Modified recurrent equation-based cubic spline interpolation for missing data recovery in phasor measurement unit (PMU)

Background

Smart grid systems require high-quality Phasor Measurement Unit (PMU) data for proper operation, control, and decision-making. Missing PMU data may lead to improper actions or even blackouts. While the conventional cubic interpolation methods based on the solution of a set of linear equations to solve for the cubic spline coefficients have been applied by many researchers for interpolation of missing data, the computational complexity increases non-linearly with increasing data size.

Methods

In this work, a modified recurrent equation-based cubic spline interpolation procedure for recovering missing PMU data is proposed. The recurrent equation-based method makes the computations of spline constants simpler. Using PMU data from the State Load Despatch Center (SLDC) in Madhya Pradesh, India, a comparison of the root mean square error (RMSE) values and time of calculation (ToC) is calculated for both methods.

Results

The modified recurrent relation method could retrieve missing values 10 times faster when compared to the conventional cubic interpolation method based on the solution of a set of linear equations. The RMSE values have shown the proposed method is effective even for special cases of missing values (edges, continuous missing values).

Conclusions

The proposed method can retrieve any number of missing values at any location using observed data with a minimal number of calculations.

A piecewise spline approach for modeling of ECG signals

This paper presents a new spline-based modeling method of electrocardiogram (ECG) signal that can reproduce normal as well as abnormal ECG beats. Large volume ECG data is required for automatic machine learning diagnostic systems, medical education, research and testing purposes but due to privacy issues, access to this medical data is very difficult. Given this, modeling an ECG signal is a very challenging task in the field of biomedical signal processing. Spline-based modeling is the latest and one of the most efficient methods with very low computational complexity in the domain of ECG signal generation. In this paper, healthy ECG and arrhythmia conditions have been considered for the synthetic generation, (namely Atrial fibrillation and Congestive heart failure ECG beats) because these are the leading causes of death globally. To validate the performance of the presented modeling method, it is tested on 100 signals, also the percentage root mean square difference (PRD) and the root mean square error (RMSE) have been determined. These calculated values are analyzed and the results are found to be very promising and show that the presented method is one of the best methods in the field of synthetic ECG signal generation. A comparison amongst relevant existing techniques and the proposed method is also presented. The performance merit values PRD and RMSE, for the proposed method obtained are 38.99 and 0.10092, respectively, which are lower than the values obtained in other compared methods. To ensure fidelity of the proposed modeling technique with respect to IEC60601 standard, few Conformance Testing Services (CTS)database signals have also been modelled with a very close resemblance with the standard signals.

Effects of sulfur dioxide and particulate matter pollution on hospital admissions for hypertensive cardiovascular disease: A time series analysis

Background and aims: Air pollution is a major environmental risk factor and the leading cause of disease burden with detrimental effects on cardiovascular systems. Cardiovascular diseases are predisposed by various risk factors, including hypertension, as the most important modifiable risk factor. However, there is a lack of sufficient data concerning the impact of air pollution on hypertension. We sought to study the associations of short-term exposure to Sulfur dioxide (SO₂) and particulate matter (PM₁₀) with the number of daily hospital admissions of hypertensive cardiovascular diseases (HCD). Methods: All hospitalized patients between March 2010 to March 2012 were recruited with the final diagnosis of HCD based on the International Classification of Diseases 10 (codes: I10-I15) from 15 hospitals in Isfahan, one of the most polluted cities in Iran. The 24-hour average concentrations of pollutants were obtained from 4 monitoring stations. In addition to single- and two-pollutant models, we used Negative Binomial and Poisson models with covariates of holidays, dew point, temperature, wind speed, and extracted latent factors of other pollutants controlling for multi-collinearity to examine the risk for hospital admissions for HCD affected by SO₂ and PM₁₀ exposures in the multi-pollutant model. Results: A total of 3132 hospitalized patients (63% female) with a mean (standard deviation) age of 64.96 (13.81) were incorporated in the study. The mean concentrations of SO2 and PM10 were 37.64 μg/m3 and 139.08 μg/m3, respectively. Our findings showed that a significantly increased risk of HCD-induced hospital admission was detected for a 10 μg/m3 increase in the 6-day and 3-day moving average of SO2 and PM₁₀ concentrations in the multi-pollutant model with a percent change of 2.11% (95% confidence interval: 0.61 to 3.63%) and 1.19% (0.33 to 2.05%), respectively. This finding was robust in all models and did not vary by gender (for SO₂ and PM₁₀) and season (for SO₂). However, people aged 35-64 and 18-34 years were vulnerable to SO2 and PM10 exposure-triggered HCD risk, respectively. Conclusions: This study supports the hypothesis of the association between short-term exposure to ambient SO₂ and PM₁₀ and the number of hospital admissions due to HCD.

Adaptive Segmentation of Streaming Sensor Data on Edge Devices

Sensor data streams often represent signals/trajectories which are twice differentiable (e.g., to give a continuous velocity and acceleration), and this property must be reflected in their segmentation. An adaptive streaming algorithm for this problem is presented. It is based on the greedy look-ahead strategy and is built on the concept of a cubic splinelet. A characteristic feature of the proposed algorithm is the real-time simultaneous segmentation, smoothing, and compression of data streams. The segmentation quality is measured in terms of the signal approximation accuracy and the corresponding compression ratio. The numerical results show the relatively high compression ratios (from 135 to 208, i.e., compressed stream sizes up to 208 times smaller) combined with the approximation errors comparable to those obtained from the state-of-the-art global reference algorithm. The proposed algorithm can be applied to various domains, including online compression and/or smoothing of data streams coming from sensors, real-time IoT analytics, and embedded time-series databases.

Empirical Evaluation of Alternative Time-Series Models for COVID-19 Forecasting in Saudi Arabia

COVID-19 is a disease-causing coronavirus strain that emerged in December 2019 that led to an ongoing global pandemic. The ability to anticipate the pandemic's path is critical. This is important in order to determine how to combat and track its spread. COVID-19 data is an example of time-series data where several methods can be applied for forecasting. Although various time-series forecasting models are available, it is difficult to draw broad theoretical conclusions regarding their relative merits. This paper presents an empirical evaluation of several time-series models for forecasting COVID-19 cases, recoveries, and deaths in Saudi Arabia. In particular, seven forecasting models were trained using autoregressive integrated moving average, TBATS, exponential smoothing, cubic spline, simple exponential smoothing Holt, and HoltWinters. The models were built using publicly available daily data of COVID-19 during the period of 24 March 2020 to 5 April 2021 reported in Saudi Arabia. The experimental results indicate that the ARIMA model had a smaller prediction error in forecasting confirmed cases, which is consistent with results reported in the literature, while cubic spline showed better predictions for recoveries and deaths. As more data become available, a fluctuation in the forecasting-accuracy metrics was observed, possibly due to abrupt changes in the data.

An Automatic Exposure Method of Plane Array Remote Sensing Image Based on Two-Dimensional Entropy

The improper setting of exposure time for the space camera will cause serious image quality degradation (overexposure or underexposure) in the imaging process. In order to solve the problem of insufficient utilization of the camera’s dynamic range to obtain high-quality original images, an automatic exposure method for plane array remote sensing images based on two-dimensional entropy is proposed. First, a two-dimensional entropy-based image exposure quality evaluation model is proposed. The two-dimensional entropy matrix of the image is partitioned to distinguish the saturated areas (region of overexposure and underexposure) and the unsaturated areas (region of propitious exposure) from the original image. The ratio of the saturated area is used as an evaluating indicator of image exposure quality, which is more sensitive to the brightness, edges, information volume, and signal-to-noise ratio of the image. Then, the cubic spline interpolation method is applied to fit the exposure quality curve to efficiently improve the camera’s exposure accuracy. A series of experiments have been carried out for different targets in different environments using the existing imaging system to verify the superiority and robustness of the proposed method. Compared with the conventional automatic exposure method, the signal-to-noise ratio of the image obtained by the proposed algorithm is increased by at least 1.6730 dB, and the number of saturated pixels is reduced to at least 2.568%. The method is significant to improve the on-orbit autonomous operating capability and on-orbit application efficiency of space camera.

Cubic-Spline Interpolation for Sparse-View CT Image Reconstruction With Filtered Backprojection in Dynamic Myocardial Perfusion Imaging

We investigated a projection interpolation method for reconstructing dynamic contrast-enhanced (DCE) heart images from undersampled x-ray projections with filtered backprojecton (FBP). This method may facilitate the application of sparse-view dynamic acquisition for ultralow-dose quantitative computed tomography (CT) myocardial perfusion (MP) imaging. We conducted CT perfusion studies on 5 pigs with a standard full-view acquisition protocol (984 projections). We reconstructed DCE heart images with FBP from all and a quarter of the measured projections evenly distributed over 360°. We interpolated the sparse-view (quarter) projections to a full-view setting using a cubic-spline interpolation method before applying FBP to reconstruct the DCE heart images (synthesized full-view). To generate MP maps, we used 3 sets of DCE heart images, and compared mean MP values and biases among the 3 protocols. Compared with synthesized full-view DCE images, sparse-view DCE images were more affected by streak artifacts arising from projection undersampling. Relative to the full-view protocol, mean bias in MP measurement associated with the sparse-view protocol was 10.0 mL/min/100 g (95%CI: −8.9 to 28.9), which was >3 times higher than that associated with the synthesized full-view protocol (3.3 mL/min/100 g, 95% CI: −6.7 to 13.2). The cubic-spline-view interpolation method improved MP measurement from DCE heart images reconstructed from only a quarter of the full projection set. This method can be used with the industry-standard FBP algorithm to reconstruct DCE images of the heart, and it can reduce the radiation dose of a whole-heart quantitative CT MP study to <2 mSv (at 8-cm coverage).

A Spline Interpolation-based Data Reconstruction Technique for Estimation of Strain Time Constant in Ultrasound Poroelastography

Ultrasound poroelastography is a cost-effective and noninvasive imaging technique, which can be used to reconstruct mechanical parameters of tissues such as Young's modulus, Poisson's ratio, interstitial permeability, and vascular permeability. To estimate interstitial permeability and vascular permeability using poroelastography, accurate estimation of the strain time constant (TC) is required. This can be a challenging task due to the nonlinearity of the exponential strain curve and noise affecting the experimental data. Due to motion artifacts caused by the sonographer, animal/patient, and/or the environment, noise affecting some strain frames can be significantly higher than the strain signal. If these frames are used for the computation of the strain TC, the resulting TC estimate can be highly inaccurate, which, in turn, can cause high errors in the reconstructed mechanical parameters. In this paper, we introduce a cubic spline-based interpolation method, which allows to use only good quality strain frames (i.e., frames with sufficiently high signal-to-noise ratio [SNR]) to estimate the strain TC. Using finite element simulations, we demonstrate that the proposed interpolation method can improve the estimation accuracy of the strain TC by 46% with respect to the case where no interpolation and filtering are used and by 37% with respect to the case where the strain frames are Kalman filtered before TC estimation (at an SNR of 30 dB). We also prove the technical feasibility of the proposed technique using in vivo experimental data. While detecting the bad frames in both simulations and experiments, we assumed the lower limit SNR to be below 10 dB. Based on our results, the proposed technique may be of great help in applications relying on the accurate assessment of the temporal behavior of strain data.

Integrated Dissection of Cysteine Oxidative Post-translational Modification Proteome During Cardiac Hypertrophy

Cysteine oxidative modification of cellular proteins is crucial for many aspects of cardiac hypertrophy development. However, integrated dissection of multiple types of cysteine oxidative post-translational modifications (O-PTM) of proteomes in cardiac hypertrophy is currently missing. Here we developed a novel discovery platform that encompasses a customized biotin switch-based quantitative proteomics pipeline and an advanced analytic workflow to comprehensively profile the landscape of cysteine O-PTM in an ISO-induced cardiac hypertrophy mouse model. Specifically, we identified a total of 1655 proteins containing 3324 oxidized cysteine sites by at least one of the following three modifications: reversible cysteine O-PTM, cysteine sulfinylation (CysSO₂H), and cysteine sulfonylation (CysSO₃H). Analyzing the hypertrophy signatures that are reproducibly discovered from this computational workflow unveiled four biological processes with increased cysteine O-PTM. Among them, protein phosphorylation, creatine metabolism, and response to elevated Ca²⁺ pathways exhibited an elevation of cysteine O-PTM in early stages, whereas glucose metabolism enzymes were increasingly modified in later stages, illustrating a temporal regulatory map in cardiac hypertrophy. Our cysteine O-PTM platform depicts a dynamic and integrated landscape of the cysteine oxidative proteome, through the extracted molecular signatures, and provides critical mechanistic insights in cardiac hypertrophy. Data are available via ProteomeXchange with identifier PXD010336.

Development of a pediatric body mass index using longitudinal single-index models

As a measure of human adiposity, the body mass index, defined as weight/height(2), has been widely used in clinical investigations. For children undergoing pubertal development, whether this function of height and weight represents an optimal way of quantifying body mass for assessing of specific health outcomes has not been carefully studied. In this study, we propose an alternative pediatric body mass measure for prediction of blood pressure based on recorded height and weight data using single-index modeling techniques. Specifically, we present a general form of partially linear single-index mixed effect models for the determination of this new metric. A methodological contribution of this research is the development of an efficient algorithm for the fitting of a general class of partially linear single-index models in longitudinal data situations. The proposed model and related model fitting algorithm are easily implementable in most computational platforms. Simulation demonstrates superior performance of the new method, as compared to the standard body mass index measure. Using the proposed method, we explore an alternative body mass measure for the prediction of blood pressure in children. The method is potentially useful for the construction of other indices for specific investigations.