impact on the suspension performance. This paper provides an in-depth study of quarter- and half-vehicle suspensions modeled with nonlinear springs and dampers, considering the stochastic uncertainty of various parameters. A mathematical model of a nonlinear vehicle suspension was developed to more accurately simulate the increased stiffness of suspension springs with travel and the energy consumption of dampers. The sparse grid-based polynomial chaos expansion is employed to construct the metamodels of the system response in both the frequency and time domains. This approach effectively captures the stochastic characteristics of the system response, reducing computational cost while improving accuracy. Based on polynomial metamodels, various performance indicators of the nonlinear suspension were analyzed, including statistical moments, probability distributions, and parameter sensitivities. The results are then compared and discussed, revealing that uncertainties in the nonlinear spring, sprung mass, and tire stiffness significantly impact the frequency response, time response, ride comfort, and safety. These findings contribute to a deeper understanding of the dynamic characteristics and behaviors of nonlinear vehicle suspensions under complex parameter uncertainties and provide a reference for enhancing suspension performance. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to conduct a thorough investigation of a stochastic eddy-current testing problem, when the geometric parameters of the system under study are characterized by uncertainty. Focusing on the case of subsurface defect detection, we devise reliable surrogates for the quantities of interest (QoI) based on the principles of the generalized polynomial chaos (PC) and using the orthogonal matching pursuit (OMP) solver to promote sparsity in the approximate models. In addition, a variance-based approach is implemented for the sequential construction of the necessary sample set, enabling more accurate estimation of the statistical metrics without imposing additional computational overhead. Apart from quantifying the inherent uncertainty, a sensitivity analysis is performed that assesses the impact of each geometric variable on the QoI, via the computation of Sobol indices. The efficiency of the OMP-PC algorithm is demonstrated in two variants of the subsurface-discontinuity problem, yielding at the same time useful conclusions regarding the properties of the stochastic outputs. [ABSTRACT FROM AUTHOR]

In this paper, a multi-objective optimization strategy for efficient design of turbo machinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined. [ABSTRACT FROM AUTHOR]

In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures. [ABSTRACT FROM AUTHOR]

This work presents a comprehensive framework for the sensitivity analysis of the Navier–Stokes equations, with an emphasis on the stability estimate of the discretized first‐order sensitivity of the Navier–Stokes equations. The first‐order sensitivity of the Navier–Stokes equations is defined using the polynomial chaos method, and a finite element‐volume numerical scheme for the Navier–Stokes equations is suggested. This numerical method is integrated into the open‐source industrial code TrioCFD developed by the CEA. The finite element‐volume discretization is extended to the first‐order sensitivity Navier–Stokes equations, and the most significant and original point is the discretization of the nonlinear term. A stability estimate for continuous and discrete Navier–Stokes equations is established. Finally, numerical tests are presented to evaluate the polynomial chaos method and to compare it to the Monte Carlo and Taylor expansion methods. [ABSTRACT FROM AUTHOR]

We introduce Gaussian Process Regression (GPR) as an enhanced method of thermodynamic extrapolation and interpolation. The heteroscedastic GPR models that we introduce automatically weight provided information by its estimated uncertainty, allowing for the incorporation of highly uncertain, high-order derivative information. By the linearity of the derivative operator, GPR models naturally handle derivative information and, with appropriate likelihood models that incorporate heterogeneous uncertainties, are able to identify estimates of functions for which the provided observations and derivatives are inconsistent due to the sampling bias that is common in molecular simulations. Since we utilize kernels that form complete bases on the function space to be learned, the estimated uncertainty in the model takes into account that of the functional form itself, in contrast to polynomial interpolation, which explicitly assumes the functional form to be fixed. We apply GPR models to a variety of data sources and assess various active learning strategies, identifying when specific options will be most useful. Our active-learning data collection based on GPR models incorporating derivative information is finally applied to tracing vapor–liquid equilibrium for a single-component Lennard-Jones fluid, which we show represents a powerful generalization to previous extrapolation strategies and Gibbs–Duhem integration. A suite of tools implementing these methods is provided at https://github.com/usnistgov/thermo-extrap. [ABSTRACT FROM AUTHOR]

AbstractFinite element models ranging from single to multiscale models have been widely used to gain valuable insights into the physiological delivery process and associated complication scenarios. However, the fetus descent simulation with the active uterine contraction is still challenging for validation and uncertainty quantification issues. The present study performed a fetus descent simulation using the active uterine contraction. Then, simulation outcomes were evaluated using theoretical and in vivo MRI childbirth data. Moreover, parameter uncertainty and propagation were also performed. A maternal pelvis model was developed. The active uterine contraction was modeled using a transversely isotropic Mooney–Rivlin material. Displacement trajectories were compared between simulation, theoretical and in vivo MRI childbirth data. Monte Carlo (M.C) and Polynomial Chaos Expansion (PCE) methods were applied to quantify uncertain parameters and their propagations. Obtained results showed that fetal descent behavior is consistent with the MRI-based observation as well as the theoretical trajectory (curve of Carus). The head downward vertical displacement ranges from 0 to approximately 47 mm. A reduction of 50% in uterine size was observed during the simulation. Three high-sensitive parameters (C1,C2,Ca0) were also identified. Our study suggested that the use of the active uterine contraction is essential for simulating vaginal delivery but the global parameter sensitivity, parameter uncertainty, and outcome evaluation should be carefully performed. As a perspective, the developed approach could be extrapolated for patient-specific modeling and associated delivery complication simulations to identify risks and potential therapeutic solutions. [ABSTRACT FROM AUTHOR]

The paper portrays a comprehensive computational procedure for determining the global structural resistances of two existing bridges made of I‐73 and KA‐61 precast post‐tensioned concrete girders using advanced statistical assessment methods in combination with nonlinear fracture mechanics‐based finite element method analysis. Although this combination is a powerful tool for realistic modeling of structures, its practical application is still very time consuming. Therefore, a statistical sampling approach for the determination of the structural design resistance is compared to selected efficient semi‐probabilistic methods based on the estimation of coefficient of variation—estimation of coefficient of variation (ECoV) method according to fib Model Code 2010 and improved approach called Eigen ECoV method. Load‐bearing capacity is determined for the ultimate as well as several serviceability limit states. The sensitivity of the input parameters burdened with uncertainties on the response of the structure is quantified using a sensitivity analysis supported by a surrogate model based on polynomial chaos expansion. The paper shows that the applicability of nonlinear modeling with respect to uncertainties is possible when using these ECoV methods and a surrogate model and can be applied in a routine manner. The shortcomings and advantages of all the used safety design/assessment methods are discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with a kinetic-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier–Stokes equations and the Vlasov– Fokker–Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation in the initial data. For the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the model, with initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Stokes number, and the error decays exponentially in time. [ABSTRACT FROM AUTHOR]

Summary: Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space‐time stochastic Galerkin boundary element method which is applied to sound‐hard, sound‐soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise. [ABSTRACT FROM AUTHOR]

Dynamic models generating time‐dependent model predictions are typically associated with high‐dimensional input spaces and high‐dimensional output spaces, in particular if time is discretized. It is computationally prohibitive to apply traditional global sensitivity analysis (SA) separately on each time output, as is common in the literature on multivariate SA. As an alternative, we propose a novel method for efficient global SA of dynamic models with high‐dimensional inputs by combining a new polynomial chaos expansion (PCE)‐driven partial least squares (PLS) algorithm with the analysis of variance. PLS is used to simultaneously reduce the dimensionality of the input and output variables spaces, by identifying the input and output latent variables that account for most of their joint variability. PCE is incorporated into the PLS algorithm to capture the non‐linear behavior of the physical system. We derive the sensitivity indices associated with each output latent variable, based on which we propose generalized sensitivity indices that synthesize the influence of each input on the variance of entire output time series. All sensitivities can be computed analytically by post‐processing the coefficients of the PLS‐PCE representation. Hence, the computational cost of global SA for dynamic models essentially reduces to the cost for estimating these coefficients. We numerically compare the proposed method with existing methods by several dynamic models with high‐dimensional inputs. The results show that the PLS‐PCE method can obtain accurate sensitivity indices at low computational cost, even for models with strong interaction among the inputs. [ABSTRACT FROM AUTHOR]

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample‐based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three‐dimensional fluid–structure interaction simulations with affordable one‐ and zero‐dimensional reduced‐order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi‐ (1D/0D) and tri‐fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single‐fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response. [ABSTRACT FROM AUTHOR]

We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H ∈ (1 / 4 , 1) . At level 0, our result yields an expression for the expected signature of such processes, which determines their law (Chevyrev and Lyons in Ann Probab 44(6):4049–4082, 2016). In particular, this formula simultaneously extends both the one for 1 / 2 < H -fBm (Baudoin and Coutin in Stochast Process Appl 117(5):550–574, 2007) and the one for Brownian motion ( H = 1 / 2 ) (Fawcett 2003), to the general case H > 1 / 4 , thereby resolving an established open problem. Other processes studied include continuous and centred Gaussian semimartingales. [ABSTRACT FROM AUTHOR]

The hypothesis of chaotic population dynamics was proposed in ecology by Robert May in the mid-1970s. At that time the idea was controversial, and it remains a fascinating and unsettled issue today. We report the results of a 20-year laboratory research programme that continued in the tradition of the pioneering ecologist Thomas Park using the Tribolium flour beetle model. We present biological evidence of complex population dynamics – including bifurcations, chaos, saddle nodes, phase switching, resonance effects, and multiple attractors – by using a low-dimensional difference equation model for Tribolium together with carefully designed, conducted, and statistically analysed experiments. The model, parameterized with data, also explains the results of historical Tribolium experiments, such as the classical competition studies of Thomas Park and his colleagues. Our research programme has inspired other studies using the Tribolium mathematical and laboratory model. This work was conducted by a multidisciplinary team, which included Jim Cushing. [ABSTRACT FROM AUTHOR]

Reliability-based control co-design (RBCCD) formulations have been developed for the design of stochastic dynamic systems. To address the limitations of their current formulations, and to enable higher-fidelity solutions for complex problems, a novel reliability-based multidisciplinary feasible (MDF) formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) and a new reliability analysis method using generalized polynomial chaos (gPC) expansion for RBCCD were developed in previous work. Although the gPC expansion method was initially selected for the reliability analysis of simulation-based RBCCD, its performance against state-of-the-art, the most-probable-point (MPP) method, has not been established yet. Therefore, in this work, the first-ever MPP-based formulations of RB-MDF-MDSDO are developed, and using two engineering test problems, the new formulations' solution efficiency and accuracy are compared to those from the gPC-based formulation. Numerical results reveal that the gPC expansion method is marginally more accurate than the MPP algorithms, and therefore, it is more suitable for accuracy-sensitive applications. Conversely, the MPP algorithms are much more efficient, and thus, are more attractive for problems where solution efficiency is the priority. [ABSTRACT FROM AUTHOR]

The focus of this paper is the design of open-loop control profiles for linear differentially flat systems whose model parameters are uncertain and are represented probabilistically. To account for the time-invariant model parameter uncertainties, polynomial chaos is used to derive a surrogate model which permits easy evaluation of the mean and variance of the uncertain states. A chance constrained optimisation problem is posed to minimise the terminal error of the stochastic states for a prescribed risk of not satisfying the terminal state bounds. To permit posing a convex optimisation problem, the cost function which is the residual energy is approximated by a hypercube circumscribing the hypersphere which bounds the terminal residual error. This relaxation permits posing a convex optimisation problem to arrive at the robust control profile. The proposed technique is illustrated on two examples including the benchmark spring-mass-dashpot system undergoing a rest-to-rest maneuver and a UAV undergoing a translation in a prescribed time. Parametric studies are conducted where the impact of varying the order of the polynomial chaos expansion and the degree of the parameterised control profiles are used to conclude that a 2–3 degree polynomial chaos expansion is sufficient to capture the time evolution of the mean and variance of the states which are required for the chance constrained optimisation problems. As expected, the design results in improved performance as the number of free variables used to parameterise the control profiles increases. [ABSTRACT FROM AUTHOR]

The main goal of this work is summed up in a univariate chaotic analysis of the runoff series using a topological approach. As such, nineteen series of daily runoff from eight large watersheds in northern Algeria were analyzed. Firstly, preliminary analyses of two traditional dynamic and metric approaches have been tested. In the dynamic approach, three algorithms have shown that the largest Lyapunov exponent for the series is positive, which supports the hypothesis of the existence of chaos. In the metric approach, the Grassberger and Procaccia algorithm clearly shows the saturation of the correlation dimension, which indicates the existence of deterministic dynamics for all studied stations. Secondly, the application of the topological approach in this study constitutes in itself a new contribution to the demonstration of chaos in hydrology by using the recurrence plot (RP) and the recurrence quantification analysis (RQA). As such, the RP structures of the runoff series seem to be more comparable to chaotic systems. In addition, RQA parameters give high values of determinism and laminarity, which supports the hypothesis of the existence of deterministic chaos. The presence of chaos in the runoff series can be identified by the existence of a strong probability of recurrence, indicating a fairly low level of complexity and fairly high predictability. Ultimately, the comparison of these approaches together made it possible to confirm the hypothesis according to which the process generating the runoff series is deterministic and suggests low-dimensional chaotic dynamics. [ABSTRACT FROM AUTHOR]

Twist angle errors along the blade radial direction are uncertain and affected by cutting force, tool wear, and other factors. In this paper, the measured twist angle errors of 13 sections of 72 rotor blades were innovatively analyzed to obtain the rational statistical distribution. It is surprisingly found that the under-deflection systematic deviation of twist angle errors shows a gradually increasing W-shaped distribution along the radial direction, while the scatter is nearly linear. Logically, the statistical model is established based on the linear correlation of the scatter by regression analysis to reduce variable dimension from 13 to 1. The influence of the radial non-uniform twist angle errors' uncertainty on the aerodynamic performance of the three-dimensional compressor rotor is efficiently quantified combining the non-intrusive polynomial chaos method. The results show that the mean values of mass flow rate, total pressure ratio, and isentropic efficiency at the typical operating conditions are lower than the nominal values due to the systematic deviation, indicating that the under-deflection twist angle errors lead to the decrease in compressor thrust. The compressor's stable operating range is more sensitive to the scatter of twist angle errors, which is up to an order of magnitude greater than that of the total pressure ratio and isentropic efficiency, indicating the compressor's safe and stable operation risk increases. Additionally, the flow field at the tip region is significantly affected by twist angle errors, especially at the shock wave position of the near-stall condition. [ABSTRACT FROM AUTHOR]

Variational modal decomposition (VMD) has proven to be an effective technique for improving the accuracy of runoff prediction and has been widely used in runoff analysis and prediction. However, the presence of noise and outliers can complicate the runoff decomposition, so obtaining purely stochastic and deterministic components is difficult. Therefore, exploring the chaotic properties of the components obtained from decomposition can provide a new perspective to reveal intrinsic variability patterns and enhance our understanding of the unity of determinism and stochasticity. In this study, a two-stage VMD framework is proposed to decompose the monthly runoff, with the chaotic characteristics analyzed by employing an unthreshold recurrence plot and the largest Lyapunov exponent. Additionally, a chaotic prediction model is developed using phase space reconstruction, Volterra filter, and wavelet neural network methodologies. The model is validated using monthly runoff data from four stations in the Yellow River Basin, China. The results demonstrate that, although the VMD method effectively isolates trend components in monthly runoff, it still exhibits challenges in separating periodic and random elements, leading to the identification of chaotic components characterized by the amalgamation of periodicity and randomness. Notably, the two-stage VMD-phase space reconstruction-Volterra-wavelet neural networks model outperforms the VMD-phase space reconstruction-Volterra-wavelet neural networks model, with a substantial increase in Nash–Sutcliffe efficiency during validation, rising from an average of 0.9271–0.9508 and reaching a maximum of 0.96 across the four stations. Overall, this study demonstrates the potential of VMD for improving the monthly runoff prediction accuracy and elucidates the interplay between determinism and stochasticity in runoff analysis, offering valuable insights for further research in this area. [ABSTRACT FROM AUTHOR]

We present an algorithm for constructing efficient surrogate frequency‐domain models of (nonlinear) parametric dynamical systems in a non‐intrusive way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach combines rational approximation and smooth interpolation. In the approximation effort, locally adaptive sparse grids are applied to effectively explore the parameter domain even if the number of parameters is modest or high. Adaptivity is also employed to build rational approximations that efficiently capture the frequency dependence of the problem. These two features enable our method to build surrogate models that achieve a user‐prescribed approximation accuracy, without wasting resources in "oversampling" the frequency and parameter domains. Thanks to its non‐intrusiveness, our proposed method, as opposed to projection‐based techniques for model order reduction, can be applied regardless of the complexity of the underlying physical model. Notably, our algorithm for adaptive sampling can be used even when prior knowledge of the problem structure is not available. To showcase the effectiveness of our approach, we apply it in the study of an aerodynamic bearing. Our method allows us to build surrogate models that adequately identify the bearing's behavior with respect to both design and operational parameters, while still achieving significant speedups. [ABSTRACT FROM AUTHOR]

Composite Tape-Spring Hinge (CTSH) is one of the basic components of space deployable structures achieving large-scale deployable mechanisms for various space missions. It is crucial to obtain the lamina parameters of the composite at the design stage to ensure that the CTSH possesses the required structural response. This work presents a strategy for extracting lamina parameters from structural response of CTSH based on optimization method. An efficient Artificial Neural Network (ANN)-based surrogate model is integrated into the optimization loop to replace the time-costing finite element simulation and establish the relationship between lamina parameters and bending response of CTSH. The inverse characterization process is achieved by minimizing the objective function defined as the error between the predefined target and output results from ANN model. The efficiency of the proposed strategy was validated by using a predefined bending moment-angle curve of CTSH with known lamina parameters, and an arbitrary bending moment-angle curve was inversely constructed to further demonstrate the capability in inverse design. It is shown that the proposed method can be applied not only to extract lamina parameters from structural response, but also to guide the selection of composite lamina based on the expected structural response of deployable structures. [ABSTRACT FROM AUTHOR]

AbstractThe present article aims at performing a global sensitivity analysis of modal properties of a frequency dependent viscoelastic sandwich plate. The latter are evaluated using a finite element model relying on Kirchhoff theory for the elastic faces and the Mindlin-Reissner approach for the viscoelastic layer. The plate’s characteristics are considered as random variables following log normal laws. Sparse polynomial chaos expansions are employed to evaluate Sobol’s indices. For high damping, the resonant frequencies and loss factors turn to be sensitive to the elastic face properties, while in the weak damping case they are mostly affected by the viscoelastic model parameters. [ABSTRACT FROM AUTHOR]

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques' efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns. [ABSTRACT FROM AUTHOR]

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC. [ABSTRACT FROM AUTHOR]

In this article, the Polynomial Chaos–Kriging (PCK) metamodel is proposed to surrogate the physical model for model-assisted probability of detection (MAPoD) analysis in eddy current non-destructive testing (ECNDT). Two popular non-intrusive metamodels, the Polynomial Chaos Expansion (PCE) and Kriging, are combined properly to replace the time-consuming boundary element method-based ECNDT forward solver for accelerating the uncertainty propagation within MAPoD analysis in NDT. In PCK, the global behaviour of the model is estimated by the trend function of PCE, and the remaining local changes of it are captured by Kriging. Both the accuracy and efficiency of the proposed PCK metamodel are demonstrated on 3D ECNDT MAPoD cases involving surface flaws on the conducting thick plate using the detecting coil with rectangular cross section. Numerical results show improved performance of PCK metamodel over PCE and Kriging metamodels, respectively, while maintaining at least two digits of accuracy of the PoD metrics. [ABSTRACT FROM AUTHOR]

As renewable energy becomes more widespread, the uncertainty of its output poses serious challenges for peak and frequency regulation of the power system. Evaluating a grid's capacity to integrate renewable energy sources can provide an early-warning and decision-making basis for grid operation and scheduling. This paper presents a method for evaluating the hosting capacity of renewable energy, considering frequency security constraints. Introducing the system frequency nadir constraint into a system ensures that the frequency does not drop to a dangerous level in the event of power disturbances. The analytical characterization relation equation for the system frequency nadir constraint is constructed based on polynomial chaos expansion (PCE) theory. Furthermore, with the goal of minimizing the reduction in renewable energy, considering multiple flexible resources, like demand response (DR), Combined Heat and Power (CHP), energy storage, and Power-to-Gas (P2G), a renewable energy hosting capacity evaluation model that considers frequency security and flexibility resources is established. Finally, based on the concept of the feasible region, the maximum hosting capacity of a system's renewable energy is visualized using the progressive vertex enumeration method. It identifies the safe operating region for renewable energy output that meets the safety constraints of power grid operations. The simulation results were validated using a modified IEEE 39 bus system. [ABSTRACT FROM AUTHOR]

In this work, the dynamic responses of an uncertain flexible shaft-disk-drum rotor under elastic support and connection are investigated, where uncertain parameters are considered as unknown but bounded interval variables. The energy method is used to derive deterministic analytical model for the flexible shaft-disk-drum rotor, which is validated by modal tests. A non-intrusive interval method based on Chebyshev polynomial approximation is introduced to evaluate the uncertain dynamic response of the flexible shaft-disk-drum rotor system. Comparative studies of Monte Carlo simulation, scanning method and the interval method are conducted to illustrate the validity and accuracy of the approach proposed here. [ABSTRACT FROM AUTHOR]

This work proposes a fast, novel, mathematically robust, and elegant unconstrained Method of Uncertainty Quantification (MUQ) for the temperature-dependent Arrhenius rate constant using Cholesky Decomposition (CD) of the covariance matrix of the Arrhenius parameters. The Arrhenius parameters of a reaction are treated as normally distributed correlated random variables. The MUQ method lends itself to an approach for Sampling of Arrhenius Curves (SAC), which automatically ensures that the generated samples are consistent with the distribution of Arrhenius parameters. The Method of Uncertainty Quantification and Sampling of Arrhenius Curves (MUQ-SAC) is used to train a quadratic polynomial response surface (PRS). Three important classes of Arrhenius curves possible within the SAC method are identified. From the total set of targets, a small subset of targets is first used to study the combinations of different classes of Arrhenius curves and their proportions within the design matrix, which is used to train PRS. Based on this understanding, response surfaces are generated for 64 ignition delay targets (Tig), which comprises of a wide range of pressure (P: 1--32.7 atm), temperature (T: 916-DIFadd-2869 K), and equivalence ratio (ϕ: 0.5--6.11), as well as for 74 laminar flame speed targets (Fls), spanning P: 1--25 atm, T: 285--600 K, and ϕ: 0.6--5. The H $ _2 $ 2 /CO sub-mechanism of FFCM1.0 is chosen for the case study in which 22 reactions (66 Arrhenius parameters) are considered active parameters. The quality of the generated PRS is measured using the relative Maximum Residual Error (MRE). The quality of PRS is also checked against the search iterations encountered during mechanism optimisation. Accurate PRS could be generated over the search iterations, validating that the SAC method is able to span the entire uncertainty domain while training the PRS. The implementation of the MUQ-SAC method is made available at . [ABSTRACT FROM AUTHOR]

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues' dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems. [ABSTRACT FROM AUTHOR]