quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

h filtering for nonlinear networked systems with randomly occurring distributed delays missing measurements and sensor saturation this paper is concerned with the h filtering problem for a class of networked systems subject to randomly occurring distributed state delays nonlinearities sensor saturation as well as missing measurements via unreliable communication channels the output measurements are affected by sensor saturation which is described by sector nonlinearities the missing measurement is modeled as a linear random variable satisfying the bernoulli distribution and the nonlinearities with the form of global lipschitz cover the well known nonlinear functions the purpose of the addressed problem is to design a full order filter such that in the simultaneous presence of distributed delays randomly occurring nonlinearities sensor saturation and missing measurements the filtering dynamic system is guaranteed to be exponentially mean square stable and the h filtering performance index is achieved a sufficient condition for the solution of the addressed problem is derived and the explicit expression of the desired filter gains is described in terms of the solution to linear matrix inequality lmi finally a numerical example is provided to show the effectiveness of the designed method

artifacts with uneven sampling of red noise the vast majority of sampling systems operate in a standard way at each tick of a fixed frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted stored or processed right away thus signal sampling at evenly spaced time intervals is the rule however this is not always the case and uneven sampling is sometimes unavoidable while periodic or quasiperiodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts it is much less obvious that the same happens with noise here i show that this is indeed the case only for long memory noise processes i e power law noises 1 f ensuremath alpha with ensuremath alpha g2 the resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples but they could also be turned to advantage and used to encode information

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

an analysis of the prothero robinson example for constructing new dirk and row methods this note analyses the order reduction phenomenon of diagonally implicit runge kutta methods dirk methods and rosenbrock wanner methods row methods applied on the prothero robinson example new order conditions to reduce order reduction are derived and a new third order dirk and row method is created the new schemes are applied to the prothero robinson example and on the semi discretised incompressible navier stokes equations numerical examples show that the new methods have better convergence properties than comparable methods

optimal estimation and control for lossy network stability convergence and performance in this paper we study the problems of optimal estimation and control i e the linear quadratic gaussian lqg control for systems with packet losses but without acknowledgment such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses for such system which is usually called as a user datagram protocol udp like system the optimal estimation is nonlinear and its calculation is time consuming making its corresponding optimal lqg problem complicated we first propose two conditions 1 the sensor has some computation abilities and 2 the control command exerted to the plant is known to the sensor for a udp like system satisfying these two conditions we derive the optimal estimation by constructing the finite and infinite product probability measure spaces for the estimation error covariances eec we give the stability condition for the expected eec and show the existence of a measurable function to which the eec converges in distribution and propose some practical methods to evaluate the estimation performance finally the lqg controllers are derived and the conditions for the mean square stability of the closed loop system are established

a scalable fully implicit compressible euler solver for mesoscale nonhydrostatic simulation of atmospheric flows a fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible euler equations to spatially discretize the euler equations on a height based terrain following mesh we apply a cell centered finite volume scheme in which an advection upstream splitting ausm up method with a piecewise linear reconstruction is employed to achieve second order accuracy for the low mach flow a second order explicit first step single diagonal coefficient diagonally implicit runge kutta esdirk method with adaptive time stepping is applied to stabilize physically insignificant fast waves and accurately integrate the euler equations in time the nonlinear system arising at each time step is solved by using a jacobian free newton krylov schwarz nks algorithm to accelerate the convergence and improve the robustness we employ a class of additive schwarz preconditioners in which the subdomain jacobian matrix is constructed using a first order spatial discretization several test cases are used to validate the correctness of the scheme and examine the performance of the solver large scale results on a supercomputer with up to 18 432 processor cores are provided to show the parallel performance of the proposed method

stability of mmse state estimators over lossy networks using linear coding this paper studies the state estimation problem for a stochastic discrete time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process to counter the effect of random packet loss we propose a linear coding method to preprocess the measured output and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present an optimal state estimator under the minimum mean square error mmse criterion is derived for the coded output when subject to packet loss the maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well known lower bound also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding and it is shown that the similar packet rate condition for stability holds

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

adaptive time step control for the incompressible navier stokes equations abstract adaptive time stepping is an important tool in computational fluid dynamics for controlling the accuracy of simulations and for enhancing their efficiency this paper presents a systematic study of three classes of implicit and linearly implicit time stepping schemes with adaptive time step control applied to a 2d laminar flow around a cylinder schemes diagonal implicit runge kutta dirk methods and rosenbrock wanner row methods the time step is controlled using embedded methods it is shown that several row methods clearly outperform the more standard schemes and the dirk methods the results depend on a prescribed tolerance in the time step control algorithm whose appropriate choice varies from scheme to scheme

analysis and application of high order implicit runge kutta schemes for unsteady conjugate heat transfer a strongly coupled approach abstract thermal interaction of fluids and solids or conjugate heat transfer cht is encountered in many engineering applications since time accurate computations of unsteady cht can be computationally demanding we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes we present a strongly coupled solution algorithm where the high order l stable explicit first stage singly diagonally implicit runge kutta esdirk schemes are used to advance the solution in time within each separate fluid and solid subdomains furthermore the stability and rate of convergence of performing gauss seidel subiterations at each stage of the esdirk schemes are analyzed the results from solving a numerical example an unsteady conjugate natural convection in an enclosure show good agreement with the performed analytical stability analysis in addition the computational work temporal precision character of several schemes in solving a strongly coupled cht problem is compared over a range of accuracy requirements from the efficiency investigation it is observed that performing subiterations with the strongly coupled esdirk algorithm is more efficient than lowering time step size using a high order loosely coupled imex algorithm in addition by using the esdirk schemes gain in computational efficiency relative to crank nicolson is observed for time accurate solutions a factor of 1 4 using the fourth order esdirk the computational gain is higher for smaller tolerances

adaptive time step control for higher order variational time discretizations applied to convection diffusion reaction equations abstract higher order variational time stepping schemes allow an efficient post processing for computing a higher order solution this paper presents an adaptive algorithm whose time step control utilizes the post processed solution the algorithm is applied to convection dominated convection diffusion reaction equations it is shown that the length of the time step properly reflects the dynamics of the solution with respect to the performance accuracy efficiency the variational time stepping schemes are compared with an adaptive crank nicolson scheme whose time step control relies on comparing two solutions computed with schemes of the same order

kalman filtering with intermittent observations convergence for semi markov chains and an intrinsic performance measure this technical note shows that the stationary distribution for the covariance of kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models semi markov chain these results are proved using the geometric properties of riccati recursions with respect to a particular riemannian distance moreover the riemannian mean induced by that distance is always bounded therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist other interesting properties of that mean include the symmetry between covariance and information matrices averaging covariances or their inverse gives the same result and its interpretation in information geometry as the natural mean for the manifold of gaussian distributions

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

hp adaptive time integration based on the bdf for viscous flows this paper presents a procedure based on the backward differentiation formulas of order 1 to 5 to obtain efficient time integration of the incompressible navier stokes equations the adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process the stepsize selection h adaptivity is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance the order selection p adaptivity relies on the idea that low accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low the selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize hence it guarantees both that 1 the used method of integration operates inside of its stability region and 2 the time integration procedure is computationally efficient the proposed time integration procedure also features a time step rejection and quarantine mechanisms a modified newton method with a predictor and dense output techniques to compute solution at off step points

time integration for ale simulations of fluid structure interaction problems stepsize and order selection based on the bdf abstract we present an adaptive algorithm for time integration of fluid structure integration problems the method relies on a fully coupled procedure to solve fsi problems in which a naturally gcl compliant ale formulation for the finite element spatial discretization is used the main originality of the proposed solution procedure is that time integration is performed using automatic order and stepsize selections hp adaptivity based on the backward differentiation formulas bdf the stepsize selection is based on a local error estimate an error controller and a step rejection mechanism it guarantees that the solution precision is within the user targeted tolerance the order selection is based on a stability test and a quarantine mechanism the selection is performed to ensure that no other methods within the family of 0 stable bdf methods would produce a solution of the targeted precision for a larger stepsize and thus a lower computational time to improve efficiency the time integration procedure also relies on a modified newton method and a predictor the time adaptive algorithm behaviors and performances are assessed on the vortex induced translational and rotational vibrations of a square cylinder and on the wake induced vibrations of 3 cylinders in an in line arrangement the algorithm yields substantial cpu time savings compared to constant stepsize and order integration while delivering solutions of prescribed accuracies

segregated runge kutta methods for the incompressible navier stokes equations in this work we propose runge kutta time integration schemes for the incompressible navier stokes equations with two salient properties first velocity and pressure computations are segregated at the time integration level without the need to perform additional fractional step techniques that spoil high orders of accuracy second the proposed methods keep the same order of accuracy for both velocities and pressures the segregated runge kutta methods are motivated as an implicit explicit runge kutta time integration of the projected navier stokes system onto the discrete divergence free space and its re statement in a velocity pressure setting using a discrete pressure poisson equation we have analysed the preservation of the discrete divergence constraint for segregated runge kutta methods and their relation in their fully explicit version with existing half explicit methods we have performed a detailed numerical experimentation for a wide set of schemes from first to third order including implicit and imex integration of viscous and convective terms for incompressible laminar and turbulent flows further segregated runge kutta schemes with adaptive time stepping are proposed

improved traditional rosenbrock wanner methods for stiff odes and daes rosenbrock wanner methods usually have order reduction if they are applied to stiff ordinary differential or differential algebraic equations therefore in several papers further order conditions are derived to reduce this effect in rang 2014 the example of prothero and robinson 1974 is analysed to find further order conditions in this paper we consider traditional row methods such as ros3p lang and verwer 2001 ros3pw rang and angermann 2005 ros3pl lang and teleaga 2008 and rodasp steinebach 1995 and improve these methods such that these further order conditions are satisfied numerical examples show the advantages of the new methods

event triggered maximum likelihood state estimation the event triggered state estimation problem for linear time invariant systems is considered in the framework of maximum likelihood ml estimation in this paper we show that the optimal estimate is parameterized by a special time varying riccati equation and the computational complexity increases exponentially with respect to the time horizon for ease in implementation a one step event based ml estimation problem is further formulated and solved and the solution behaves like a kalman filter with intermittent observations for the one step problem the calculation of upper and lower bounds of the communication rates from the process side is also briefly analyzed an application example to sensorless event based estimation of a dc motor system is presented and the benefits of the obtained one step event based estimator are demonstrated by comparative simulations

pressure corrected implicit θ schemes for the incompressible navier stokes equations abstract in this note the crank nicolson and the fractional step scheme are applied on the semi discretised incompressible navier stokes equations in a first step the formulation of the methods is modified such that the methods have optimal order for the pressure p i e the pressure p 0 is included in the scheme the main idea of this paper is that the fractional step scheme can be written as a diagonally implicit runge kutta method dirk method in this context it can easily be shown that the fractional step schemes have only stage order q 1 whereas the crank nicolson scheme has stage order q 2 hence the fractional step scheme may have order reduction if the method is applied on stiff odes and daes i e the semi discretised incompressible navier stokes equations some theoretical results and numerical examples illustrate this phenomena moreover it is shown that it is impossible to improve the fractional step method such that the scheme has the stage order q 2 and is strongly a stable or has the order p 3

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

a comparison of time discretization linearization approaches for the incompressible navier stokes equations abstract this paper presents a numerical study of two ways for discretizing and linearizing the time dependent incompressible navier stokes equations one approach consists in first applying a semi discretization in time by a fully implicit scheme then in each discrete time the equations are linearized by a fixed point iteration the number of iterations to reach a given stopping criterion is a priori unknown in this approach in the second approach rosenbrock schemes with s stages are used as temporal discretization the non linearity of the navier stokes equations is treated internally in the rosenbrock methods in each discrete time exactly s linear systems of equations have to be solved the numerical study considers five two dimensional problems with distinct features four implicit time stepping schemes and five rosenbrock methods are involved

optimal estimation in udp like networked control systems with intermittent inputs stability analysis and suboptimal filter design we investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator most existing results for this setup are concerned with the design of controller while the optimal estimation and its performance evaluation have been rarely treated in this paper we show that unlike many other cases such as intermittent observations or tcp like systems the system state follows a gaussian mixture distribution with exponentially increasing terms which leads to a gaussian sum filter based optimal estimation we develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices it is revealed that the stability is independent of the packet loss rate and is not affected by the lack of acknowledgment a suboptimal filtering algorithm with improved computational efficiency is then developed numerical examples and simulations are employed to illustrate the theoretical results

stability and convergence of the numerical solution for the species equation of a model for pemfcs abstract many mathematical models for fuel cells are presented in the literature however few studies of numerical analysis of these models are found the novelty of this work is the proof of stability and convergence of the equation of chemical species providing greater reliability to the mathematical model in this work a mathematical model is proposed that calculates the flow and concentration of species for proton exchange membrane fuel cells using the finite element method for spatial discretization and the crank nicolson method for temporal discretization the model takes into account the losses overpotentials at the anode and at the cathode the numerical results confirm the proof of convergence which is demonstrated in this work finally a numerical result is shown for the fuel cell power relative to current density and the result has good relation with the experimental data

lqg control for mimo systems over multiple erasure channels with perfect acknowledgment this technical note concerns control applications over lossy data networks sensor data is transmitted to an estimation control unit over a network and control commands are issued to subsystems over the same network sensor and control packets may be randomly lost according to a bernoulli process in this context the discrete time linear quadratic gaussian lqg optimal control problem is considered in schenato a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively here a nontrivial generalization for mimo systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet no aggregation in such a framework it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver moreover the optimal lqg control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels such a dependence is not present in the single channel case considered in mean square in the infinite horizon case stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities lmis

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

exact numerical simulation of power law noises many simulations of stochastic processes require colored noises i describe here an exact numerical method to simulate power law noises the method can be extended to more general colored noises and is exact for all time steps even when they are unevenly spaced as may often happen for astronomical data see e g n r lomb astrophys space sci 39 447 1976 the algorithm has a well behaved computational complexity it produces a nearly perfect gaussian noise and its computational efficiency depends on the required degree of noise gaussianity

on kalman filtering for detectable systems with intermittent observations we consider the problem of kalman filtering when observations are available according to a bernoulli process it is known that there exists a critical probability pc such that if measurements are available with probability greater than pc then the expected prediction covariance is bounded for all initial conditions otherwise it is unbounded for some initial conditions we show that when the system observation matrix restricted to the observable subspace is invertible the known lower bound on pc is in fact the exact critical probability this result is based on a novel decomposition of positive semidefinite matrices

a local projection stabilization continuous galerkin petrov method for incompressible flow problems abstract a local projection stabilization lps method in space is considered to approximate the evolutionary oseen equations optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous in time case for both the velocity and pressure approximation in addition the fully discrete case in combination with higher order continuous galerkin petrov cgp methods is studied error estimates of order k 1 are proved where k denotes the polynomial degree in time assuming that the convective term is time independent numerical results show that the predicted order is also achieved in the general case of time dependent convective terms

analysis of the pressure stabilized petrov galerkin method for the evolutionary stokes equations avoiding time step restrictions optimal error estimates for the pressure stabilized petrov galerkin method for the evolutionary stokes equations are proved in the case of regular solutions without restriction on the length of the time step these results clarify the instability of the discrete pressure for small time steps reported in the literature first the limit situation of the continuous in time discretization is considered and second the numerical analysis for the backward euler scheme is carried out the main results are applicable to higher order finite elements the analytical results are strongly based on an appropriate approach for computing the initial velocity which is suggested in this paper numerical studies confirm the theoretical results showing in particular that this instability does not occur for the proposed initial condition