Time-varying Threshold Research Articles

A robust algorithm for heart rate variability time series artefact correction using novel beat classification

Purpose: Heart rate variability is a commonly used measurement to evaluate functioning of autonomic nervous system, psychophysiological stress, and exercise intensity and recovery. HRV measurements contain artefacts such as extra, missed or misaligned beat detections, which can produce significant distortion on HRV parameters. In this paper, a robust automatic method for artefact detection from HRV time series is proposed.Methods: The proposed detection method is based on time-varying thresholds estimated from distribution of successive RR-interval differences combined with a novel beat classification scheme. The method is validated using simulated extra, missed and misaligned beat detections as well as real artefacts such as atrial and ventricular ectopic beats.Results: The sensitivity of the algorithm to detect simulated missed/extra beats was 100%. The sensitivity to detect real atrial and ventricular ectopic beats was 96.96%, the corresponding specificity being 99.94%. The mean error in HRV parameters after correction was <2% for missed and extra beats as well as for misaligned beats generated with large displacement factors. Misaligned beats with smallest displacement factor were the most difficult to detect and resulted in largest HRV parameter errors after correction, largest errors being <8%.Conclusions: The HRV artefact correction algorithm presented in this study provided comparable specificity and better sensitivity to detect ectopic beats as compared to state-of-the-art algorithms. The proposed algorithm detects abnormal beats with high accuracy, is relatively easy to implement, and secures reliable HRV analysis by reducing the effect of possible artefacts to tolerable level.

A Tradeoff Approach for Optimal Event-Triggered Fault Detection

In this paper, an optimal fault detection scheme is presented for a closed-loop control system, where an event-triggering mechanism is utilized for the transmission of output measurements, addressing the design of residual generation and evaluation, while considering the effects associated with unknown disturbances and faults in the system and event-triggered transmission errors on the generated residual. The triggering parameter-dependent residual generation is designed to achieve a best tradeoff between robustness against unknown disturbances and sensitivity to faults, and the residual evaluation is designed to deliver a time-varying threshold that accounts for the effects of disturbances and event-triggered transmission errors on the generated residual. The results are general and simplify to those developed for optimal fault detection in time-triggered systems. In addition, a vehicle lateral dynamic system is adopted to demonstrate the applicability of the proposed optimal fault detection scheme as well as its advantages over an existing widely used event-triggered fault detection scheme.

Testing Optimal Timing in Value-Linked Decision Making

Influential theories of the decision making process hold that a choice is made once the cumulative weight of noisily sampled information reaches a desired level. While these theories were originally motivated as optimal solutions to statistical problems, the extent to which people optimally spend time deliberating is less well explored. I conduct an experimental test of optimality in a setting where the speed of information processing reflects the difference in value between options. In this case, spending a long time without having arrived at a conclusion signals both that the problem is hard and that the options are similar in value, so the confidence level required to trigger a decision should decline over time. I find that a recently developed theory of the optimal time-varying threshold improves model fit by accurately predicting observed truncation of response time tails. Principles of optimality may thus help account for patterns of choice and response time that characterize the process of deliberation.

A Tradeoff Approach for Optimal Fault Detection of Networked Control Systems With Event-Triggered Scheme

An optimal fault detection (FD) approach for a class of networked control systems (NCSs) is concerned in this work. To improve the accuracy of the FD, a new event-triggered scheme (ETS) is addressed, where the output measurement transmitted or not is determined by a set of conditions instead of a single condition. Moreover, output measurements in these conditions are not only the last transmitted data, but also the data in the past period of time. The structure of fault detection and isolation (FDI) consisting of the residual generation and residual evaluation can detect faults as accurately as possible, and show robustness to disturbances in the meantime. Optimal observer gains can be obtained by utilizing the discrete-time Riccati equation (DTRE), and the time-varying threshold can be specified by employing the linear matrix inequality (LMI). Finally, a numerical simulation and the application on closed-loop continuous stirred-tank reactor (CSTR) are adopted to prove the superiority of the proposed approach.

Moving Average Threshold Heterogeneous Autoregressive (MAT-HAR) Models

We propose moving average threshold heterogeneous autoregressive (MAT-HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT-HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time-varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT-HAR has sharp in-sample and out-of-sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT-HAR has a higher forecast accuracy than the HAR.

Dynamic and Non-Centric Networking Approach Using Virtual Gateway Platforms for Low Power Wide Area Systems

To actively develop and promote Internet of Things related techniques, we propose a dynamic and non-centric networking approach using virtual gateway platforms, and evaluate it based on low-power wide-area networks that adopt the traditional star and mesh topologies. In our approach, for each local device, we first present a device management method in which two working modes are set to indicate whether the device works as a virtual gateway (VGW) or provides relay services. Then an internal parameter is defined to manage the mode by considering the device’s current states, such as battery power remaining, presence or absence of an external power supply, etc. We thereafter propose a mode switching method where two time-varying threshold values are configured and help a local device to switch between the two modes through the use of an internal parameter. Finally, a path determination algorithm is applied to find routes for data transmission with or without devices playing the role of VGWs. Computer simulation results indicate that the proposed networking approach can take advantage of both traditional star and mesh systems, enables dynamic and non-centric changes in network configurations, and finally ensures that in most cases, the transmission performance is equivalent to or better than that of other network setups.

H-/L∞ fault detection observer design for uncertain linear systems

ABSTRACTThis paper studies fault detection problem in the finite-frequency domain for linear systems with parameter uncertainties. We design an fault detection observer to generate residual that is robust against disturbance and sensitive to a fault. In the design, we use the finite-frequency performance index to measure fault sensitivity and introduce performance index to measure the effect of disturbance on residual. The obtained fault detection observer exhibits a peak-to-peak disturbance attenuation performance, which provides a time-varying threshold for residual evaluation. Therefore the proposed design method integrates residual generation and threshold calculation together. To facilitate the observer design process, sufficient conditions of the proposed fault detection observer are formulated as a set of linear matrix inequalities. Numerical simulations are given to verify the effectiveness of the proposed approach.

One‐bit compressive sensing with time‐varying thresholds in synthetic aperture radar imaging

In this study, the authors introduce a new framework for 1-bit compressed synthetic aperture radar (SAR) imaging by using time-varying thresholding. They show how to recover sparse SAR images from noisy measurements which have been quantised to 1-bit with time-varying thresholds. In the conventional 1-bit compressive sensing (CS) SAR imaging methods, 1-bit quantisation is implemented by comparing the received signal to a zero threshold. This makes the information about the magnitude of the signal to be lost and exact signal recovery becomes impossible. One-bit quantisation with time-varying thresholds allows them to reconstruct the magnitude of the signal more accurately and an explicit unit-norm constraint is no longer required in the proposed optimisation formulation. Using the proposed approach, the authors formulate 1-bit CS SAR imaging reconstruction problem as an unconstrained optimisation problem where the objective function includes an l 2 data-fidelity term and a non-smooth regularisation function. In order to solve this unconstrained optimisation problem, they use variable splitting and the alternating direction method of multipliers based approach which is computationally efficient and easy to implement. The results from experiments with synthetic and real SAR images validate the effectiveness of the proposed method named as BCST-SAR (binary CS with time-varying thresholds in SAR imaging).

Modelling extreme peak electricity demand during a heatwave period: a case study

A frequency analysis of the occurrence of extreme peak electricity demand during the non-winter period using South African data for the period 2007–2013 is discussed in this paper. It is during the non-winter period when Eskom, South Africa’s power utility company usually carries out its maintenance of power plants. Extreme peak loads together with high unplanned and planned outages usually cause disruptions to the power plants’ maintenance programmes during this period. A detailed analysis of peak electricity demand is useful to maintain the stability of the power grid. If not properly managed this may result in negative economic impacts as electricity is one of the major drivers of any economy. Initially the data is detrended using a time-varying threshold. A sufficiently high threshold is obtained by using bounded corrected extremal mixture models. We then decluster the exceedances and fit a peaks-over-threshold model to cluster maxima. Empirical results show that demand of electricity significantly increases as a result of heat which builds up with consecutive days of extreme high temperatures. The main contribution of this paper is in the application of extreme value theory models in assessing the frequency of occurrence of extreme peak loads to assist power utilities in the planning of maintenance of generating units. The other contribution is in the development of a modelling framework which shows that as temperature converges to its upper bound, the marginal increase of electricity demand also converges. Most of the cluster maxima are experienced during the months October, November and February, suggesting that these may not be good months for scheduling maintenance of generating plants during the non-winter period in South Africa. This modelling approach may help system operators in scheduling and dispatching of electricity during the heatwave period.

Fault detection for linear discrete‐time descriptor systems

Sensor fault detection of discrete-time descriptor systems with bounded disturbances is studied. The authors propose a new structure of a fault detection observer by augmenting the output, which can broaden the application scope. A H − / L ∞ criterion is used to achieve the fault sensitivity and disturbance attenuation ability of the residual simultaneously. The residual generation and time-varying threshold calculation are integrated together based on L ∞ analysis. Furthermore, sufficient conditions for the H − / L ∞ performance of the proposed observer are formulated in terms of linear matrix inequalities. Numerical simulations of a direct current motor and a flight vehicle are conducted to verify the applicability of the proposed fault detection observer design method.

Threshold models with time-varying threshold values and their application in estimating regime-sensitive Taylor rules

Abstract The literature of time series models with threshold effects makes the assumption of a constant threshold value over different periods. However, this time-homogeneity assumption tends to be too restrictive owing to the fact that the threshold value that triggers regime switching could possibly be time-varying. This study herein proposes a threshold model in which the threshold value is assumed to be a latent variable following an autoregressive (AR) process. The newly proposed model was estimated using a Markov Chain Monte Carlo (MCMC) algorithm under a Bayesian framework. The Monte Carlo simulations are presented to assess the effectiveness of the Bayesian approaches. An illustration of the model was made through an application to a regime-sensitive Taylor rule employing U.S. data.

Use of cardiorespiratory coherence to separate spectral bands of the heart rate variability

Abstract Regulation of heart rate variability (HRV) is dependent on the autonomic nervous system (ANS). The regulation is achieved by the two ANS activity branches distribution, namely the parasympathetic and the sympathetic activities. Their fluctuations can be observed in the HRV signal spectral domain through respective dissociated frequency domains. Power spectrum parameters in low frequency (LF) and high frequency (HF) domains are classically estimated using predetermined fixed frequency ranges which are [0.04–0.15 Hz] band for LF domain and [0.15–0.4 Hz] band for HF domain. However, the 0.15 Hz frequency threshold is controversial in dynamic situations or positions changing. Several studies advanced that the observed cardiac and respiratory oscillation interactions could reflect the functionality of the ANS. These interactions can be estimated by the cardiorespiratory spectral coherence tool which quantifies the existence and strength of linearity between the two modes. We propose in this paper to jointly use the heart rate variability (HRV) and respiration modes by exploiting the cardiorespiratory spectral coherence tool for the time-varying frequency threshold definition between LF and HF bands. The instantaneous center frequency computed on the time-frequency coherence estimator is the proposed variable threshold (VT). The VT method was implemented on both simulated data and real data acquired from the experimental orthostatic test protocol with 10 healthy subjects. The classical 0.15 Hz fixed threshold (FT) and the individual time-dependent spectral boundaries method (AT) using the lower limit of the respiratory HF band as a time-varying threshold are used for comparison. The proposed VT strategy makes it possible to obtain: (i) a strengthened data-dependent definition of boundaries for the HF domain; (ii) instantaneous estimations of the LF and HF band energies; (iii) a better discrimination between the two positions SUPINE and UPRIGHT of the classical orthostatic test.

Debt and growth: Is there a constant tipping point?

This paper highlights the crucial role of a time-varying threshold effect of public debt on economic growth. Our contribution is twofold. First, we extend the constant-threshold regression kink model of Hansen (2017) by allowing for a time-varying, state-dependent threshold. Second, we apply our model to investigate the effect of debt on growth, using data from the U.S. over the period of 1791–2009. Our empirical results clearly support a nonlinear debt-threshold effect and the threshold is time-varying and state-dependent.

Dynamic and Tunable Threshold Voltage in Organic Electrochemical Transistors

In recent years, organic electrochemical transistors (OECTs) have found applications in chemical and biological sensing and interfacing, neuromorphic computing, digital logic, and printed electronics. However, the incorporation of OECTs in practical electronic circuits is limited by the relative lack of control over their threshold voltage, which is important for controlling the power consumption and noise margin in complementary and unipolar circuits. Here, the threshold voltage of OECTs is precisely tuned over a range of more than 1 V by chemically controlling the electrochemical potential at the gate electrode. This threshold voltage tunability is exploited to prepare inverters and amplifiers with improved noise margin and gain, respectively. By coupling the gate electrode with an electrochemical oscillator, single-transistor oscillators based on OECTs with dynamic time-varying threshold voltages are prepared. This work highlights the importance of electrochemistry at the gate electrode in determining the electrical properties of OECTs, and opens a path toward the system-level design of low-power OECT-based electronics.

Deceptive SAR Jamming Based on 1-bit Sampling and Time-Varying Thresholds

This paper addresses the issue of deceptive jamming against synthetic aperture radar (SAR) by using 1-bit sampling and time-varying threshold (TVT). With 1-bit intercepted SAR signal, the multipliers involved in a convolution is replaced by xnor gates, which considerably simplify the jamming signal generation. Moreover, the TVT is used for 1-bit quantization before retransmission to retain the relative amplitude information of the jamming signal. As a result, the proposed deceptive jamming schemes are superior to their conventional counterpart in terms of realization. Effects of harmonics and oversampling are analyzed to evaluate the performance degradations caused by the 1-bit sampling and TVT. Simulation results are provided to confirm the validity of the proposed schemes.

A structure for representation of localized time-frequency distributions in presence of noise

This paper considers multi-component non-stationary signals contaminated with additive white Gaussian noise and suggests a structure to remove high noise from quadratic time-frequency distribution (QTFD) of these signals while localizing auto-terms. Proposed structure includes three steps. It first reduces some of the noise power by filtering the distribution in ambiguity domain and thus enhances signal-to-noise ratio. In the second step, the regions corresponding to the auto-terms are determined and by presenting a time-varying threshold, the noise out of auto-terms is eliminated in each time interval. Finally, using reassignment principle, the auto-terms are concentrated to local centroids of their energy. The typical reassignment method localizes both auto-terms and noise components while the proposed procedure relocates only the auto-terms to their original positions. Simulation results illustrate the performance of the proposed structure as compared to more standard state-of-the-art QTFDs.

A Threshold-Parameter-Dependent Approach to Designing Distributed Event-Triggered H∞ Consensus Filters Over Sensor Networks.

This paper is concerned with distributed event-triggered H∞ consensus filtering for a discrete-time linear system over a sensor network. Different from some existing event-triggered communication schemes (ETCSs), a new distributed ETCS is first developed to reduce the communication frequency of neighboring sensors, where the threshold parameter in an event triggering condition is time-varying with attainable upper and lower bounds. Then a threshold-parameter-dependent approach is proposed to derive criteria for designing the desired H∞ consensus filters and the ETCS such that the resultant filtering error system is asymptotically stable with the prescribed H∞ performance while maintaining satisfactory resource efficiency. Furthermore, a polytope-like transformation with regard to time-varying threshold parameters is performed and a recursive algorithm is presented to determine the threshold-parameter-dependent filter matrix sequences and event triggering weighting matrix sequence. Two illustrative examples are employed to show the effectiveness of the developed approach.

Fault Diagnosis of Uncertain Hybrid Systems

This paper presents an online monitoring and fault diagnosis architecture for hybrid systems with nonlinear uncertain discrete-time dynamics. The architecture features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme can detect both discrete and parametric faults using a mode dependent time-varying threshold that guarantees no false-positives alarms due to modeling uncertainty. The fault isolation scheme can anticipate which fault events may have occurred and dynamically employs only the necessary number of isolation estimators that try to isolate the fault by calculating residual thresholds and approximating the unknown parameter values. Simulation results of a two-tank hybrid system example illustrate the effectiveness of the proposed approach.

Integration of Time-Varying threshold-based Fault Detection and Tolerant Control

An integrated fault detection and fault-tolerant control scheme are proposed for uncertain strict-feedback systems with unmeasurable states in this paper. A fault detector, which comprises a residual generator with a prescribed performance and a tight time-varying threshold calculated from the prescribed performance bound, is first designed. After the faults are detected, a fault-tolerant controller is then proposed where the residual generator is regarded as the reference model of the virtual actuator. It is shown that all system states and estimation errors are uniformly bounded before the detection of faults and converge to zero when the proposed fault-tolerant controller is deployed. A simulation example is provided to manifest the effectiveness of the proposed scheme.

Bayesian Modelling of Kenya Extreme Debt with Correction for Budgetary Leakage

Total public debt levels in Kenya are exponentially increasing due to rising budget deficit, poor public fund management as well as movement of various macro-economic indicators such as balance of payments, inflation, Gross Domestic Product, exchange rates, and grants leading to worries on whether or not the high debt levels would be sustainable in future. The major concern is that a huge portion of the country’s revenue is committed to debt repayment and budgetary leakage strains the repayment efforts, thereby accelerating the country's debt unsustainability. This study sought to model extreme debt in Kenya with correction for budgetary leakage using a Bayesian approach to Extreme Value Theory (EVT) the main aim being to estimate the maximum debt tolerable for the country. A non-stationary Generalized Pareto Distribution (GPD) model is used for modeling the public debt extremes which depend on some covariates (macro-economic indicators) and Bayesian methods used to directly estimate the threshold and the GPD parameters. A major contribution of this study is the introduction of a compensator to allow for possible leakage due budgetary leakage through corruption, tax evasion, money laundering, and other forms of financial fraud, modelling it as a function of budget deficit. The established debt threshold is approximately KShs. 2 trillion which is the standard amount that should be borrowed, beyond which values are considered extremes. The results indicate that the movements in the macro-economic debt indicators significantly affect total public debt levels, and that budgetary leakage reduces Kenya's debt tolerance. The research concluded that the current debt level of around KShs. 5 trillion is still sustainable but high budgetary leakage may accelerate the country's long-run debt unsustainability. For further work, it is recommended to use a time-varying threshold to capture seasonality of the public debt series.