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The impact of the distribution in space of the inlet velocity in the numerical simulations of the hemodynamics in the thoracic aorta is systematically investigated. A real healthy aorta geometry, for which in-vivo measurements are available, is considered. The distribution is modeled through a truncated cone shape, which is a suitable approximation of the real one downstream of a trileaflet aortic valve during the systolic part of the cardiac cycle. The ratio between the upper and the lower base of the truncated cone and the position of the center of the upper base are selected as uncertain parameters. A stochastic approach is chosen, based on the generalized Polynomial Chaos expansion, to obtain accurate response surfaces of the quantities of interest in the parameter space. The selected parameters influence the velocity distribution in the ascending aorta. Consequently, effects on the wall shear stress are observed, confirming the need to use patient-specific inlet conditions if interested in the hemodynamics of this region. The surface base ratio is globally the most important parameter. Conversely, the impact on the velocity and wall shear stress in the aortic arch and descending aorta is almost negligible. [ABSTRACT FROM AUTHOR]

It has been well established in the literature that the predator-induced fear has indirect impact on prey but can have comparable effects on prey population as direct killing, and that the crowding effect or self-limitation of population plays pivotal roles in determining the dynamics and interactions among populations. In this paper, we first propose and investigate a deterministic prey-predator model incorporating simultaneously fear effect in prey and crowding effect in predators. The model has rich dynamics, including one up to three positive equilibria, complex bifurcations (saddle-node, Hopf and Bogdanov-Takens bifurcations), and two types of bistability (between two interior equilibria or between an interior equilibrium and an interior limit cycle). Thus the model is easily affected by external environmental fluctuations. When environmental noises are involved, some new dynamics can be observed for the developed stochastic model. Especially, for the scenarios when the deterministic model exhibits bistability, we can observe noise-induced frequent transitions between two different interior attractors (two interior equilibria or an interior equilibrium and an interior limit cycle). The tipping points of noise intensities for the occurrence of such transitions are estimated by constructing the confidence ellipse/band for the equilibrium/limit cycle. These indicate that the predators and prey can coexist in two different modes and switch randomly between them. [ABSTRACT FROM AUTHOR]

In this paper, by the example of 3D model of enzyme reaction, we study mechanisms of noise-induced generation of complex multimodal chaotic oscillations in the monostability zone where only simple deterministic cycles are observed. In such a generation, a constructive role of deterministic toroidal transients is revealed. We perform a statistical analysis of these phenomena and localize the intensity range of the noise that causes stochastic P - and D -bifurcations connected with transitions to chaos and qualitative changes in the probability density. Constructive possibilities of the stochastic sensitivity function technique in the analytical study of these phenomena are demonstrated. [ABSTRACT FROM AUTHOR]

We perform a stochastic sensitivity analysis of the experimental setup of a mock circulatory loop for in vitro hemodynamics analysis in the ascending thoracic aorta at a patient-specific level. The novelty of the work is that, for the first time, we provide a systematic sensitivity analysis of the effect of the inflow conditions, viz. the stroke volume, the cardiac cycle period, and the spatial distribution of the velocity in in-vitro experiments in a circulatory mock loop. We considered three different patient-specific geometries of the ascending thoracic aorta, viz. a healthy geometry, an aortic aneurysm, and a coarctation of the aorta. Three-dimensional-printed phantoms are inserted in a mock circulatory loop, and velocity and pressure measurements are carried out for the different setup conditions. The stochastic approach, performed using the generalized polynomial chaos, allows us to obtain continuous and accurate response surfaces in the parameter space, limiting the number of experiments. The main contributions of this work are that (i) the flow rate and pressure waveforms are mostly affected by the cardiac cycle period and the stroke volume, (ii) the impact of the spatial distribution of the inlet velocity profile is negligible, and (iii), from a practical viewpoint, this analysis confirms that in experiments it is also important to replicate the patient-specific inflow waveform, while the length of the pipe connecting the pump and the phantom of the aorta can be varied to comply with particular requirements as, for instance, those implied by the use of MRI in experiments. [ABSTRACT FROM AUTHOR]

We perform a stochastic sensitivity analysis of the experimental setup of a mock circulatory loop for in vitro hemodynamics analysis in the ascending thoracic aorta at a patient-specific level. The novelty of the work is that, for the first time, we provide a systematic sensitivity analysis of the effect of the inflow conditions, viz. the stroke volume, the cardiac cycle period, and the spatial distribution of the velocity in in-vitro experiments in a circulatory mock loop. We considered three different patient-specific geometries of the ascending thoracic aorta, viz. a healthy geometry, an aortic aneurysm, and a coarctation of the aorta. Three-dimensional-printed phantoms are inserted in a mock circulatory loop, and velocity and pressure measurements are carried out for the different setup conditions. The stochastic approach, performed using the generalized polynomial chaos, allows us to obtain continuous and accurate response surfaces in the parameter space, limiting the number of experiments. The main contributions of this work are that (i) the flow rate and pressure waveforms are mostly affected by the cardiac cycle period and the stroke volume, (ii) the impact of the spatial distribution of the inlet velocity profile is negligible, and (iii), from a practical viewpoint, this analysis confirms that in experiments it is also important to replicate the patient-specific inflow waveform, while the length of the pipe connecting the pump and the phantom of the aorta can be varied to comply with particular requirements as, for instance, those implied by the use of MRI in experiments.

Reliability-based design optimization (RBDO) derives an optimum design that satisfies target reliability and minimizes an objective function by introducing probabilistic constraints that take into account failures caused by uncertainties in random inputs. However, existing RBDO studies treat all failures equally and derive the optimum design without considering the magnitude of failure exceeding the limit state. Since the damage caused by failure varies according to the magnitude of failure, a probabilistic framework that considers the magnitude of failure differently is necessary. Therefore, this study proposes a weighted RBDO (WRBDO) framework that assigns a different weight to each failure according to the magnitude of failure and derives an optimum design that quantitatively reflects the magnitude of failures. In the WRBDO framework, the weight function is modeled based on warranty cost or damage cost according to the magnitude of failure, and the weighted failure is determined by assigning different weights according to the magnitude of failure through the weight function. Then, weighted probabilistic constraints reflecting the weighted failure are evaluated. Sampling-based reliability analysis using the direct Monte Carlo simulation (MCS) is performed to evaluate the weighted probabilistic constraints. Stochastic sensitivity analysis that calculates the sensitivities of the weighted probabilistic constraints is derived, and it is verified through numerical examples that the stochastic sensitivity analysis is more accurate and efficient than the sensitivity analysis using the finite difference method (FDM). To enable the practical application of WRBDO, AK-MCS for WRBDO in which the Kriging model is updated to identify both the limit state and the magnitude of failures in the failure region is proposed. The results of various WRBDO problems show that the WRBDO yields conservative designs than a conventional RBDO, and more conservative designs are derived as the slope of weight functions and the nonlinearity of constraint functions increase. The optimum results of a 6D arm model show that the cost increases by 3.39% and the number of failure samples decreases by 88.48% in WRBDO and the weighted failures of WRBDO are averagely 9.1 times larger than those of RBDO. The results of applying AK-MCS for WRBDO to the 6D arm model verify that the AK-MCS for WRBDO enables practical application of WRBDO with a small number of function evaluations. [ABSTRACT FROM AUTHOR]

The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics. This phenomenon is examined by simulating electrophysiology of a single cortex neuron. Magnetic flux is captured by using a polynomial approximation of a memristor embedded into Hodgkin–Huxley model, equivalent electrical circuit of a neuron cell. Bifurcation analysis is carried out for two different electrical modes associated with the nature of the external neuronal stimulus. Aiming to determine the true influence of the variability of ion channels conductivity, the stochastic sensitivity analysis is undertaken post hoc. Additionally, numerical simulations are enriched with uncertainty quantification, observing values of ion channel conductivity as random variables. The aim of the study is to computationally determine the sensitivity of the action potential dynamics with respect to changes in conductivity of each ion channel so that the future experimental procedures, most often medical treatments, may be adapted to different individuals in various environmental conditions. [ABSTRACT FROM AUTHOR]

Summary: This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI. [ABSTRACT FROM AUTHOR]

The aim of this study is to further investigate the accuracy and the reliability of the actuator line model (ALM) predictions for turbulent separated wakes. Large eddy simulations (LES) of the flow around a NACA0009 airfoil are performed mimicking the geometry with the immersed boundary method. Results are validated against experiments and used to assess the accuracy of the ALM predictions for the same airfoil, with different values of the spreading parameter and of the reference velocity and for two values of the angle of attack. It is found that the ALM setup recently derived from linearized inviscid analysis leads to accurate results for the lower angle of attack, while at the higher one for which a significant separation of the boundary layer occurs, the ALM requires a different set of model parameters. This calls for a systematic investigation of the sensitivity to the ALM parameters for separated flows, which is carried out herein through a stochastic approach allowing continuous response surfaces to be obtained in the parameter space. The ALM parameters are calibrated against the results obtained with the immersed boundaries. With the calibrated model parameters, the ALM gives good predictions of the velocity and turbulent kinetic energy in the far wake. Finally, the proposed model parameters are used to predict the flow past a different geometry, a flat plate, at high angle of attack. The accuracy of the prediction of the far wake is again good, showing the robustness of the identified setup. [ABSTRACT FROM AUTHOR]

Both the public and the academic discourse of the post-crisis era have produced most controversial views concerning adequate national savings rates. We add to this discussion by analyzing the role of the savings rate for the dynamics of an economy embedded in a turbulent environment. To this end we study the dynamics of a stochastic Goodwin-type business cycle model using a mix of analytical- and simulation techniques. Focussing on a region of the parameter space that exhibits multi-stability, we apply the stochastic sensitivity function technique and Lyapunov exponents to scrutinize the dynamics of the stochastic economic system. We find that the savings rate affects the sensitivity of the economic system, as well as the distribution of economic states. The sensitivity of the system is inversely related to the level of the savings rate. Specifically, we demonstrate that high volatility phases of the cycle vary as the savings rate is changed. For low (high) levels of the savings rate the stochastic Goodwin economy will remain relatively often in sensitive (robust) states. Our theoretical investigation suggests that strategies involving reasonably high national savings rates might help to avoid the negative welfare implications of sensitive and even chaotic income dynamics along the cycle. [ABSTRACT FROM AUTHOR]

Engineering analyses of structures may be confronted with many sources of uncertainty, which may be of different types, such as parametric uncertainties versus modeling errors, and which may pertain to different structural components when complex structures are analyzed. Soize, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, Int. J. Numer. Meth. Eng., 81:939–970, 2010 has recently introduced a generalized probabilistic modeling approach, which can individually represent parametric uncertainties and modeling errors and which can individually represent sources of uncertainty pertaining to different structural components of complex structures. In this paper, we propose to augment this generalized probabilistic modeling approach with a stochastic sensitivity analysis in order to quantify and gain insight into separate impacts of distinct sources of uncertainty on quantities of interest. We demonstrate the proposed methodology by applying it to two computational-mechanics models involving uncertainty. [ABSTRACT FROM AUTHOR]

A stochastic analysis of the sensitivity to grid resolution and modeling of large-eddy simulations (LES) results is carried out for the flow around a 5:1 rectangular cylinder, which is the object of an international benchmark (BARC) collecting experimental and numerical flow realizations. Significant dispersion of the BARC predictions was observed for some quantities, also in LES, and deterministic sensitivity analyses were not conclusive. LES are carried out here by using a spectral-element numerical method. An explicit quadratic low-pass filter in the modal space is used, characterized by a cut-off value and by a weight function, which provides dissipation of the modes higher than the cut off and acts as a SGS dissipation. The uncertain parameters are the size of the spectral elements in the spanwise direction and the weight of the explicit filter. The impact of the uncertainty in these parameters is evaluated through generalized polynomial chaos. The analysis is repeated for two different grid resolutions in the streamwise and lateral directions. The most-probable values and the stochastic variance of the results are compared with the ensemble average and with the overall dispersion of the BARC predictions respectively. [ABSTRACT FROM AUTHOR]

(Special section 'Design, modelling and control of electric vehicles') This study provides a detailed deterministic and stochastic sensitivity analysis of the propulsion energy cost of electric vehicles (EVs) with respect to environmental variables. In particular, the effects of wind speed, rolling resistance, parasitic power and temperature are highlighted. The study provides exact analytical expressions as well as simulations to illustrate the key results. It is shown that the sensitivity of energy consumption with respect to the four environmental variables greatly vary with operating conditions of the vehicle. These environmental effects can have a profound effect on the overall energy consumption of EVs and drastically affect range. The significance of the authors' findings for vehicle range estimation is discussed and potential avenues to exploit the strong dependency between propulsion energy and environmental factors are proposed. [ABSTRACT FROM AUTHOR]

We motivate and specify a stochastic Goodwin-type business cycle model. Our analysis focusses on a subset of the parameter space where several attractors coexist. Applying a semi-numerical approach based on the stochastic sensitivity function and confidence domains due to Milstein and Ryashko (1995) , we study random transitions between stable attractors in the context of the Goodwin-type economy embedded in an uncertain environment. Relying on a mix of analytical considerations and simulations we demonstrate that under weak noise levels regime switching is a prominent feature in the presence of low saving rates. Moreover, we explain how increased uncertainty can induce an essentially unpredictable income process out of an apparently stable high-income level situation. All dynamic phenomena are explained in terms of key concepts constituting the stochastic sensitivity function method. [ABSTRACT FROM AUTHOR]

Identifying the specific reservoir properties that influence oil production is an essential part of field development planning. Distinguishing the relative influence of variables and eliminating those that have no influence assists the design of enhanced oil recovery processes. The conventional approach to identify the most influential variables is the multiple linear regression (MLR) step-wise elimination. Bayesian averaging (BA), a stochastic method, offers a novel alternative approach by generating fifty models compared to each other to select the best one with of the most influential parameters based on the highest R2 and posterior probability with the lowest value of Bayesian information criterion (BIC). BA and MLR step-wise elimination are compared in the evaluation of a simulated immiscible carbon dioxide-assisted gravity drainage (CO 2 -AGD) system applied to the multi-layered, heterogeneous, upper sandstone oil reservoir of the South Rumaila field. A history-matched compositional simulation covering the nearly 57 years of prior production is used for sensitivity analysis of reservoir variables in relation to CO 2 -AGD implementation over 10 future years with 22 additional CO 2 injection wells and 11 new production wells. Oil is displaced downwards towards the new horizontal production wells installed above the oil water contact. The influential variables evaluated are permeability (K), permeability anisotropy (K v /K h) and porosity (ɸ) considered separately across multiple heterogeneous reservoir layers. BA and step-wise elimination methods identify K as the most influential variable in all reservoir layers. K v /K h is moderately influential in the production layers and underlying water zone but not in injection or transition reservoir layers. ɸ in all reservoir layers has no influence on oil recovery from the CO 2 -AGD producing wells. More specifically, the BA-based influential parameters were determined after selecting the best model among the fifty generated models. The best model achieved that highest values of R2 of 0.848 and posterior probability of 0.234, and the lowest value of BIC of −149 with 12 identified influential geological parameters across the reservoir layers. Based on validation tests, varying K, K v /K h. and ɸ substantially across all reservoir layers confirms these findings and agrees more closely with the BA-derived reduced variable models than those generated by MLR step-wise elimination. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient but simple method to determine the approximate stationary probability distribution around periodic attractors of nonautonomous nonlinear systems under multiple time-dependent parametric noises and estimate the critical noise intensity for noise-induced explosive bifurcations under a given confidence probability. After adopting a stroboscopic map constructed by a method with higher accuracy and efficiency, nonautonomous dynamical systems around periodic attractors are transformed into mapping ones. Then the mean-square analysis method of discrete systems is used to derive the stochastic sensitivity function. Based on the confidence ellipses of stochastic attractors and the global structure of deterministic nonlinear systems, the critical noise intensity of noise-induced explosive bifurcations under a given confidence probability is estimated. A Mathieu-Duffing oscillator under both multiplicative and additive noises is studied to show the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, a post optimization technique for a correction of inaccurate optimum obtained using first-order reliability method (FORM) is proposed for accurate reliability-based design optimization (RBDO). In the proposed method, RBDO using FORM is first performed, and then the proposed second-order reliability method (SORM) is performed at the optimum obtained using FORM for more accurate reliability assessment and its sensitivity analysis. In the proposed SORM, the Hessian of a performance function is approximated by reusing derivatives information accumulated during previous RBDO iterations using FORM, indicating that additional functional evaluations are not required in the proposed SORM. The proposed SORM calculates a probability of failure and its first-order and second-order stochastic sensitivity by applying the importance sampling to a complete second-order Taylor series of the performance function. The proposed post optimization constructs a second-order Taylor expansion of the probability of failure using results of the proposed SORM. Because the constructed Taylor expansion is based on the reliability method more accurate than FORM, the corrected optimum using this Taylor expansion can satisfy the target reliability more accurately. In this way, the proposed method simultaneously achieves both efficiency of FORM and accuracy of SORM. [ABSTRACT FROM AUTHOR]

The extraction of 18 flutter derivatives of bridge decks from three degree-of-freedom (3-DOF) free vibration data using a novel direct approach is addressed in this study. Different with many conventional methods that construct a system state matrix, this approach directly extracts 18 flutter derivatives using the aeroelastically modified modal parameters. No state matrix is concerned, and thus it is more straightforward from the physical essence viewpoint. The validity and accuracy are demonstrated by a 3-DOF numerical example for bridge deck model. Afterward, the 18 flutter derivatives of two exact bridge decks with representative streamlined and bluff sections are extracted. Detailed deterministic and stochastic vulnerability analyses on identification accuracy of modal parameters and flutter derivatives were conducted for the numerical model and two bridge decks. For the free vibration method, the potential uncertainties in aeroelastic parameter determination are investigated, and the causes of low accuracy of some flutter derivatives (e.g., H4*, A4*, P1~4*) are attributed to the imperfection of the linear mathematical model, testing technique, and constraint conditions, and inherent low participation and/or coupling intensities of aeroelastic components. The aeroelastic characteristics and the influence of complex aerodynamic coupling on flutter performance of both streamlined and bluff bridge decks are examined and compared to unveil the mechanisms of two kinds of flutter. [ABSTRACT FROM AUTHOR]

We present a shape optimization method using a sampling-based RBDO method linked with a commercial finite element analysis (FEA) code ANSYS, which is applicable to residual deformation problems of the ship hull structure in welding process. The programming language ANSYS Parametric Design Language (APDL) and shell elements are used for the thermo-elasto-plastic analysis. The shape of the ship hull structure is modeled using the bicubic Ferguson patch and coordinate components of vertices, tangential vectors of boundary curves are selected as design variables. The sensitivity of probabilistic constraint is calculated from the probabilistic sensitivity analysis using the score function and Monte Carlo Simulation (MCS) on the surrogate model constructed by using the Dynamic Kriging (DKG) method. The sequential quadratic programming (SQP) algorithm is used for the optimization. In two numerical examples, the suggested optimization method is applied to practical residual deformation problems in welding ship hull structures, which proves the sampling-based RBDO can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problem of thermo-elasto-plasticity. [ABSTRACT FROM PUBLISHER]

Using a sampling-based reliability-based design optimization method, we present a shape reliability-based design optimization method for coupled fluid–solid interaction problems. For the fluid–solid interaction problem in arbitrary Lagrangian–Eulerian formulation, a coupled variational equation is derived from a steady state Navier–Stokes equation for incompressible flows, an equilibrium equation for geometrically nonlinear solids, and a traction continuity condition at interfaces. The fluid–solid interaction problem is solved using the finite element method and the Newton–Raphson scheme. For the fluid mesh movement, we formulated and solved a pseudo-structural sub-problem. The shape of the solid is modeled using the Non-Uniform Rational B-Spline (NURBS) surface, and the coordinate components of the control points are selected as random design variables. The sensitivity of the probabilistic constraint is calculated using the first-order score functions obtained from the input distributions and from the Monte Carlo simulation on the surrogate model constructed by using the Dynamic Kriging method. The sequential quadratic programming algorithm is used for the optimization. In two numerical examples, the proposed optimization method is applied to the shape design problems of solid structure which is loaded by prescribed fluid flow, and this proves that the sampling-based reliability-based design optimization can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problems. [ABSTRACT FROM AUTHOR]

A new method, which is an alternative to the score function method, is developed. Unlike the score function from the literature, this proposed method uses the derivatives of response function incorporating with Kernel Density Estimation for stochastic design sensitivity analysis. Two analytical examples are used to demonstrate effectiveness and robustness of the proposed stochastic sensitivity analysis method. The sensitivity analysis method is then applied to solve two reliability-based design optimization examples. [ABSTRACT FROM AUTHOR]

For many engineering design problems, traditional most probable point (MPP)-based reliability analysis using sensitivity information to find the MPP is difficult for practical use. In addition, the sensitivities of performance function are often unavailable for problems such as crashworthiness. Using Monte Carlo simulation method to calculate the sensitivities of probabilistic responses, which are often obtained by using finite difference method, is very time consuming and inaccurate. This paper presents a stochastic sensitivity-analysis method for computing the sensitivities of probabilistic response by using Monte Carlo simulation incorporated with a metamodel, which is selected by using Bayesian metric considering data uncertainty. An adaptive sampling-based RBDO methodology based on Bayesian metric and stochastic sensitivity analysis is developed for design optimisation of large-scale complex problems. This method not only produces an accurate metamodel, but also yields an accurate optimal design efficiently. This methodology is demonstrated by a crashworthiness optimisation example. [ABSTRACT FROM AUTHOR]

• A new method is proposed for system reliability-based design optimization. • A composite active learning strategy is proposed for locally refining Kriging. • Multiple Kriging uncertainty is considered in the termination of Kriging update. • Results of four examples verify the accuracy and efficiency of proposed method. This paper proposes a sampling-based system reliability-based design optimization (SRBDO) method with local approximation of constraints. To enhance the optimization efficiency of SRBDO problems with time-consuming constraints, Kriging metamodels are employed to replace the true constraint functions. A new composite active learning strategy based on the possibility of correctly predicting the state of the cut-set system is developed to locally approximate constraints. Furthermore, to ensure the accuracy of the system reliability analysis at the final SRBDO solution, the Kriging update in the developed strategy is terminated by quantifying the influence of the Kriging uncertainty on the prediction of the system failure probability and the confidence that the solution satisfies the prescribed system failure probability. This approach can avoid the unnecessary burden of Kriging construction during system reliability analysis at intermediate solutions far from the final solution. Based on the updated Kriging metamodel, the system failure probability of constraints is estimated by Monte Carlo simulation, and its partial derivative is calculated by stochastic sensitivity analysis. The performance of the proposed method is tested and verified by using four examples. Compared with the existing methods, the proposed method has high computational accuracy and efficiency for solving SRBDO problems. [ABSTRACT FROM AUTHOR]