Time-varying Case Research Articles

Explosive strong periodic autoregression with multiplicity one

It is well known that the asymptotic distribution of the ordinary least squares estimate (OLSE) for a strong periodic autoregression (PAR) driven by an independent innovation is Gaussian under periodic stationarity and functional of the Brownian motion under periodic integration. This paper studies the asymptotic distribution of OLSE for strong pth order PAR(p) models in the explosive case with multiplicity one, i.e. when a certain autoregressive parameter lies outside both the periodic stationarity domain and its boundary, while all remaining parameters are inside the periodic stationarity region. It will be shown that the OLSE for PAR(1), scaled by a function of the monodromy parameter, converges in distribution to a random vector whose distribution reduces under the normality assumption to the standard multivariate Cauchy distribution. Furthermore, for a PAR(p) model, the OLSE, scaled by a function of the design matrix of the Gaussian model, is asymptotically Gaussian with independent components. Thus, the knife edge effect known for linear time-invariant AR models is still valid in the strong periodically time-varying case.

Temporal variability of spectro-temporal receptive fields in the anesthetized auditory cortex.

Temporal variability of neuronal response characteristics during sensory stimulation is a ubiquitous phenomenon that may reflect processes such as stimulus-driven adaptation, top-down modulation or spontaneous fluctuations. It poses a challenge to functional characterization methods such as the receptive field, since these often assume stationarity. We propose a novel method for estimation of sensory neurons' receptive fields that extends the classic static linear receptive field model to the time-varying case. Here, the long-term estimate of the static receptive field serves as the mean of a probabilistic prior distribution from which the short-term temporally localized receptive field may deviate stochastically with time-varying standard deviation. The derived corresponding generalized linear model permits robust characterization of temporal variability in receptive field structure also for highly non-Gaussian stimulus ensembles. We computed and analyzed short-term auditory spectro-temporal receptive field (STRF) estimates with characteristic temporal resolution 5–30 s based on model simulations and responses from in total 60 single-unit recordings in anesthetized Mongolian gerbil auditory midbrain and cortex. Stimulation was performed with short (100 ms) overlapping frequency-modulated tones. Results demonstrate identification of time-varying STRFs, with obtained predictive model likelihoods exceeding those from baseline static STRF estimation. Quantitative characterization of STRF variability reveals a higher degree thereof in auditory cortex compared to midbrain. Cluster analysis indicates that significant deviations from the long-term static STRF are brief, but reliably estimated. We hypothesize that the observed variability more likely reflects spontaneous or state-dependent internal fluctuations that interact with stimulus-induced processing, rather than experimental or stimulus design.

Wave energy distribution and morphological development in and around the shadow zone of an embayed beach

BackgroundThe curved shoreline shape of embayed beaches is one of its most notable characteristics and can be described using the parabolic bay shape equation (PBSE). Wave diffraction in and around the shadow zone is often regarded as the primary forcing mechanism leading to the prominent curvature of the shoreline. However, wave climate variables (wave direction, directional spreading and wave height) are shown to be influential in redistributing wave energy throughout the bay and in the shadow zone. MethodsIn this study, a process-based morphological model (Delft3D) is used for hydrodynamic and morphodynamic simulations of a schematic embayed beach. Wave forcing conditions are systematically varied between a mixture of time-invariant and time-varying cases. ResultsThe role of diffraction is shown to be dominant only when the wave conditions are both narrow-banded (<20°) and when the PBSE angle β is high (>30°). Otherwise, as little as 6% variation in wave direction within a 90° range can account for the shoreline curvature in and around the shadow zone. ConclusionThe degree to which wave direction and directional spreading vary through time therefore has a large effect on the equilibrium orientation and shoreline planform of the bay.

Performance Assessment of a Concrete Gravity Dam at Shenwo Reservoir of China Using Deterministic and Probabilistic Methods

This paper performs degradation assessment and safety evaluation of a concrete gravity dam at Shenwo reservoir in Liaoning province of China by using two methods, i.e. deterministic method and probabilistic method, respectively. The deterministic responses of representative sluice piers are computed through static pushover and dynamic analyses. The probabilistic uncertainty analysis, including time invariant and time variant reliability analyses, is based on finite element (FE) reliability theory. For time invariant case, the material and loading parameters are considered as random variables, including elastic modulus, Poisson's ratio, mass density and pushover forces. For time variant case, the earthquake history is simulated by using random process, and the first-order reliability method (FORM) approximation combined with Koo's analytical solution is used to compute the mean upcrossing rate for given performance functions, through which the failure probabilities are calculated. Based on the analysis results using these two methods, the safety and reliability of the dam is assessed. Furthermore, the performance assessments of the dam in its current state are compared with those in the original state (i.e. when the dam was built) to quantify its performance degradation. Finally, the assessment results of using the deterministic and probabilistic methods are compared, and the discrepancies between them are quantified and explained. The computation is based on a general FE analysis platform for earthquake engineering simulation, OpenSees.

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.

Inflight Parameter Identification and Icing Location Detection of the Aircraft: The Time-Varying Case

This paper considers inflight parameter identification and icing location detection of the aircraft in a more common time-varying nature. In particular, ice accumulation is modeled as a continuous process, and the effect of the ice upon aircraft dynamics is to be accreted with time. Time-varying case of the Hinf algorithm is implemented to provide inflight estimate of aircraft dynamic parameters, and the estimated results are delivered to a probabilistic neural network to decide icing location of the aircraft; an excitation measure of the aircraft is also adopted in the network input layer. A database corresponding to different icing cases and severities was generated for the training and test of the detection network. Based on the test results, the icing detection framework presented in this paper is believed to be with promising applicableness for our further studies.

Steady-State Response of Periodically Switched Linear Circuits via Augmented Time-Invariant Nodal Analysis

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.

New Global Synchronization Analysis for Complex Networks with Coupling Delay

Global synchronization analysis for complex networks with coupling delay is investigated. Firstly the constant time delay is analyzed and then the case for time-varying delay is considered. Sufficient conditions for network synchronization are given based on Lyapunov functional, linear matrix inequality, and Kronecker product technique. The unknown variables in the sufficient conditions are fewer than those in the recent reference. Moreover, for the time-varying delay case, we find that the conditions are dependent on the bounds of both time delay and its derivative, and the derivative of the time-varying delay can be any value in the bounds. Finally, numerical examples are given to validate the effectiveness of the obtained results.

Maximum-Likelihood Parameter Estimation for Detecting Local Concentration from a Carbon Nanotube-based Sensor

This paper proposes an optimal parameter estimation method for a stochastic process involving monomolecular adsorption and desorption occurring at the nano-scale. Recently, several carbon nanotube sensors that can selectively detect target molecules at a trace concentration level have been developed. These sensors make use of light intensity changes mediated by the adsorption or desorption phenomena on their surfaces. However, the molecular-level events are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), which contains a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the inherent stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should outperform deterministic parameter estimation formulated based on the continuum model. Motivated by this expectation, we formulate the maximum likelihood estimation (MLE) based on an analytical solution of the relevant CME for both the constant and time-varying parameter cases. The performance of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process.

Model reduction of linear time-varying systems over finite horizons

We consider the problem of approximating a linear time-varying p×m discrete-time state space model S of high dimension by another linear time-varying p×m discrete-time state space model Sˆ of much smaller dimension, using an error criterion defined over a finite time interval. We derive the gradients of the norm of the approximation error and show how this can be solved via a fixed point iteration. We compare this to the classical H2 norm approximation problem for the infinite horizon time-invariant case and show that our solution extends this to the time-varying and finite horizon case.

On equivalent hydraulic conductivity for oscillation–free solutions of Richard’s equation

Abstract The estimation of numerical equivalent conductivity remains a crucial issue for the accuracy and stability of the solution of the non-linear Richards’ equation (RE) when modeling variably saturated flow. In the literature, it appears that this topic has been typically considered for one-dimensional discretization despite the growing interest in multidimensional problems. After reviewing different possibilities of equivalent hydraulic conductivity estimation, we evaluate their ability to yield monotonic results. Hence, the monotonicity analysis provided by Forsyth and Kropinski (1997) has been generalized for the different equivalent conductivity formulations. On one hand, the upstream mean is unconditionally stable but is also known to overestimate the conductivity. On the other hand, other formulations, including Darcian mean approximations, can be accurate and straightforward to adapt in multidimensional codes but do not always provide monotonic solutions of the RE. An adaptive algorithm is presented, which adapts the conductivity in function of the monotonicity condition, i.e., a variable criterion based on the conductivity at nodal points, the conductivity averaging technique and the piezometric head variation. The proposed numerical method can be implemented in existing multidimensional codes. Numerical investigations in steady state and time-varying conditions, 1D and 2D cases, and homogeneous and heterogeneous media confirm the interest in the proposed algorithm.

Permanental Partition Models and Markovian Gibbs Structures

We study both time-invariant and time-varying Gibbs distributions for configurations of particles into disjoint clusters. Specifically, we introduce and give some fundamental properties for a class of partition models, called permanental partition models, whose distributions are expressed in terms of the α-permanent of a similarity matrix parameter. We show that, in the time-invariant case, the permanental partition model is a refinement of the celebrated Pitman–Ewens distribution; whereas, in the time-varying case, the permanental model refines the Ewens cut-and-paste Markov chains (J. Appl. Probab. 43(3):778–791, 2011). By a special property of the α-permanent, the partition function can be computed exactly, allowing us to make several precise statements about this general model, including a characterization of exchangeable and consistent permanental models.

Modeling tendon-sheath mechanism with flexible configurations for robot control

SUMMARYSurgical and search/rescue robots often work in environments with very strict spatial constraints. The tendon-sheath mechanism is a promising candidate for driving such systems, allowing power sources and actuation motors placed outside to transmit force and energy to the robot at the distal end through the constrained environment. Having both compactness and high force capability makes it very attractive for manipulation devices. On the other hand, the friction attenuation of tendon tension is nonlinear and configuration-dependent due to tendon/sheath interactions throughout the transmission path. This is a major obstacle for the tendon-sheath mechanism to be widely adopted. Here, we focus on the friction analysis for flexible and time-varying tendon-sheath configurations: the most challenging but yet commonly encountered case for real-world applications. Existing results on fixed-path configurations are reviewed, revisited, and extended to flexible and time-varying cases. The effect of tendon length to friction attenuation is modeled. While focusing on tension transmission, tendon elongation is also discussed with the length effect applied. In the end, two-dimensional results are extended to three-dimensional tendon-sheath configurations. All propositions and theorems are validated on a dedicated experimental platform.

Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

In this paper, cluster consensus of multiagent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: intracluster synchronization, the state at which differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, the state at which agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus, including the spanning trees, scramblingness, infinite stochastic matrix product, and Hajnal inequality, are extended. As a result, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then the static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T-length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified non-Bayesian social learning model to illustrate the effectiveness of our results.

Spatio-temporal symmetries in control systems: an application to formation control

With the aim of addressing the stabilization problem of periodic trajectories in systems composed of identical interconnected subsystems, we introduce the class of “spatio-temporally symmetric” nonlinear systems. We address in detail the linear, time-varying case and present conditions for the synthesis of a static and a dynamic stabilizing controller. We show that linear spatio-temporally symmetric systems can be reduced to hybrid systems, described by a periodic linear system with periodic state jumps. As an application example, we present the stabilization of a formation of unicycle robots in cyclic pursuit.

Economics of Electric Vehicle Charging: A Game Theoretic Approach

In this paper, the problem of grid-to-vehicle energy exchange between a smart grid and plug-in electric vehicle groups (PEVGs) is studied using a noncooperative Stackelberg game. In this game, on the one hand, the smart grid, which acts as a leader, needs to decide on its price so as to optimize its revenue while ensuring the PEVGs' participation. On the other hand, the PEVGs, which act as followers, need to decide on their charging strategies so as to optimize a tradeoff between the benefit from battery charging and the associated cost. Using variational inequalities, it is shown that the proposed game possesses a socially optimal Stackelberg equilibrium in which the grid optimizes its price while the PEVGs choose their equilibrium strategies. A distributed algorithm that enables the PEVGs and the smart grid to reach this equilibrium is proposed and assessed by extensive simulations. Further, the model is extended to a time-varying case that can incorporate and handle slowly varying environments.

A new NARX-based Granger linear and nonlinear casual influence detection method with applications to EEG data

A new NARX-based Granger linear and nonlinear casual influence detection method is presented in this paper to address the potential for linear and nonlinear models in data with applications to human EEG data analysis. Considering two signals initially, the paper introduces four indexes to measure the linearity and nonlinearity of a single signal, and one signal influencing the second signal. This method is then extended to the time-varying and multivariate cases. An adaptation of an Orthogonal Least Squares routine is employed to select the significant terms in the models. A numerical example is provided to illustrate the effectiveness of the new algorithms together with the application to real EEG data collected from 4 patients.

Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows

AbstractKinetic theory provides a rigorous foundation for calculating the dynamics of gas flow at arbitrary degrees of rarefaction, with solutions of the Boltzmann equation requiring numerical methods in many cases of practical interest. Importantly, the near-continuum regime can be examined analytically using asymptotic techniques. These asymptotic analyses often assume steady flow, for which analytical slip models have been derived. Recently, developments in nanoscale fabrication have stimulated research into the study of oscillatory non-equilibrium flows, drawing into question the applicability of the steady flow assumption. In this article, we present a formal asymptotic analysis of the unsteady linearized Boltzmann–BGK equation, generalizing existing theory to the oscillatory (time-varying) case. We consider the near-continuum limit where the mean free path and oscillation frequency are small. The complete set of hydrodynamic equations and associated boundary conditions are derived for arbitrary Stokes number and to second order in the Knudsen number. The first-order steady boundary conditions for the velocity and temperature are found to be unaffected by oscillatory flow. In contrast, the second-order boundary conditions are modified relative to the steady case, except for the velocity component tangential to the solid wall. Application of this general asymptotic theory is explored for the oscillatory thermal creep problem, for which unsteady effects manifest themselves at leading order.

Subspace Instability Monitoring for Linear Periodically Time-Varying Systems

Most subspace-based methods enabling instability monitoring are restricted to the linear time-invariant (LTI) systems. In this paper, a new subspace method of instability monitoring is proposed for the linear periodically time-varying (LPTV) case. For some LPTV systems, the system transition matrices may depend on some parameter and are also periodic in time. A certain range of values for the parameter leads to an unstable transition matrix. Early warning should be given when the system gets close to that region, taking into account the time variation of the system. Using the theory of Floquet, some symptom parameter of stability- or residual- is defined. Then, the parameter variation is tracked by performing a set of parallel cumulative sum (CUSUM) tests. Finally, the method is tested on a simulated model of a helicopter with hinged blades, for monitoring the ground resonance phenomenon.

Time-Varying Jamming Modeling and Classification

In this correspondence, we provide a general jamming model, through which all the existing models can be summarized and extended to the time-varying case under one unified framework. We analyze the time varying jamming power spectral density, and propose a new jamming classification scheme by introducing the concepts of time-varying jamming coherence time and time-frequency jamming coherence bandwidth. Specific methods on power spectrum estimation are provided for time-varying jamming that is stationary or locally stationary.