Time Window Length Research Articles

Length of exposure to long working hours and night work and risk of sickness absence: a register-based cohort study

BackgroundThere is inconsistent evidence that long working hours and night work are risk factors for sickness absence, but few studies have considered variation in the length of exposure time window as a potential source of mixed findings. We examined whether the association of long working hours and night work with sickness absence is dependent on the length of exposure to the working hour characteristics.MethodsWe analysed records of working hours, night work and sickness absence for a cohort of 9226 employees in one hospital district in Finland between 2008 and 2019. The exposure time windows ranged from 10 to 180 days, and we used Cox’s proportional hazards models with time-dependent exposures to analyse the associations between working-hour characteristics and subsequent sickness absence.ResultsLonger working hours for a period of 10 to 30 days was not associated with the risk of sickness absence whereas longer working hours for a period of 40 to 180 days was associated with a lower risk of sickness absence. Irrespective of exposure time window, night work was not associated with sickness absence.ConclusionsIt is important to consider the length of exposure time window when examining associations between long working hours and sickness absence, whereas the association between night work and sickness absence is not similarly sensitive to exposure times.

Adaptive time window convolutional neural networks concerning multiple operation modes with applications in energy efficiency predictions

Energy efficiency prediction models promote the efficient uses of energy and low consumptions of raw materials. The Convolutional neural network (CNN) is one of the most effective deep learning networks for complex process modeling. However, when applied to real industrial processes, the performance of the CNN would be restricted by the change of operating conditions, such as swings in feedstock qualities, different manufacturing strategies and variations in product specifications. A globally invariant model is unable to adapt the time-varying conditions. Therefore, we proposed a multiple operation modes adaptive time window convolutional neural network (MOM-ATWCNN). Here, a hierarchical clustering approach is suggested to determine the numbers and locations of the modes. Then, an optimal length of time window is selected to match with each mode accordingly. Lastly, the improved deep learning model is used to extract the varying features hidden in different modes. To verify the effectiveness, the proposed method is compared to several typical deep learning models by the data collected from a real industrial atmospheric and vacuum distillation process. The results show that the energy prediction accuracy of the MOM-ATWCNN is 6.5%, 2.9% and 10.2% higher than those of the traditional CNN, LSTM, BPNN, respectively. Furthermore, the proposed method exhibit its superiority regarding various performance indexes. The improvement of the algorithm is beneficial to the reduction of energy consumptions thus achieving economic goals.

Study on the length of diagnostic time window of CUP-VISAR

One-dimensional line velocity interferometer system for any reflectors (VISARs) acts as a significant diagnostic device in the process of the inertial confinement fusion, which can be used to measure the free surface velocity and the history of shockwave velocity in transparent media over time. But the lack of spatial information makes it impossible to measure the flatness of wavefront. The compressed ultrafast photography (CUP) system developed in recent years can realize two-dimensional ultrafast photography. We have designed a new two-dimensional VISAR diagnosis system by combining the CUP with line-VISAR, called the CUP-VISAR, which will be of great significance in two-dimensional shockwave front measurement. In this paper, a data simulation method of CUP-VISAR is proposed to study the length of diagnostic time window of the device. A series of original VIASR images are firstly generated and then the compressed images are simulated after image encoding and compression. Finally, two-step iterative shrinkage thresholding algorithm is used to reconstruct the compressed images, which results in corresponding reconstructed images. In order to verify the restoration effect of the algorithm, we calculate the velocity error and image correlation coefficient value. Finally the relationship between the image reconstruction quality and the number of images is preliminarily obtained, which provides reference for the actual experiment.

A novel method to identify sub-seasonal clustering episodes of extreme precipitation events and their contributions to large accumulation periods

Abstract. Temporal (serial) clustering of extreme precipitation events on sub-seasonal timescales is a type of compound event. It can cause large precipitation accumulations and lead to floods. We present a novel, count-based procedure to identify episodes of sub-seasonal clustering of extreme precipitation. We introduce two metrics to characterise the prevalence of sub-seasonal clustering episodes and their contribution to large precipitation accumulations. The procedure does not require the investigated variable (here precipitation) to satisfy any specific statistical properties. Applying this procedure to daily precipitation from the ERA5 reanalysis data set, we identify regions where sub-seasonal clustering occurs frequently and contributes substantially to large precipitation accumulations. The regions are the east and northeast of the Asian continent (northeast of China, North and South Korea, Siberia and east of Mongolia), central Canada and south of California, Afghanistan, Pakistan, the southwest of the Iberian Peninsula, and the north of Argentina and south of Bolivia. Our method is robust with respect to the parameters used to define the extreme events (the percentile threshold and the run length) and the length of the sub-seasonal time window (here 2–4 weeks). This procedure could also be used to identify temporal clustering of other variables (e.g. heat waves) and can be applied on different timescales (sub-seasonal to decadal). The code is available at the listed GitHub repository.

A bi-objective model for eco-efficient dial-a-ride problems

Environmental impact becomes an emerging problem since global warming has caused climate change issues, especially natural disasters in recent years. Based on International Energy Agency (IEA), the concentration of CO2 in 2015 was 399 parts per million by volume and was about 40% higher than in the mid-1800s. Since the transportation sector accounts for great responsibility for emissions, how to reduce CO2 emissions and keep the efficiency of transportation has become a more important issue. Dial-a-ride Problem (DARP) is a new form of mobility-on-demand public transportation, and the route and schedule of DARP are flexible to accommodate customer needs. This study aims at integrating the concept of eco-efficiency into DARP, and a bi-objective dial-a-ride problem with time-dependent costs is formulated. Two objectives, CO2 emissions and travel time, are explicitly considered. The formulation considers the perspective of eco-efficiency and fluctuation of travel time for the dial-a-ride problem. A revised branch-and-price solution algorithm with a large neighbor search (LNS) is adopted to solve the problem. In order to solve the two objectives simultaneously, this study applies the weighted sum with the normalization approach. Due to the difficulties of estimating emissions, a traffic simulation model is incorporated with the solution algorithm to provide emissions values. Several experiments based on a city network are conducted to evaluate objectives based on different factors, including traffic condition, time window, and maximum ride time. The results show that (1) weights for objectives need to be designed appropriately to reflect the preference; (2) the travel times and CO2 emissions reduce with respect to the increase of time window length; (3) The total travel time and CO2 emissions decrease with respect to the length of maximum ride time.

Sentinel-1&2 Multitemporal Water Surface Detection Accuracies, Evaluated at Regional and Reservoirs Level

Water stock monitoring is a major issue for society on a local and global scale. Sentinel-1&2 satellites provide frequent acquisitions to track water surface dynamics, proxy variables to enable water surface volume monitoring. How do we combine such observations along time for each sensor? What advantages and disadvantages of single-date, monthly or time-windowed estimations? In this context, we analysed the impact of merging information through different types and lengths of time-windows. Satellite observations were processed separately on optical (Sentinel-2) and radar (Sentinel-1) water detectors at 10 m resolution. The analysis has been applied at two scales. First, validating with 26 large scenes (110 × 110 km) in different climatic zones in France, time-windows yielded an improvement on radar detection (F1-score improved from 0.72 to 0.8 for 30 days on average logic) while optical performances remained stable (F1-score 0.89). Second, validating reservoir area estimations with 29 instrumented reservoirs (20–1250 ha), time-windows presented in all cases an improvement on both optical and radar error for any window length (5–30 days). The mean relative absolute error in optical area detection improved from 16.9% on single measurements to 12.9% using 15 days time-windows, and from 22.15% to 15.1% in radar detection). Regarding reservoir filling rates, we identified an increased negative bias for both sensors when the reservoir is nearly full. This work helped to compare accuracies of separate optical and radar capabilities, where optical statistically outperforms radar at both local and large scale to the detriment of less frequent measurements. Furthermore, we propose a geomorphological indicator of reservoirs to predict the quality of radar area monitoring (R2 = 0.58). In conclusion, we suggest the use of time-windows on operational water mapping or reservoir monitoring systems, using 10–20 days time-windows with average logic, providing more frequent and faster information to water managers in periods of crisis (e.g., water shortage) compared to monthly estimations.

Estimation of initial conditions for surface suspended sediment simulations with the adjoint method: A case study in Hangzhou Bay

In this paper, an improved numerical scheme is developed to estimate the initial conditions (ICs) based on a three-dimensional suspended sediment transport model (3D SSTM) with adjoint data assimilation, and the method is then applied to Hangzhou Bay as an example. Specifically, the ICs are estimated by assimilating artificial observations in twin experiments and suspended sediment concentrations (SSCs) retrieved from the Geostationary Ocean Color Imager (GOCI) in practical experiments. In the twin experiments, the sensitivity of the estimated ICs to several influential factors is discussed. The results demonstrate that the conjugate descent algorithm of Fletcher is proven to be better than the steepest descent, finite memory BFGS, and five other conjugate gradient algorithms in estimating the ICs; the estimated ICs are sensitive to initial guess values, and appropriate initial values are necessary for improving the efficiency of convergence and obtaining good results. Additionally, the errors of observations can significantly influence the estimated results. In contrast, the estimated results are not very sensitive to cloud coverage, errors in the background flow field, and length of the assimilation time window. In practical experiments, according to the conclusions of twin experiments, an improved 3D SSTM with the adjoint method is developed for Hangzhou Bay, and the surface GOCI-retrieved SSCs during typical neap and spring tidal cycles are assimilated to estimate the practical ICs. The experimental results imply that with the present estimation method, more accurate ICs can be obtained, which indicates that the adjoint method is effective in the estimation of the ICs in SSTMs. Furthermore, this study verifies that accurate ICs are critical for the numerical modeling of SSCs on the tidal cycle scale. This study is not only useful for further improving the accuracy of ICs in SSTMs but also suggestive for the initialization schemes of other matter transport models.

Efficient methods for acute stress detection using heart rate variability data from Ambient Assisted Living sensors

BackgroundUsing Ambient Assisted Living sensors to detect acute stress could help people mitigate the harmful effects of everyday stressful situations. This would help both the healthy and those affected more by sudden stressors, e.g., people with diabetes or heart conditions. The study aimed to develop a method for providing reliable stress detection based on heart rate variability features extracted from portable devices.MethodsFeatures extracted from portable electrocardiogram sensor recordings were used for training various classification algorithms for stress detection purposes. Data were recorded in a clinical trial with 7 participants and two stressors, the Trier Social Stress Test and the Stroop colour word test, both validated by standardised questionnaires. Different heart rate variability feature sets (all, time-domain and non-linear only, frequency-domain only) were tested to investigate how classification performance is affected, in addition to various time window length setups and participant-wise training sessions. The accuracy and F1 score of the trained models were compared and analysed.ResultsThe best results were achieved with models using time-domain and non-linear heart rate variability features with 5-min-long overlapping time windows, yielding 96.31% accuracy and 96.26% F1 score. Shorter overlapping windows had slightly lower performance, with 91.62–94.55% accuracy and 91.77–94.55% F1 score ranges. Non-overlapping window configurations were less effective, with both accuracy and F1 score below 88%. For participant-wise learning, average F1 scores of 99.47%, 98.93% and 96.1% were achieved for feature sets using all, time-domain and non-linear, and frequency-domain features, respectively.ConclusionThe tested stress detector models based on heart rate variability data recorded by a single electrocardiogram sensor performed just as well as those published in the literature working with multiple sensors, or even better. This suggests that once portable devices such as smartwatches provide reliable hear rate variability recordings, efficient stress detection can be achieved without the need for additional physiological measurements.

Bayesian Detection of Streamflow Response to Earthquakes

AbstractDetecting whether and how river discharge responds to strong earthquake shaking can be time‐consuming and prone to operator bias when checking hydrographs from hundreds of gauging stations. We use Bayesian piecewise regression models to show that up to a fifth of all gauging stations across Chile had their largest change in daily streamflow trend on the day of the Mw 8.8 Maule earthquake in 2010. These stations cluster distinctly in the near field though the number of detected streamflow changes varies with model complexity and length of time window considered. Credible seismic streamflow changes at several stations were the highest detectable in eight months, with an increased variance of discharge surpassing the variance of discharge following rainstorms. We conclude that Bayesian piecewise regression sheds new and unbiased insights on the duration, trend, and variance of streamflow response to strong earthquakes, and on how this response compares to that following rainstorms.

Using electroencephalogram for emotion recognition based on filter-bank long short-term memory networks

Emotion plays an important role in people's cognition and communication. By analyzing electroencephalogram (EEG) signals to identify internal emotions and feedback emotional information in an active or passive way, affective brain-computer interactions can effectively promote human-computer interaction. This paper focuses on emotion recognition using EEG. We systematically evaluate the performance of state-of-the-art feature extraction and classification methods with a public-available dataset for emotion analysis using physiological signals (DEAP). The common random split method will lead to high correlation between training and testing samples. Thus, we use block-wise K fold cross validation. Moreover, we compare the accuracy of emotion recognition with different time window length. The experimental results indicate that 4 s time window is appropriate for sampling. Filter-bank long short-term memory networks (FBLSTM) using differential entropy features as input was proposed. The average accuracy of low and high in valance dimension, arousal dimension and combination of the four in valance-arousal plane is 78.8%, 78.4% and 70.3%, respectively. These results demonstrate the advantage of our emotion recognition model over the current studies in terms of classification accuracy. Our model might provide a novel method for emotion recognition in affective brain-computer interactions.

Optimal dispatching of an energy system with integrated compressed air energy storage and demand response

The integrated energy system is considered to be an important way to avoid energy supply risks by virtue of advantages in meeting diversified energy demand and improving energy utilization efficiency. Energy storage enables microgrid operators to respond to variability or loss of generation sources. In view of the difficulty of battery to fully improve the energy utilization efficiency and solve the problems of clean energy power large-scale consumption, and the difficulty of single demand response to significantly improve the operational reliability and economy of the integrated energy system, a rolling optimization planning framework and model of an integrated energy system considering compressed air energy storage and sliding time window-based electric and heating integrated response demand is proposed, which can obtain both optimal resource configuration and energy management strategy. The planning problem is to coordinate the output of various dispatching resources on the basis of satisfying the constraints, so as to minimize the total cost. Taking into account the uncertainty of wind power and photovoltaic output and the unplanned outage risk of the unit, a stochastic optimization model is constructed based on the probability density function of the risk variable, and finally the cost probability distribution is obtained. The results verify the universality of the planning model. The comparison of five different energy system configuration schemes and multiple time window length schemes verifies the validity and superiority of the model. The simulation results show that the integrated energy system scheme proposed by this planning model has better economy than the scheme without compressed air energy storage, and the operating cost decreases by 11.9% and the total cost decreases by 4.5%. In addition, the results show that through the introduction of demand response, the operating economy and flexibility of the integrated energy system are improved, and as the sliding window length increases, the total cost gradually decreases.

Aquifer Diffusivity Estimation Through Joint Inversion of the Amplitude Ratios and Time Lags of Dominant Frequencies of Fluctuating Head

AbstractThis note introduces the estimation of aquifer diffusivity (D) through simultaneous inversion of the attenuation and lag of multiple head fluctuation frequencies due to a dynamic source or boundary, that is, a river. Spectral analysis, with optimized moving time window length and step size, was used to extract the dominant constituents and their attenuation through space; the cross‐power spectral density method was used to determine time lags. The Jacob‐Ferris analytical model was then used for inverting forD. Unlike most similar applications to date, here we propose using all frequencies with robust signal‐to‐noise ratios (five total in our test cases) and both the amplitude attenuation and time lag in the inversion. The method was implemented using observations from wells in the banks of the fluctuating Meghna River in Bangladesh that is connected with a semi‐confined sandy alluvial aquifer. The estimatedDusing the technique provides estimates that are very similar to those from pumping tests. The estimates are more accurate compared to previous implementation of the Jacob‐Ferris model on the same data that used only a dominant frequency's amplitude attenuation or time lag. The workflow and codes for the analysis are provided for straightforward implementation of the robust and cost‐effective method.

Parameter determination and performance evaluation of time-series-based leakage detection method

ABSTRACT The spatiotemporal correlations typically exist between the monitoring data provided by the devices distributed at the water distribution system (WDS). The leakage detection method featured by the utilization of the spatiotemporal correlation of the monitoring data had been proposed in our previous study and parameter settings have a significant impact on the detection performance of the method. This paper focuses on the optimization of two key parameters of this method, Scanning Time Window Length (STWL) and Rate of False Alarm of the k th scan (RF k ). STWL determines the length of the time-series data participating in the correlation analysis, and RF k determines the weight of each scan in a complete scan process. The proposed method is applied in a realistic and full-scale water distribution network with the consideration of the demand uncertainty, leakage flow rates, and sensor noise. The results show that the optimized parameter settings could improve the leakage Detection Probability (DP).

Driver lane change intention recognition in the connected environment

The connected environment provides information on surrounding traffic and areas beyond the visual range to improve driving behavior and avoid dangerous incidents. However, due to the novelty of the connected environment and the scarcity of connected data, current research on driver lane change intention in this field has received little attention. In this work, we designed a typical lane change scenario in the connected environment based on a driving simulator and real-time collection of multi-modal data from eye trackers, driving simulators, and a connected platform. The driver’s eye movement, head rotation, vehicle movement, and the driver’s maneuver parameters were analyzed, revealing a significant difference between the lane change intention and lane keep stages in the connected environment. In addition, the length of the intention time window with connected information (6.5 s) was longer than that without connected information (4 s). The bi-directional long and short-term memory network based on the attention mechanism (AT-BiLSTM) was used to establish a lane change intention model. The accuracy of the lane change intention model based on the proposed AT-BiLSTM algorithm surpassed that of existing machine learning algorithms. The recognition accuracy of the lane change intention model was 93.33% at 3 s prior to the lane change. The conclusions of this study are of great significance for the development of a side warning assist system in future connected environments.

An integrated methodology for real-time driving risk status prediction using naturalistic driving data

Real-time driving risk status prediction is critical for developing proactive traffic intervention strategies and enhance driving safety. However, the optimal observation time window length and prediction time window length, which should be the prerequisite for the timeliness and accuracy of real-time driving risk status prediction model, have been rarely explored in previous studies. In this study, a methodology which integrates driving risk status identification, rolling time window-based feature extraction, real-time driving risk status prediction and driving risk influencing factors analysis was proposed to accurately evaluate and predict real-time driving risk status. The methodology was tested based on 1,440 car-following events from Shanghai Naturalistic Driving Study. Results show that four driving risk statuses (safe, low-risk, median-risk and high-risk) are most appropriate to establish risk labelling criteria. In addition, results from driving risk status prediction show that when the observation time window length is 0.5 s, the accuracy rate of predicting medium-risk or high-risk status occurring in the next 0.7 s is higher than 85 % using multi-layer perceptron model. Meanwhile, the results from the analysis of influencing factors show that the input variables related to the risk status score higher in the ranking of feature importance. A part from that, speed difference, headway distance, speed and acceleration are still important in predicting driving risk status. The proposed methods in this paper can be applied in connected and autonomous vehicle (CAV) to reduce driver cognitive workload and hence improve driving safety fed with naturalistic driving data collected using in-vehicle systems.

A Time-Domain Finite Difference Decomposition Method for Boulders in the Cultivated Layers Based on Ground-Penetrating Radar

Afinite difference time domain (FDTD) model of the electromagnetic wave of the two-dimensional Maxwell's discrete equation is established, based on the optimization of the Ground-penetrating radar (GPR) antenna frequency (recommended 100MHz), time window length, and sampling interval parameters. In our study, three test schemes are designed: The electromagnetic wave enters the boulder medium from the soil to have the first reflection (top reflection) when a boulder point appears in the homogeneous soil, and then passes through the boulder in the water and re-enters the soil. The secondary reflection (bottom reflection) is generated, and radar image interpretation shows that the size of the boulder is the same as the designed size (0.5m).Then, the interference phenomenon of the reflection waves of the two boulders can be simulated when two boulders appear in a homogeneous soil, and the spatial position and size of the two boulders can be distinguished. For the cultivated soil layer with obvious horizontal stratification, the upper soil layer does not affect the reflection of the boulder when the boulder is located in the lower layer, and the location and size of the boulder can still be accurately interpreted. Numerical test results show that the FDTD method is a very effective method to forward simulate the boulder phenomenon in the cultivated soil layer, which has the advantages of simple principle, high simulation accuracy and fast calculation speed.

Online Bus Speed Prediction With Spatiotemporal Interaction: A Laplace Approximation-Based Bayesian Approach

This study proposes a novel Bayesian hierarchical approach for online bus speed prediction by explicitly accounting for the spatiotemporal interaction (STI) of speed observations. The use of Laplace approximation can expedite the estimation of Bayesian models and enable the implementation of online prediction. Large numbers of trials are carried out to identify significant predictors and the optimal length of the look-back time window to achieve the highest prediction accuracy. The spatiotemporal interacting patterns are also explored, and results show that the Type IV model assuming the structured spatial effect interacts with the structured temporal effect can best accommodate the bus speed data. Besides, prediction errors of the Type IV model randomly distribute over time and space. The proposed model can achieve high prediction accuracy and computational efficiency without compromising the interpretability of the contributing factors and the unobserved spatiotemporal heterogeneity. The proposed model can be used to assist public transit operation and management, such as bus scheduling, congestion warning, and the development of proactive measures to mitigate bus delays.

A New Advanced Method for an Accurate Assessment of Harmonic and Supraharmonic Distortion in Power System Waveforms

Waveforms distortion is a pressing concern in Smart Grids where a massive presence of new technologies in distributed energy resources and in advanced smart metering systems is expected. In this context, the increasing diffusion of high switching frequencies static converters and the growing usage of Power Line Communication push for research dealing with the assessment of waveforms with spectral components up to 150 kHz. The analysis of such waveforms is a challenge for researchers due to the contemporaneous presence of a high number of spectral components in the range of low- (up to 2 kHz) and high- (up to 150 kHz) frequencies, with their opposite needs in term of time window length (and frequency resolution). The main idea of this paper is to improve the performances of existing methods by using a joint method of analysis based on a profitable strategy of divide and conquer; the method guarantees the best compromise between accuracy and computational efforts. A Discrete Wavelet Transform initially divides the original waveform to obtain two frequency bands: the wavelet suitability for conducting multi-resolution time-frequency analysis on waveforms in different frequency bands with different frequency resolution is effectively exploited. Then, the sliding-window modified ESPRIT method and the sliding-window Discrete Fourier Transform which uses a Nuttal window are used for the analysis of the low- and high-frequency bands, respectively; the positive characteristics of each method are exploited, minimizing the drawbacks and integrating their behavior so that the whole joint method allows an accurate estimation of each low- and high-frequency spectral component with the required acceptable computational efforts. The proposed method is tested on synthetic and measured waveforms in terms of accuracy and computational efforts. The analysis of the numerical application results clearly reveals that the proposed method improves the performances of existing methods of analysis in the examined cases.

Auditory Noise Leads to Increased Visual Brain-Computer Interface Performance: A Cross-Modal Study.

Noise has been proven to have a beneficial role in non-linear systems, including the human brain, based on the stochastic resonance (SR) theory. Several studies have been implemented on single-modal SR. Cross-modal SR phenomenon has been confirmed in different human sensory systems. In our study, a cross-modal SR enhanced brain–computer interface (BCI) was proposed by applying auditory noise to visual stimuli. Fast Fourier transform and canonical correlation analysis methods were used to evaluate the influence of noise, results of which indicated that a moderate amount of auditory noise could enhance periodic components in visual responses. Directed transfer function was applied to investigate the functional connectivity patterns, and the flow gain value was used to measure the degree of activation of specific brain regions in the information transmission process. The results of flow gain maps showed that moderate intensity of auditory noise activated the brain area to a greater extent. Further analysis by weighted phase-lag index (wPLI) revealed that the phase synchronization between visual and auditory regions under auditory noise was significantly enhanced. Our study confirms the existence of cross-modal SR between visual and auditory regions and achieves a higher accuracy for recognition, along with shorter time window length. Such findings can be used to improve the performance of visual BCIs to a certain extent.

Error Estimation of Ultra-Short Heart Rate Variability Parameters: Effect of Missing Data Caused by Motion Artifacts.

Application of ultra–short Heart Rate Variability (HRV) is desirable in order to increase the applicability of HRV features to wrist-worn wearable devices equipped with heart rate sensors that are nowadays becoming more and more popular in people’s daily life. This study is focused in particular on the the two most used HRV parameters, i.e., the standard deviation of inter-beat intervals (SDNN) and the root Mean Squared error of successive inter-beat intervals differences (rMSSD). The huge problem of extracting these HRV parameters from wrist-worn devices is that their data are affected by the motion artifacts. For this reason, estimating the error caused by this huge quantity of missing values is fundamental to obtain reliable HRV parameters from these devices. To this aim, we simulate missing values induced by motion artifacts (from 0 to 70%) in an ultra-short time window (i.e., from 4 min to 30 s) by the random walk Gilbert burst model in 22 young healthy subjects. In addition, 30 s and 2 min ultra-short time windows are required to estimate rMSSD and SDNN, respectively. Moreover, due to the fact that ultra-short time window does not permit assessing very low frequencies, and the SDNN is highly affected by these frequencies, the bias for estimating SDNN continues to increase as the time window length decreases. On the contrary, a small error is detected in rMSSD up to 30 s due to the fact that it is highly affected by high frequencies which are possible to be evaluated even if the time window length decreases. Finally, the missing values have a small effect on rMSSD and SDNN estimation. As a matter of fact, the HRV parameter errors increase slightly as the percentage of missing values increase.