Numerical Investigations of Relaxation Phenomena in Cavitating Nozzle Flows

Numerical simulations of cavitating flows are frequently performed by applying simple law of state‐models. In this study an advanced law of state‐model on the basis of a Landau‐type approach is used that focusses on the physical treatment of relaxation phenomena. Relaxation phenomena or phase non‐equilibrium effects occur within the scope of two‐phase fluid dynamics if the time scale of the flow problem is small. This appears e.g. in the case of cavitating flow in injector nozzles of diesel engines. The aim of this study is the determination of the relaxation parameter of the advanced law of state‐model. For this reason a theoretical approach is presented as well as simulations of unsteady cavitating nozzle flows that are compared with experimental data. Concerning the calculation of 2‐D unsteady cavitating flow the evolution equation for the vapor fraction is solved by a modified Volume‐of‐Fluid algorithm.     

The dynamic programming method in systems with states in the form of distributions

The problem of optimal control of a system with the initial state in the form of a known distribution function specified on a fixed time segment is considered. To solve this problem, an approach is used in which the state of the system is understood as a coordinate distribution at each instant of time. Analogs of the equations in the Hamiltonian formalism for the problem of minimizing the integral functional are derived. The solution to the problem of optimal control in the closed form for a linear system with an integral quadratic functional is presented.     

3D free vibration analysis of laminated cylindrical shell integrated piezoelectric layers using the differential quadrature method

This paper addresses the free vibration problem of multilayered shells with embedded piezoelectric layers. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. The shell has arbitrary end boundary conditions. For the simply supported boundary conditions closed-form solution is given by making the use of Fourier series expansion. Applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free end conditions. Natural frequencies of the hybrid laminated shell are presented by solving the eigenfrequency equation which can be obtained by using edges boundary condition in this state equation. Accuracy and convergence of the present approach is verified by comparing the natural frequencies with the results obtained in the literatures. Finally, the effect of edges conditions, mid-radius to thickness ratio, length to mid-radius ratio and the piezoelectric thickness on vibration behaviour of shell are investigated.     

Life Prediction of FRP Composites by a Direct Method

A direct computational approach for lifetime prediction of fibre-reinforced polymer (FRP) composites is presented. The approach is based on a direct method which allows predicting the fatigue life from the stabilised damage state. The classical direct method is generalised to the case of coupled plasticity with damage mechanics of the UD-FRP composite materials [1]. The constitutive model is based on a continuous damage meso-scale approach [2]. By analysing damage variables and thermodynamical forces associated with damage at the stabilised state, fatigue life prediction law is proposed as a power law function of stabilised thermodynamic forces. The obtained numerical results have been validated by experimental test results on standard glass-fibre/epoxy angle-ply and cross-ply laminate plates. The proposed approach could serve as a useful tool for the design of FRP composites. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ship Capsize Risk Assessment and Designing Against Capsize

A promissing approach for assessing ship safety against capsize is presented by Melnikov's method. The mean zero up‐crossing rate of the dynamical system's associated Melnikov process provides an upper bound for the mean capsizing rate in a stationary sea state. Due to its moderate computational effort if low dimensional systems are considered, this approach is particularly suited for applications in ship design.     

Multilevel optimization of a supersonic aircraft

This paper investigates the application of a multilevel preconditioned algorithm for the sonic boom reduction of a supersonic business jet. The optimization algorithm relies on a gradient approach with an adjoint state evaluation. The multi-level preconditioner is designed from an analysis of the gradient regularity loss. The sonic boom reduction is achieved in an indirect way by minimizing what we call the sonic boom downwards emission, which is computed in the near field. Additional aerodynamic performances like lift and drag forces are also guaranteed by including their evaluation in the problem's cost functional. Applications to 3D geometries are presented.     

Cryptanalyzing the polynomial-reconstruction based public-key system under optimal parameter choice

In Eurocrypt 2004 Augot and Finiasz presented a coding theoretic public key cryptosystem that suggests a new approach for designing such systems based on the Polynomial Reconstruction Problem (PR). Their cryptosystem is an instantiation of this approach under a specific choice of parameters which, given the state of the art of coding theory, we show in this work to be sub-optimal. Coron showed how to attack the Augot and Finiasz cryptosystem. A question left open is whether the general approach suggested by the cryptosystem works or not. In this work, we show that the general approach (rather than only the instantiation) is broken as well.      

New Approach to Linear Exact Model Matching for a Class of Nonlinear Systems

In this paper, a new approach to the linear exact model matching problem for a class of nonlinear systems, using static state feedback, is presented. This approach reduces the problem of determining the state feedback control law to that of solving a system of first-order partial differential equations. Based on these equations, two major issues are resolved: the necessary and sufficient conditions for the problem to have a solution and the general analytical expression for the feedback control law. Furthermore, the proposed approach is extended to solve the same problem via static output feedback.     

An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures

This paper presents an efficient third-moment saddlepoint approximation approach for probabilistic uncertainty analysis and reliability evaluation of random structures. By constructing a concise cumulant generating function (CGF) for the state variable according to its first three statistical moments, approximate probability density function and cumulative distribution function of the state variable, which may possess any types of distribution, are obtained analytically by using saddlepoint approximation technique. A convenient generalized procedure for structural reliability analysis is then presented. In the procedure, the simplicity of general moment matching method and the accuracy of saddlepoint approximation technique are integrated effectively. The main difference of the presented method from existing moment methods is that the presented method may provide more detailed information about the distribution of the state variable. The main difference of the presented method from existing saddlepoint approximation techniques is that it does not strictly require the existence of the CGFs of input random variables. With the advantages, the presented method is more convenient and can be used for reliability evaluation of uncertain structures where the concrete probability distributions of input random variables are known or unknown. It is illustrated and examined by five representative examples that the presented method is effective and feasible.     

On the Control of a Nonlinear Dynamic System in a Time-Optimal Problem with State Constraints

An optimal control problem for a nonlinear dynamic system is studied. The required control must satisfy given constraints and provide the fulfilment of a number of conditions on the current state of the system. For the construction of admissible controls in this problem, we propose an approach based on the ideas of solution of control problems with a guide. The results of numerical simulation are presented.     

Feedback control based on discrete-time state observations on synchronization of stochastic impulsive coupled systems

In this paper, feedback control based on discrete-time state observations is used to study the inner synchronization of stochastic impulsive coupled systems (SICSs). Therein, the coupling strength of SICSs is state-dependent switching and time-varying under each switching. Besides, by means of average impulsive interval approach, the Lyapunov method and the graph theory, a synchronization criterion of SICSs is presented. As an application, stochastic impulsive coupled Chua’s circuits with state-dependent switching coupling strength are investigated for the first time and some sufficient conditions are given. Finally, in order to illustrate the effectiveness of our main results, some numerical simulations are presented.     

On the numerical determination of optimal inputs

The design of optimal inputs for linear and nonlinear system identification involves the maximization of a quadratic performance index subject to an input energy constraint. In the classical approach, a Lagrange multiplier is introduced whose value is an unknown constant. In recent papers, the Lagrange multiplier has been determined by plotting a curve of the Lagrange multiplier as a function of the critical interval length or a curve of input energy versus the interval length. A new approach is presented in this paper in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. Numerical results are given for both a linear and a nonlinear dynamic system.     

Reduction of overestimation in interval arithmetic simulation of biological wastewater treatment processes

A novel interval arithmetic simulation approach is introduced in order to evaluate the performance of biological wastewater treatment processes. Such processes are typically modeled as dynamical systems where the reaction kinetics appears as additive nonlinearity in state. In the calculation of guaranteed bounds of state variables uncertain parameters and uncertain initial conditions are considered. The recursive evaluation of such systems of nonlinear state equations yields overestimation of the state variables that is accumulating over the simulation time. To cope with this wrapping effect, innovative splitting and merging criteria based on a recursive uncertain linear transformation of the state variables are discussed. Additionally, re-approximation strategies for regions in the state space calculated by interval arithmetic techniques using disjoint subintervals improve the simulation quality significantly if these regions are described by several overlapping subintervals. This simulation approach is used to find a practical compromise between computational effort and simulation quality. It is pointed out how these splitting and merging algorithms can be combined with other methods that aim at the reduction of overestimation by applying consistency techniques. Simulation results are presented for a simplified reduced-order model of the reduction of organic matter in the activated sludge process of biological wastewater treatment.     

Refined Numerical Schemes for a Stressed-Strained State of Structural Joints of Layered Elements

A numerical approach based on block-variational modeling of a stressed state of structural joints of layered elements is developed. A refined theory based on a kinematic hypothesis for every layer and joints and numerical results are presented.     

Expected Power-Utility Maximization Under Incomplete Information and with Cox-Process Observations

We consider the problem of maximization of expected terminal power utility (risk sensitive criterion). The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main novelty is due to the fact that prices are observed and the portfolio is rebalanced only at random times corresponding to a Cox process where the intensity is driven by the unobserved Markovian factor process as well. This leads to a more realistic modeling for many practical situations, like in markets with liquidity restrictions; on the other hand it considerably complicates the problem to the point that traditional methodologies cannot be directly applied. The approach presented here is specific to the power-utility. For log-utilities a different approach is presented in Fujimoto et al. (Preprint, 2012).     

Control of a fourth-order linear system with mixed constraints

A controlled fourth-order linear mechanical system, containing a vibrating member, is considered. Geometric constraints are imposed on the control and phase variables. The problem of bringing the system to a given state in a finite time is solved. The solution employs an approach based on Kalman's general scheme for constructing controls as linear combinations of characteristic motions of the uncontrolled system. Results of a numerical simulation of the dynamics of a closed system are presented     

On a class of nonconvex and nonlinear optimal control problems

We propose two relaxation approaches for the existence of solutions of a nonconvex optimal control problem with a nonlinear dynamics and two fixed endpoints. The first approach adds to the functional a term depending on the final state; the second one introduces a new scalar control into both the functional and the dynamics. Our results generalize those obtained in the linear case. We assume that the integrand be concave w.r.t. the state variable, and provide an example showing that a strict concavity condition, in the nonlinear case, is essential. Finally, a result without relaxation is presented.     

Pole placement by dynamic output feedback of minimal order

In the present contribution, an approach for calculating a dynamic output feedback of minimal order is presented. The feedback is of minimal order in the sense that the controller state has lowest possible dimension among all controllers placing the poles of the closed loop system as desired. The main idea is to extend the system under consideration succesively by independent integrators until a static compensator can be computed. This is also discussed on a computational example. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Optimal Control of a Free Surface Flow

We discuss an optimal control approach for a 2D Stokes flow with a free surface. The aim is to optimize the shape of a polymer film by adjusting the ambient pressure in a casting process. The resulting minimization problem is solved by the method of steepest descent. Numerical results will be presented. Furthermore we state the adjoint system for the Lagrangian formalism. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating Relative Risk on the Line Using Nearest Neighbor Statistics

This paper considers a non-parametric method for identifying intervals on the line where the relative risk of cases to controls exceeds a pre-specified level. The method is based on the kth nearest neighbor (kNN) approach for density estimation. An asymptotic result is presented that yields an explicit formula for constructing a confidence interval for the relative risk at a given point. Numerical simulations are used to compare this approach with a kernel density estimation procedure. An application is made to a case-control study in which the relative risk of motor vehicle crashes caused by female drivers is compared to male drivers in the state of Kentucky as a function of age and then by time of day.