Error Time Series Research Articles

Prediction of reliability and public safety from covered rates using time series modeling for distribution systems

The overhead distribution system has been constructed using mainly bare wires, but the bare wire is not insulated. Covered conductors used in overhead lines have achieved positive results during the recent year. For overhead distribution systems, the reliability of covered overhead lines could potentially be improved using various alternative technologies. The reliability index is a time series to be observed and collected per year in distribution systems. In addition, another time series is still to be concerned about the public safety on the occurred number of public received electric shocks per year in Taiwan Power Company (TPC). This paper tries to study both worthy of discussion on the effect of the reliability and the public life safety for distribution systems using covered conductors. The covered rate (CR) is the ratio of the line length using covered conductors to the total line length in a distribution system. The another purpose is to focus on how to predict the reliability and the public safety from covered rates using time series modeling in model-building process. This paper focuses on how to forecast the reliability indices and public safety on covered rates using two regression models which are logistic regression and dynamic regression models. The dynamic regression model is to combine the logistic regression model with time series errors in autoregressive-moving average analysis process. Results of the fitted regression models, the logistic regression and dynamic regression models, with the square of the correlation are presented from TPC. Copyright © 2010 John Wiley & Sons, Ltd.

Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control

The subject of this article is the modelling of the influence of non-minimum phase discrete-time system dynamics on the performance of norm optimal iterative learning control (NOILC) algorithms with the intent of explaining the observed phenomenon and predicting its primary characteristics. It is established that performance in the presence of one or more non-minimum phase plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L 2 error norm (mean square error) followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over a finite number of trials is apparent convergence to a non-zero error. The source of this slow convergence is identified using the singular value distribution of the system's all pass component. A predictive model of the onset of slow convergence behaviour is developed as a set of linear constraints and shown to be valid when the iteration time interval is sufficiently long. The results provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm and associated error time series are obtained for single-input single-output systems with several non-minimum phase zeros outside the unit circle using Lagrangian techniques. Numerical simulations are given to confirm the validity of the analysis.

Processing arctic eddy‐flux data using a simple carbon‐exchange model embedded in the ensemble Kalman filter

Continuous time-series estimates of net ecosystem carbon exchange (NEE) are routinely made using eddy covariance techniques. Identifying and compensating for errors in the NEE time series can be automated using a signal processing filter like the ensemble Kalman filter (EnKF). The EnKF compares each measurement in the time series to a model prediction and updates the NEE estimate by weighting the measurement and model prediction relative to a specified measurement error estimate and an estimate of the model-prediction error that is continuously updated based on model predictions of earlier measurements in the time series. Because of the covariance among model variables, the EnKF can also update estimates of variables for which there is no direct measurement. The resulting estimates evolve through time, enabling the EnKF to be used to estimate dynamic variables like changes in leaf phenology. The evolving estimates can also serve as a means to test the embedded model and reconcile persistent deviations between observations and model predictions. We embedded a simple arctic NEE model into the EnKF and filtered data from an eddy covariance tower located in tussock tundra on the northern foothills of the Brooks Range in northern Alaska, USA. The model predicts NEE based only on leaf area, irradiance, and temperature and has been well corroborated for all the major vegetation types in the Low Arctic using chamber-based data. This is the first application of the model to eddy covariance data. We modified the EnKF by adding an adaptive noise estimator that provides a feedback between persistent model data deviations and the noise added to the ensemble of Monte Carlo simulations in the EnKF. We also ran the EnKF with both a specified leaf-area trajectory and with the EnKF sequentially recalibrating leaf-area estimates to compensate for persistent model-data deviations. When used together, adaptive noise estimation and sequential recalibration substantially improved filter performance, but it did not improve performance when used individually. The EnKF estimates of leaf area followed the expected springtime canopy phenology. However, there were also diel fluctuations in the leaf-area estimates; these are a clear indication of a model deficiency possibly related to vapor pressure effects on canopy conductance.

Climate‐Driven Annual Vertical Deformation of the Solid Earth Calculated From GRACE

AbstractThe seasonal variation of atmosphere, ocean, and continent water masses causes variation in surface deformation, which is detectable using Gravity Recovery and Climate Experiment (GRACE) and GPS observations. In comparison with the surface deformation simulated with atmosphere, ocean, and land water models, the deformation derived from GRACE has no errors related to the accuracy uncertainties of the models. In this paper the climate‐driven seasonal vertical deformation of the solid Earth in China and neighboring areas is calculated from GRACE monthly time‐variable gravity field coefficients truncated to degree and order 60, and the results are compared with seasonal signals measured at 42 GPS sites in the same region. In the calculation we use de‐stripe filtering and de‐stripe plus 3×105 m Gaussian smoothing respectively, and we find that the former filtering result is better than the latter one. Computing the annual vertical crustal deformation from GRACE using de‐stripes, we find that at all GPS sites the amplitudes and phases of deformation from GRACE are close to those from GPS observations. Obvious discrepancy at some sites suggests that it might be caused by a local geophysical process or GPS site analysis error and GPS time series discontinuity. In the mainland of China and adjacent areas the smallest amplitude of deformation is about 1 × 10−3 m in the southeast of station TASH and the greatest is 10 × 10−3 m in the region of Ganges‐Lancang River Basin. These results demonstrate that GRACE can be a new effective tool for monitoring large‐scale annual vertical deformation of the solid Earth in China and adjacent areas.

OVERVIEW OF THE KEPLER SCIENCE PROCESSING PIPELINE

The Kepler Mission Science Operations Center (SOC) performs several critical functions including managing the ~156,000 target stars, associated target tables, science data compression tables and parameters, as well as processing the raw photometric data downlinked from the spacecraft each month. The raw data are first calibrated at the pixel level to correct for bias, smear induced by a shutterless readout, and other detector and electronic effects. A background sky flux is estimated from ~4500 pixels on each of the 84 CCD readout channels, and simple aperture photometry is performed on an optimal aperture for each star. Ancillary engineering data and diagnostic information extracted from the science data are used to remove systematic errors in the flux time series that are correlated with these data prior to searching for signatures of transiting planets with a wavelet-based, adaptive matched filter. Stars with signatures exceeding 7.1 sigma are subjected to a suite of statistical tests including an examination of each star's centroid motion to reject false positives caused by background eclipsing binaries. Physical parameters for each planetary candidate are fitted to the transit signature, and signatures of additional transiting planets are sought in the residual light curve. The pipeline is operational, finding planetary signatures and providing robust eliminations of false positives.

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.

Identifying error and maintenance intervention of pavement roughness time series with minimum message length inference

Pavement roughness is a useful measure of pavement condition. One method of comparing alternative sections of pavements is the roughness progression rate (RPR). The objective of this paper is to describe difficulties in identifying RPR from real data and provide a new type of criteria to overcome these difficulties. Selecting appropriate regression functions for time-series roughness presents two major problems. Roughness time series can include roughness data that appear erroneous, acting independent of the observed time-series trend. Including likely error values will bias the calculated RPR. The problem of identifying likely error is made more difficult with the possibility of maintenance intervention, which may reduce the roughness level and/or progression rate. A minimum message length (MML) criterion to select RPR is introduced and is referred to herein as MML RPR. We perform simulated comparisons of common segmentation criterion and conclude that MML RPR is the preferred criterion.

Modeling the Error of Continuous Glucose Monitoring Sensor Data: Critical Aspects Discussed through Simulation Studies

Knowing the statistical properties of continuous glucose monitoring (CGM) sensor errors can be important in several practical applications, e.g., in both open- and closed-loop control algorithms. Unfortunately, modeling the accuracy of CGM sensors is very difficult for both experimental and methodological reasons. It has been suggested that the time series of CGM sensor errors can be described as realization of the output of an autoregressive (AR) model of first order driven by a white noise process. The AR model was identified exploiting several reference blood glucose (BG) samples (collected frequently in parallel to the CGM signal), a procedure to recalibrate CGM data, and a linear time-invariant model of blood-to-interstitium glucose (BG-to-IG) kinetics. By resorting to simulation, this work shows that some assumptions made in the Breton and Kovatchev modeling approach may significantly affect the estimated sensor error and its statistical properties. Three simulation studies were performed. The first simulation was devoted to assessing the influence of CGM data recalibration, whereas the second and third simulations examined the role of the BG-to-IG kinetic model. Analysis was performed by comparing the "original" (synthetically generated) time series of sensor errors vs its "reconstructed" version in both time and frequency domains. Even small errors either in CGM data recalibration or in the description of BG-to-IG dynamics can severely affect the possibility of correctly reconstructing the statistical properties of sensor error. In particular, even if CGM sensor error is a white noise process, a spurious correlation among its samples originates from suboptimal recalibration or from imperfect knowledge of the BG-to-IG kinetics. Modeling the statistical properties of CGM sensor errors from data collected in vivo is difficult because it requires perfect calibration and perfect knowledge of BG-to-IG dynamics. Results suggest that correct characterization of CGM sensor error is still an open issue and requires further development upon the pioneering contribution of Breton and Kovatchev.

Adaptation and criticality in human control behaviour.

Human behavior shows power-law distributed fluctuations. • Control using optimal short-time estimation of parameters • can induce critical points as attractors. A model with realistic constraints on reaction time and con• trol strength can reproduce many features of human control behavior. Minimal mean squared control errors coincide error distribu• tions in between the Levyand the Gaussian regime. Fig. 3: A: Control errors in simulated (thick black lines tr =170 ms, γ =1.07; tm =140 ms, t = 250 ms, σ=5 s-0.5) and experimental time series (thin grey lines, see below). B: Complementary cumulative distribution function. Corresponding probability density function (pdf) tail-exponents d were fitted using the Hillestimator. C: Powerspectrum (using Welch’s method and log-binning). D: Standard deviation of the cumulated magnitudes (red) and mean displacement (blue) for different time intervals with Hurst exponents 145

Change detection in linear regression with time series errors

AbstractA new test for detecting a change in linear regression parameters assuming a general weakly dependent error structure is given. It extends earlier methods based on cumulative sums assuming independent errors. The novelty is in the new standardization method and in smoothing when the time series is dominated by high frequencies. Simulations show the excellent performance of the test. Examples are taken from environmental applications. The algorithm is easy to implement. Testing for multiple changes can be done by segmentation. The Canadian Journal of Statistics 38:65–79; 2010 © 2009 Statistical Society of Canada

The Secret Life of Motion Covariates

Abstract Motion covariates are often added to subject-level design matrices to reduce the effects of subject motion. This has been dem-onstrated to increase t-statistics despite the lack of a clear model between these covariates and EPI signal magnitude. Three studies were analyzed with a variety of choices for motion covariates. Results demonstrate that in addition to removing varianc e due to motion, the extra “secret” dimensions in the motion covariates remove signal and noise components unrelated to motion. Although not shown to be harmful at the group level, their lack of specificity and efficacy calls their use into question. Introduction Rigid body motion introduces error in EPI time-series both through misalignment of anatomical structures and through dis-ruption of the spin-history steady-state. Six degree-of-freedom realignment algorithms such as those in AFNI, SPM, and FSL accurately compensate for anatomical misalignment across frames but spin-history effects are more problematic. Motion es-sentially redefines slice boundaries such that the new boundaries contain spins formerly in neigboring slices at different stag es of T1 relaxation. The relatively large differences in the magnitude between adjacent slices leads to relatively large signal changes even for small motions. Steady-state is restored after several seconds (depending on the flip angle), so each discrete motion causes an excursion in signal magnitude lasting beyond the frame in which it occursJ. Three approaches have been used to compensate for spin-history effects: 1. Omitting subjects with excessive motion from the analysis, 2. Omitting frames following a large motion from the analysis, and 3) Incorporating a regressor into the general linear model to model signal excursions introduced by motion (Jiang 1995,Friston 1996, Johnstone 2006). The first two are straightforward and effective if motion is infrequent. The third approach of adding regressors to the design matrixe is widely used. The most frequent choices are the rotation and translation parameters of the rigid body transformation. This has sever al shortcomings. First, the regressors do not model the relaxation effects, so they cannot match the temporal dynamics of the signal. Second, the signs of the angles and translations differ randomly from the sign of moton-induced signal changes. Third , they comprise a 6-dimensional subspace when only one is required. And finally, the motion covariates best represent in-plane motion that has little effect on the signal while poorly representing through-slice motion (due to thick slices). The initial goal of this research was to develop improved regressors at both the volume and slice levels. The underlying i dea is that the large signal excursion caused by motion can also be thought of as an excellent signal for estimating its magnitude of its effect, and that this signal can be formed into a more effective regressor if it is decoupled from task-related and phys iologi-cal noise effects. The result of testing these regressors has been to show that motion regressors are ineffective in general.

Estimating Population Size and Hidden Demographic Parameters with State‐Space Modeling

Recent research has shown how process variability and measurement error in ecological time series can be separated using state-space modeling techniques to combine individual-based data with population counts. We extend the current maximum likelihood approaches to allow the incorporation of sex- and age-dependent counts and provide an application to data from a population of Soay sheep living on the St. Kilda archipelago. We then empirically evaluate the performance and potential of the method by sequentially omitting portions of the data available. We show that the use of multivariate time series extends the power of the state-space modeling approach. The variance of measurement error was found to be smaller for males and the sex ratio of lambs to be skewed toward females and constant over time. Our results indicated that demographic parameters estimated using state-space modeling without relevant individual-based data were in close agreement with those obtained from mark-recapture-recovery analyses alone. Similarly, estimates of population size obtained when the corresponding count observations were unavailable were close to those from the entire data set. We conclude that the approach illustrated here has great potential for estimating hidden demographic parameters, planning studies on population monitoring, and estimating both historical and future population size.

Simulation of the daily average PM 10 concentrations at Ta-Liao with Box–Jenkins time series models and multivariate analysis

Southern Taiwan has experienced severe PM 10 problems for over a decade. The present paper describes the establishment of a simulation model for the daily average PM 10 concentrations at Ta-Liao, southern Taiwan. The study used a regression with time series error models (RTSE models) (multivariate ARIMA time series model), including an explanatory variable resulting from principal component analyses to complete the PM 10 simulation. Factor 1 estimated from the factor analyses explained the variance of 44–49%, which indicated the important contribution from the neighbor-city PM 10 at Mei-Nung, Lin-Yuang, Zuoying, Chao-Chou, local ozone and NOx. Factor 1 can be interpreted with regional PM 10 plus photochemical reactions. To improve the predictability of extremely high PM 10, different results from the principal component analysis were introduced to the RTSE models. We constructed four kinds of RTSE models: RTSE model without PC, with PC4S (PM 10 at Mei-Nung, Lin-Yuang, Zuoying, and Chao-Chou), with PCTL (meteorological variables and co-pollutants at Ta-Liao), and with PCTL4S (the combination of the above two) and evaluated the statistics model performance. Ozone, dew point temperature, NOx, wind speed, wind directions, and the PC trigger were the significant variables in the RTSE models most of time. When the neighbor-city PM 10 was included in the PC trigger, the predictability was apparently improved. The closeness of fit with the inclusion of PC4S and PCTL4S was improved by reducing SEE from 0.117 to 0.092. Using the RTSE models with PC4S or PCTL4S, POD was improved by an increase of 33%, FAR was reduced 30%, and CSI was increased 39%, when simulating the daily average PM 10 > 150 μg m −3. Evidently we need to survey source impacts prior to establishing a simulation model. Factor analysis is a useful method to investigate sources that contributed PM 10 to a target site prior to establishing a simulation model.

Control Loop Performance Monitoring using the Permutation Entropy of Error Residuals

The predictability of a control-loop behavior beyond its control horizon is an unambiguous indication of loop malfunctioning. Based on the dynamic complexity of the error residual time series the permutation entropy is proposed to define a sensitive index for performance monitoring using data from close-loop operation. A generic framework to understand and quantify the distinctive increase in predictability of the controller error resulting from ill-tuning, sensor errors and actuator faults using a entropy-like index is presented. The dynamic complexity of a well-performing control loop should correspond to the maximum entropy. As loop performance degrades the entropy of its residual time series decreases and any loss of dynamic complexity in the control system gives rise to an increase of the predictability of the control error time series. Results obtained using the proposed performance index along with its confidence interval for industrial data sets are presented to discuss the influence of the sample size, control horizon, and variance estimation in the assessment of close-loop performance.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely. Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. If populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta.

Errors in the Estimation of Approximate Entropy and Other Recurrence-Plot-Derived Indices Due to the Finite Resolution of RR Time Series

An analysis of the errors due to the finite resolution of RR time series in the estimation of the approximate entropy (ApEn) is described. The quantification errors in the discrete RR time series produce considerable errors in the ApEn estimation (bias and variance) when the signal variability or the sampling frequency is low. Similar errors can be found in indices related to the quantification of recurrence plots. An easy way to calculate a figure of merit [the signal to resolution of the neighborhood ratio (SRN)] is proposed in order to predict when the bias in the indices could be high. When SRN is close to an integer value n, the bias is higher than when near n - 1/2 or n + 1/2. Moreover, if SRN is close to an integer value, the lower this value, the greater the bias is.

Short-term prediction of rain attenuation level and volatility in Earth-to-Satellite links at EHF band

Abstract. This paper shows how nonlinear models originally developed in the finance field can be used to predict rain attenuation level and volatility in Earth-to-Satellite links operating at the Extremely High Frequencies band (EHF, 20–50 GHz). A common approach to solving this problem is to consider that the prediction error corresponds only to scintillations, whose variance is assumed to be constant. Nevertheless, this assumption does not seem to be realistic because of the heteroscedasticity of error time series: the variance of the prediction error is found to be time-varying and has to be modeled. Since rain attenuation time series behave similarly to certain stocks or foreign exchange rates, a switching ARIMA/GARCH model was implemented. The originality of this model is that not only the attenuation level, but also the error conditional distribution are predicted. It allows an accurate upper-bound of the future attenuation to be estimated in real time that minimizes the cost of Fade Mitigation Techniques (FMT) and therefore enables the communication system to reach a high percentage of availability. The performance of the switching ARIMA/GARCH model was estimated using a measurement database of the Olympus satellite 20/30 GHz beacons and this model is shown to outperform significantly other existing models. The model also includes frequency scaling from the downlink frequency to the uplink frequency. The attenuation effects (gases, clouds and rain) are first separated with a neural network and then scaled using specific scaling factors. As to the resulting uplink prediction error, the error contribution of the frequency scaling step is shown to be larger than that of the downlink prediction, indicating that further study should focus on improving the accuracy of the scaling factor.

How the study of food intake as a dynamical system may provide an explanation for variable feeding responses to stress: Changes in forecasting error of feeding time series with increased plasma cortisol levels

How the study of food intake as a dynamical system may provide an explanation for variable feeding responses to stress: Changes in forecasting error of feeding time series with increased plasma cortisol levels

Robust monotone gradient‐based discrete‐time iterative learning control

AbstractThis paper considers the use of matrix models and the robustness of a gradient‐based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data‐dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean‐square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well‐known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non‐causal controller dynamics. The results are compared with recently published results for robust inverse‐model‐based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high‐frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

Abstract. The deterministic chaotic behaviour of magnetosphere was analyzed, using AE index time series. The significant chaotic quantifiers like, Lyapunov exponent, spatio-temporal entropy and nonlinear prediction error for AE index time series under various physical conditions were estimated and compared. During high solar activity (1991), the values of Lyapunov exponent for AE index time series representing quiet conditions (yearly mean = 0.5±0.1 min−1) have no significant difference from those values for corresponding storm conditions (yearly mean = 0.5±0.17 min−1). This implies that, for the cases considered here, geomagnetic storms may not be an additional source to increase or decrease the deterministic chaotic aspects of magnetosphere, especially during high solar activity. During solar minimum period (1994), the seasonal mean value of Lyapunov exponent for AE index time series belong to quiet periods in winter (0.7±0.11 min−1) is higher compared to corresponding value of storm periods in winter (0.36±0.09 min−1). This may be due to the fact that, stochastic part, which is Dst dependent could be more prominent during storms, thereby increasing fluctuations/stochasticity and reducing determinism in AE index time series during storms. It is observed that, during low solar active period (1994), the seasonal mean value of entropy for time series representing storm periods of equinox is greater than that for quiet periods. However, significant difference is not observed between storm and quiet time values of entropy during high solar activity (1991), which is also true for nonlinear prediction error for both low and high solar activities. In the case of both high and low solar activities, the higher standard deviations of yearly mean Lyapunov exponent values for AE index time series for storm periods compared to those for quiet periods might be due to the strong interplay between stochasticity and determinism during storms. It is inferred that, the external driving forces, mainly due to solar wind, make the solar-magnetosphere-ionosphere coupling more complex, which generates many active degrees of freedom with various levels of coupling among them, under various physical conditions. Hence, the superposition of a large number of active degrees of freedom can modify the stability/instability conditions of magnetosphere.