Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.

Random vibration testing with controlled samples

This paper proposes a novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models. The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov transformation. The control force is selected so as to reduce the sampling variance of the estimator. The study observes that an acceptable choice for the control force can be made solely based on experimental techniques and the estimator for the reliability can be deduced without taking recourse to mathematical model for the structure under study. This permits the proposed procedure to be applied in the experimental study of time-variant reliability of complex structural systems that are difficult to model mathematically. Illustrative example consists of a multi-axes shake table study on bending-torsion coupled, geometrically non-linear, five-storey frame under uni/bi-axial, non-stationary, random base excitation. Copyright (c) 2014 John Wiley & Sons, Ltd.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

Girsanov Transformation-Based Reliability Modeling and Testing of Actively Controlled Structures

The problem of estimation of the time-variant reliability of actively controlled structural dynamical systems under stochastic excitations is considered. Monte Carlo simulations, reinforced with Girsanov transformation-based sampling variance reduction, are used to tackle the problem. In this approach, the external excitations are biased by an additional artificial control force. The conflicting objectives of the two control forces-one designed to reduce structural responses and the other to promote limit-state violations (but to reduce sampling variance)-are noted. The control for variance reduction is fashioned after design-point oscillations based on a first-order reliability method. It is shown that for structures that are amenable to laboratory testing, the reliability can be estimated experimentally with reduced testing times by devising a procedure based on the ideas of the Girsanov transformation. Illustrative examples include studies on a building frame with a magnetorheologic damper-based isolation system subject to nonstationary random earthquake excitations. (C) 2014 American Society of Civil Engineers.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Global Response Sensitivity Analysis of Randomly Excited Dynamic Structures

The response of structural dynamical systems excited by multiple random excitations is considered. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger's metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the l2 norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented, and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations attributable to random support motions and guide-way unevenness. (C) 2015 American Society of Civil Engineers.