Uncertain Boundary Research Articles

Input Calibration and Validation of RELAP5 Against CIRCUS-IV Single Channel Tests on Natural Circulation Two-Phase Flow Instability

RELAP5 is a system thermal-hydraulic code that is used to perform safety analysis on nuclear reactors. Since the code is based on steady state, two-phase flow regime maps, there is a concern that RELAP5 may provide significant errors for rapid transient conditions. In this work, the capability of RELAP5 code to predict the oscillatory behavior of a natural circulation driven, two-phase flow at low pressure is investigated. The simulations are compared with a series of experiments that were performed in the CIRCUS-IV facility at the Delft University of Technology. For this purpose, we developed a procedure for calibration of the input and code validation. The procedure employs (i) multiple parameters measured in different regimes, (ii) independent consideration of the subsections of the loop, and (iii) assessment of importance of the uncertain input parameters. We found that predicted system parameters are less sensitive to variations of the uncertain input and boundary conditions in high frequency oscillations regime. It is shown that calculation results overlap experimental values, except for the high frequency oscillations regime where the maximum inlet flow rate was overestimated. This finding agrees with the idea that steady state, two-phase flow regime maps might be one of the possible reasons for the discrepancy in case of rapid transients in two-phase systems.

Protein Function Prediction Using Neighbor Counting with Dynamic Threshold from Protein-Protein Interaction Network

In recent years, a large number of proteins of different organisms have been discovered but due to high experimental cost and uncertain time boundary, yet it is not possible to find out all of the functionalities of those proteins. With the recent advent of huge protein-protein interactions, it becomes an opportunity to computationally predict a protein’s functionality based on its interacting partners. In this work, we mainly try to find out a way by which we can predict functionality of a target protein with low computational complexity. We propose a simple approach for protein function prediction based on Classical Neighbor Counting method. We also investigate the functional dependency of a protein to its direct neighbors in the interaction network. We find that when majority of its interacting partners have more experimentally known annotation, then more accurately we can predict a protein’s functionality using Neighbor Counting technique.

Influence of the Parameterization in the Interval Solution of Elastic Beams

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.

The Ashgate Research Companion to Monsters and the Monstrous (Asa Simon Mittman and Peter J. Dendle, eds.)

<i>The Ashgate Research Companion to Monsters and the Monstrous</i> (Asa Simon Mittman and Peter J. Dendle, eds.)

Constructive epistemic modeling of groundwater flow with geological structure and boundary condition uncertainty under the Bayesian paradigm

• BMA trees of model weights, prediction and variance serve as a learning tool. • Candidate propositions are tested to learn about individual model components. • Posterior model probability is a degree of belief given our state of knowledge. • Geological structure uncertainty is larger than boundary condition uncertainty. • Model structure uncertainty is larger than parameter uncertainty. Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using hierarchical Bayesian model averaging (BMA), this study shows that segregating different uncertain model components through a BMA tree of posterior model probability, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater flow model of a siliciclastic aquifer-fault system. We consider four uncertain model components. With respect to geological structure uncertainty, we consider three methods for reconstructing the hydrofacies architecture of the aquifer-fault system, and two formation dips. We consider two uncertain boundary conditions, each having two candidate propositions. Through combinatorial design, these four uncertain model components with their candidate propositions result in 24 base models. The study shows that hierarchical BMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models.

A boundary element model for acoustic responses in the ear canal and its statistical validation and updating

A boundary element method (BEM) model for acoustic responses in individual ear canals was developed, and its validity was assessed and updated using a statistical approach. The BEM model was developed using high resolution computed tomography (CT) scanning from a healthy male adult. The BEM model, which was discretized adaptively for a frequency band of up to 22 kHz, included the head, pinna, ear canals, and tympanic membranes. The variability of the BEM model due to the uncertain acoustic boundary conditions and measurement locations was predicted using the eigenvector dimension reduction (EDR) method. Then, the likelihood function estimation approach was introduced in order to measure the agreement between the acoustic responses of the simulation model and experimental results. In order to enhance the simulation model performance, the acoustic boundary conditions of the BEM model were updated using a statistical calibration approach that maximizes the likelihood function value between the calculated probability density functions (PDFs) of the simulation model and the measurement data. The results of the validation and calibration procedures applied to the BEM model demonstrated that the proposed method provides a very effective method of verifying the model validity and enhancing the performance of the simulation model.

Boundary conditions in quantitative elastic modulus imaging

Quantitative elastic modulus imaging from quasistatic strain fields has several advantages over other approaches. It requires no specialized hardware, provides spatial resolution nearly commensurate with Bmode, and may be extended to quantitative nonlinear modulus imaging in a straightforward way. It has the drawback, however, of requiring the solution of a complex inverse problem with an ultrasound measured displacement field. The most common approach to solving the inverse problem is iterative optimization. To solve the inverse problem, the experimental configuration is simulated. Material property distributions in the simulated experiment are then varied until the simulated deformation field matches the observed deformation field. The weak link in this process is uncertainty in the experimental conditions. In the context of iterative inversion, this translates into uncertainty in the boundary conditions of the forward model. In this talk, we discuss how different choices of displacement and/or traction boundary conditions affect the inverse problem's solution using phantom and clinical breast data. We show that a Bayesian estimate of the displacement field in the face of uncertain boundary conditions can be implemented by spring finite elements on the domain boundary. [Authors gratefully acknowledge funding from NSF and NIH (NSF SI2 Grant No. 1148111; NIH NCI-R01CA140271).]

Stress gradient versus strain gradient constitutive models within elasticity

A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Hellinger–Reissner type variational principle. The main differences between the Eringen stress gradient model and the concomitant Aifantis strain gradient model are pointed out. A rigorous formulation of the stress gradient Euler–Bernoulli beam is provided; the response of this beam model is discussed as for its sensitivity to the stress gradient effects and compared with the analogous strain gradient beam model.

An Observation-Based Model for Secondary Inorganic Aerosols

An observation-based model for secondary inorganic aerosol (OBM-SIA) is developed to determine the sensitivity of formation of sulfate (SO42–) and nitrate (NO3–) to changes in their precursors. The model incorporates CB05 chemical mechanism with inclusion of two recently discovered OH enhancement pathways and essential aqueous phase chemical reactions, thermodynamic equilibriums for gas-aerosol phase apportionment and size distribution of SO42– and NO3–. A sequence of present time-frame observations of precursors and particle compositions are used to drive the simulation and to determine responses to perturbed emission rates of precursors. OBM-SIA obviates the need for uncertain emission inventories and boundary layer dynamic conditions, and makes use of data that are increasingly available due to recent advances in online instruments for various gaseous and aerosol components, thereby offering a cost-effective tool for the analysis of SIA-precursor relationships in the atmosphere. OBM-SIA is applied to hourly gaseous and particulate composition data during a wintertime pollution episode in Hong Kong. The major pathway responsible for the production of NO3– is the reaction of OH and NO2 in the gas phase, while the gas phase oxidation of SO2 by OH and aqueous phase oxidation of S(IV) by O3 contribute most significantly on SO42– production. NO3– production is more sensitive to the reduction of NOx and anthropogenic VOCs. Reduction of SO42– formation is however most sensitive to SO2 reduction and it becomes more effective as more SO2 is reduced. The work illustrates the utility of OBM-SIA in suggesting evidence-based control strategies for effective reduction of targeted SIAs.

An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling

We present an adaptive observer design for a first-order hyperbolic system of Partial Differential Equations with uncertain boundary parameters. The design relies on boundary measurements only, and is based on a backstepping approach. Using a Gradient Descent technique, we prove exponential convergence of the distributed system and estimation of the parameter. This method is applied to the estimation of uncertain parameters during the process of oil well drilling.

Rough Set and K-Means Clustering Algorithm Based on Ant Colony Algorithm

Traditional K-means clustering methods have great attachment to the selection of the initial value and easily get into the local extreme value. This paper proposes a synthetic clustering algorithm of rough set and K-means based on Ant colony algorithm. While the rough set theory presents processing method of uncertain boundary objects, Ant colony algorithm is a bionic optimization algorithm, which has strong robustness, easily with other method unifies, solving efficiency higher characteristic.. Therefore, the K-means algorithm based on Ant colony algorithm in this paper combines rough set theory with simulated annealing algorithm and K-means, in which K means cluster number and initial cluster centers can be obtained dynamically with the principle of maximum minimum, and processing boundary objects with upper and lower approximation of rough set theory. Finally, the UCIs Iris set is used to test the algorithm. The experimental results show that the algorithm has higher accuracy rate, faster execution time and more stable performance.

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

Abstract. Comprehensive flood risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of particular importance in the case of flood hazard assessments along dike-protected reaches, where the possibility of occurrence of dike failures may considerably enhance the uncertainty. We present a methodology to derive probabilistic flood maps in dike-protected flood prone areas, where several sources of uncertainty are taken into account. In particular, this paper focuses on a 50 km reach of River Po (Italy) and three major sources of uncertainty in hydraulic modelling and flood mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in dike failures. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed through a copula-based bivariate analysis of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterised by uncertainty in the rating curve with confidence intervals which reflect discharge measurement and interpolation errors. The effects of uncertainties in boundary conditions and randomness of dike failures are assessed by means of the Inundation Hazard Assessment Model (IHAM), a recently proposed hybrid probabilistic-deterministic model that considers three different dike failure mechanisms: overtopping, piping and micro-instability due to seepage. The results of the study show that the IHAM-based analysis enables probabilistic flood hazard mapping and provides decision-makers with a fundamental piece of information for devising and implementing flood risk mitigation strategies in the presence of various sources of uncertainty.

High order optimal control of space trajectories with uncertain boundary conditions

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth–Mars transfer.

Hierarchical Clustering Algorithm of the Minimum Risk

Clustering analysis is grouping a set of physical or abstract objects into the similar class. In traditional clustering algorithm, objects are usually divided into a certain cluster. This paper applies the risk evaluation of decision-theoretic rough set model in clustering analysis which solves the problem of uncertain boundary region, and proposes a hierarchical clustering algorithm of the minimum risk which can adjust threshold value to construct a clustering evaluation function in order to find the solution to optimize the result. At last, the case analysis shows the algorithm is feasible. It could provide a strong support for marine environment monitoring system and so on.

Determination of stay cable force based on effective vibration length accurately estimated from multiple measurements

Due to its easy operation and wide applicability, the ambient vibration method is commonly adopted to determine the cable force by first identifying the cable frequencies from the vibration signals. With given vibration length and flexural rigidity, an analytical or empirical formula is then used with these cable frequencies to calculate the cable force. It is, however, usually difficult to decide the two required parameters, especially the vibration length due to uncertain boundary constraints. To tackle this problem, a new concept of combining the modal frequencies and mode shape ratios is fully explored in this study for developing an accurate method merely based on ambient vibration measurements. A simply supported beam model with an axial tension is adopted and the effective vibration length of cable is then independently determined based on the mode shape ratios identified from the synchronized measurements. With the effective vibration length obtained and the identified modal frequencies, the cable force and flexural rigidity can then be solved using simple linear regression techniques. The feasibility and accuracy of the proposed method is extensively verified with demonstrative numerical examples and actual applications to different cable-stayed bridges. Furthermore, several important issues in engineering practice such as the number of sensors and selection of modes are also thoroughly investigated.

Remedy to Overestimation of Classical Interval Analysis: Analysis of Beams with Uncertain Boundary Conditions

This study investigates both the static and dynamic behaviors for the uniform beam supported at its ends by rotational supports. The stiffness coefficients of these supports are treated as interval variables. It is first demonstrated on the static problem that the classical interval analysis may lead to overestimation of the response. The paper introduces a remedy for this "ill" of the classical interval analysis. The artificial interval parameter is introduced and the extrema of the static displacements and natural frequencies are determined. Finally, the hybrid case of uncertain boundary conditions and uncertain mass density is treated with attendant interesting results.

Remedy to overestimation of classical interval analysis: Analysis of beams with uncertain boundary conditions

This study investigates both the static and dynamic behaviors for the uniform beam supported at its ends by rotational supports. The stiffness coefficients of these supports are treated as interval variables. It is first demonstrated on the static problem that the classical interval analysis may lead to overestimation of the response. The paper introduces a remedy for this ill of the classical interval analysis. The artificial interval parameter is introduced and the extrema of the static displacements and natural frequencies are determined. Finally, the hybrid case of uncertain boundary conditions and uncertain mass density is treated with attendant interesting results.

Adaptive Boundary Control for a Class of Uncertain Heat Equations

This paper investigates the adaptive state-feedback boundary control design for a class of heat equations with uncertain control coefficient and boundary disturbance.By Lyapunov method,the desirable controller is explicitly constructed,which only needs the boundary state of the system.It is shown that the closed-loop system state is L2[0,1] stable,and particularly,the state converges to zero when the boundary disturbance vanishes.Moreover,by skillfully choosing the initial condition of parameter updating law,the restriction on the initial condition of the system is moderately relaxed,which is usually described by the so-called compatible condition in the related literature.A simulation example is presented to illustrate the effectiveness of the proposed method.

Vibration-based estimation of axial force for a beam member with uncertain boundary conditions

Focusing on the application for diagonal braces, tie-bars and short thick cables, this work proposes a new technique to identify the axial force of a two-dimensional Euler–Bernoulli beam member. Bending stiffness effects are taken into account. On the basis of the dynamic measurements from at least five sensors, the proposed method is capable of estimating the axial force as well as the translational and rotational stiffness at both beam ends. When fixing some end constraints, the required number of sensors can be reduced. Finite element simulations are performed for verification purpose, accounting for a wide range of bending stiffness. A laboratory experiment is conducted to investigate the feasibility and accuracy of the proposed method.

Adaptive coupling synchronization in complex network with uncertain boundary

It is difficult that all the boundaries of chaotic system were estimated precisely; this is why the coupling coefficient cannot be determined beforehand in the problem of synchronization of complex networks. Thus, an estimation of coupling coefficient should be given before designing some controllers. In addition, to realize the synchronization, the estimated coupling coefficient has to be large enough. However, it is not true that the larger the coupling coefficient the better the synchronization is. In fact, a coupling coefficient which is larger than what it needs to be means the energy waste. To overcome this difficulty, in this paper we propose an adaptive coupling method. And a new concept about asymptotic stability is presented. Numerical simulations are implemented on different complex networks. The results indicate that the synchronization can be achieved without a large estimated coefficient.