Time-varying signal processing using multi-wavelet basis functions and a modified block least mean square algorithm

This paper introduces a novel parametric modeling and identification method for linear time-varying systems using a modified block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be used to track rapidly or even sharply varying processes and is more suitable for recursive estimation of process parameters by combining wavelet approximation theory with a modified block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstatinoary processes

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

An adaptive tracking observer for failure-detection systems

The design problem of adaptive observers applied to linear, constant and variable parameters, multi-input, multi-output systems, is considered. It is shown that, in order to keep the observer's (or Kalman filter) false-alarm rate (FAR) under a certain specified value, it is necessary to have an acceptable proper matching between the observer (or KF) model and the system parameters. An adaptive observer algorithm is introduced in order to maintain desired system-observer model matching, despite initial mismatching and/or system parameter variations. Only a properly designed adaptive observer is able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability and FAR. Conditions for convergence for the adaptive process were obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors and accurate and fast parameter identification, in both deterministic and stochastic cases

Quantifying sudden changes in dynamical systems using symbolic networks

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every node weights represents the probability of an ordinal patterns (OPs) to appear in the symbolic sequence and each edges weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.Comment: 18 pages, 9 figures, to appear in New Journal of Physic

Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

Identification of unusual events in multi-channel bridge monitoring data

Peer reviewedPostprin

Tipping points near a delayed saddle node bifurcation with periodic forcing

We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping refers to the dramatic change in dynamical behavior characterized by a rapid transition away from a previously attracting state. In the absence of the periodic forcing, it is well-known that a slowly varying bifurcation parameter produces a delay in this transition, beyond the bifurcation point for the static case. Using a multiple scales analysis, we consider the effect of amplitude and frequency of the periodic forcing relative to the drifting rate of the slowly varying bifurcation parameter. We show that a high frequency oscillation drives an earlier tipping when the bifurcation parameter varies more slowly, with the advance of the tipping point proportional to the square of the ratio of amplitude to frequency. In the low frequency case the position of the tipping point is affected by the frequency, amplitude and phase of the oscillation. The results are based on an analysis of the local concavity of the trajectory, used for low frequencies both of the same order as the drifting rate of the bifurcation parameter and for low frequencies larger than the drifting rate. The tipping point location is advanced with increased amplitude of the periodic forcing, with critical amplitudes where there are jumps in the location, yielding significant advances in the tipping point. We demonstrate the analysis for two applications with saddle node-type bifurcations