Time Interpolation Research Articles

Implementation of 5.3 ps RMS precision and 350 M samples/second throughput time-to-digital converters with event sampling architecture in a Kintex-7 FPGA

Unlike the conventional field programmable gate array (FPGA) based time-to-digital converter (TDC) with clock sampling architecture, the TDC with event sampling architecture implemented in this paper propagates the system clock signal along the tapped-delay line (TDL) and the TDL status is sampled by a hit signal for time interpolation. Since there are several “1–0” and “0–1” transitions in the sampled TDL status, the TDC naturally realizes multiple measurements in parallel without increasing the resource consumption and the measurement dead time. Using a Xilinx Kintex-7 FPGA, we increase the number of equivalent TDC bins approximately to twice the number of physical delay cells in the TDL, which means the TDC resolution is about twice as good as the original. The average RMS precision is measured as 5.3 ps with two identical TDC channels measuring the time intervals in the range 0 to 20 ns. The proposed encoding scheme is so efficient that the TDC measurement throughput can reach 350 M samples per second. The test results show that the event sampling architecture is effective in FPGA as well. The performance that can be achieved is comparable with the performance of their counterparts that use the clock sampling architecture.

A Three-Dimensional Trajectory Model with Advection Correction for Tropical Cyclones: Algorithm Description and Tests for Accuracy

Abstract When computing trajectories from model output, gridded winds are often temporally interpolated to a time step shorter than model output intervals to satisfy computational stability constraints. This study investigates whether trajectory accuracy may be improved for tropical cyclone (TC) applications by interpolating the model winds using advection correction (AC) instead of the traditional linear interpolation in time (LI) method. Originally developed for Doppler radar processing, AC algorithms interpolate data in a reference frame that moves with the pattern translation, or advective flow velocity. A previously developed trajectory AC implementation is modified here by extending it to three-dimensional (3D) flows, and the advective flows are defined in cylindrical rather than Cartesian coordinates. This AC algorithm is tested on two model-simulated TC cases, Hurricanes Joaquin (2015) and Wilma (2005). Several variations of the AC algorithm are compared to LI on a sample of 10 201 backward trajectories computed from the modeled 5-min output data, using reference trajectories computed from 1-min output to quantify position errors. Results show that AC of 3D wind vectors using advective flows defined as local gridpoint averages improves the accuracy of most trajectories, with more substantial improvements being found in the inner eyewall where the horizontal flows are dominated by rotating cyclonic wind perturbations. Furthermore, AC eliminates oscillations in vertical velocity along LI backward trajectories run through deep convective updrafts, leading to a ~2.5-km correction in parcel height after 20 min of integration.

A multi-timestep Robin–Robin domain decomposition method for time dependent advection-diffusion problems

Many physical processes present separated evolution time scales in different regions, such as windblown sand in the desert. The evolution of bed-surface locally affects the sandy-wind flow, which erodes the sand in turns, while few meters higher from the ground the airflow is almost stationary. This and other applications suggest to improve the overall computational efficiency by locally adapting the time advancing step to the evolution in each region. We propose a multi-timestep Robin-Robin domain decomposition method, which uses mutually proportional time steps, based on a predictor-corrector strategy, coupled with linear interpolation in time. The resulting algorithm is completely segregated. Several numerical tests, obtained by the finite volume code OpenFOAM, are reported to show its stability and convergence properties.

Analysis of the Impact of Interpolation Methods of Missing RR-intervals Caused by Motion Artifacts on HRV Features Estimations.

Wearable physiological monitors have become increasingly popular, often worn during people’s daily life, collecting data 24 hours a day, 7 days a week. In the last decade, these devices have attracted the attention of the scientific community as they allow us to automatically extract information about user physiology (e.g., heart rate, sleep quality and physical activity) enabling inference on their health. However, the biggest issue about the data recorded by wearable devices is the missing values due to motion and mechanical artifacts induced by external stimuli during data acquisition. This missing data could negatively affect the assessment of heart rate (HR) response and estimation of heart rate variability (HRV), that could in turn provide misleading insights concerning the health status of the individual. In this study, we focus on healthy subjects with normal heart activity and investigate the effects of missing variation of the timing between beats (RR-intervals) caused by motion artifacts on HRV features estimation by randomly introducing missing values within a five min time windows of RR-intervals obtained from the nsr2db PhysioNet dataset by using Gilbert burst method. We then evaluate several strategies for estimating HRV in the presence of missing values by interpolating periods of missing values, covering the range of techniques often deployed in the literature, via linear, quadratic, cubic, and cubic spline functions. We thereby compare the HRV features obtained by handling missing data in RR-interval time series against HRV features obtained from the same data without missing values. Finally, we assess the difference between the use of interpolation methods on time (i.e., the timestamp when the heartbeats happen) and on duration (i.e., the duration of the heartbeats), in order to identify the best methodology to handle the missing RR-intervals. The main novel finding of this study is that the interpolation of missing data on time produces more reliable HRV estimations when compared to interpolation on duration. Hence, we can conclude that interpolation on duration modifies the power spectrum of the RR signal, negatively affecting the estimation of the HRV features as the amount of missing values increases. We can conclude that interpolation in time is the optimal method among those considered for handling data with large amounts of missing values, such as data from wearable sensors.

Probabilistic Interpolation of Uncertain Local Activation Times on Human Atrial Manifolds.

Local activation time (LAT) mapping of the atria is important for targeted treatment of atrial arrhythmias, but current methods do not interpolate on the atrial manifold and neglect uncertainties associated with LAT observations. In this paper, we describe novel methods to, first, quantify uncertainties in LAT arising from bipolar electrogram analysis and assignment of electrode recordings to the anatomical mesh, second, interpolate uncertain LAT measurements directly on left atrial manifolds to obtain complete probabilistic activation maps, and finally, interpolate LAT jointly across both the manifold and different S1-S2 pacing protocols. A modified center of mass approach was used to process bipolar electrograms, yielding a LAT estimate and error distribution from the electrogram morphology. An error distribution for assigning measurements to the anatomical mesh was estimated. Probabilistic LAT maps were produced by interpolating on a left atrial manifold using Gaussian Markov random fields, taking into account observation errors and characterizing LAT predictions by their mean and standard deviation. This approach was extended to interpolate across S1-S2 pacing protocols. We evaluated our approach using recordings from three patients undergoing atrial ablation. Cross-validation showed consistent and accurate prediction of LAT observations both at different locations on the left atrium and for different S1-S2 intervals. Interpolation of scalar and vector fields across anatomical structures from point measurements is a challenging problem in biomedical engineering, compounded by uncertainties in measurements and meshes. New methods and approaches are required, and in this paper, we have demonstrated an effective method for probabilistic interpolation of uncertain LAT.

Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane.

The electro-kinetic instability in a pressure driven shear flow near an ion exchange membrane is considered. The electrochemical system, through which an electrical potential drop is applied, consists in a polarization layer in contact with the membrane and a bulk. The numerical investigation contained two aspects: analysis of the instability modes and description of the Lagrangian transport of fluid and ions. Regarding the first aspect, the modes were analyzed as a function of the potential drop. The analysis revealed how the spatial distribution of forces controls the dynamics of vortex association and dissociation. In particular, the birth of a counter-clockwise vortex between two clockwise vortices, and the initiation of clusters constituting one or two envelopes wrapping a vortex group, were examined. In regards to the second aspect, the trajectories were computed with the fourth order Runge Kutta scheme for the time integration and with the biquadratric upstream scheme for the spatial and time interpolation of the fluid velocity and the ion flux. The results for the periodic mode showed two kinds of trajectories: the trochoidal motion and the longitudinal one coupled with a periodic transverse motion. For the aperiodic modes, other mechanisms appeared, such as ejection from the mixing layer, trapping by a growing vortex or merging vortices. The analysis of the local velocity field, the vortices’ shape, the spatial distribution of the forces and the ion flux components explained these trajectories.

Reconciling Canopy Interception Parameterization and Rainfall Forcing Frequency in the Community Land Model for Simulating Evapotranspiration of Rainforests and Oil Palm Plantations in Indonesia

AbstractBy mediating evapotranspiration processes, plant canopies play an important role in the terrestrial water cycle and regional climate. Substantial uncertainties exist in modeling canopy water interception and related hydrological processes due to rainfall forcing frequency selection and varying canopy traits. Here we design a new time interpolation method “zero” to better represent convective‐type precipitation in tropical regions. We also implement and recalibrate plant functional type‐specific interception parameters for rainforests and oil palm plantations, where oil palms express higher water interception capacity than forests, using the Community Land Model (CLM) versions 4.5 and 5.0 with CLM‐Palm embedded. Reconciling the interception scheme with realistic precipitation forcing produces more accurate canopy evaporation and transpiration for both plant functional types, which in turn improves simulated evapotranspiration and energy partitioning when benchmarked against observations from our study sites in Indonesia and an extensive literature review. Regional simulations for Sumatra and Kalimantan show that industrial oil palm plantations have 18–27% higher transpiration and 15–20% higher evapotranspiration than forests on an annual regional average basis across different ages or successional stages, even though the forests experience higher average precipitation according to reanalysis data. Our land‐only modeling results indicate that current oil palm plantations in Sumatra and Kalimantan use 15–20% more water (mean 220 mm or 20 Gt) per year compared to lowland rainforests of the same extent. The extra water use by oil palm reduces soil moisture and runoff that could affect ecosystem services such as productivity of staple crops and availability of drinking water in rural areas.

Δ elta

The continuously increasing degree of automation in many areas (e.g. manufacturing engineering, public infrastructure) lead to the construction of cyber-physical systems and cyber-physical networks. To both, time and energy are the most critical operating resources. Considering for instance the Tactile Internet specification, end-to-end latencies in these systems must be below 1ms, which means that both communication and system latencies are in the same order of magnitude and must be predictably low. As control loops are commonly handled over different variants of network infrastructure (e.g. mobile and fibre links) particular attention must be payed to the design of reliable, yet fast and energy-efficient data-transmission channels that are robust towards unexpected transmission failures. As design goals are often conflicting (e.g. high performance vs. low energy), it is necessary to analyze and investigate trade-offs with regards to design decisions during the construction of cyber-physical networks. In this paper, we present Δelta, an approach towards a tool-supported construction process for cyber-physical networks. Δelta extends the previously presented X-L AP tool by new analysis features, but keeps the original measurements facilities unchanged. Δelta jointly analyzes and correlates the runtime behavior (i.e. performance, latency) and energy demand of individual system components. It provides an automated analysis with precise thread-local time interpolation, control-flow extraction, and examination of latency criticality. We further demonstrate the applicability of Δelta with an evaluation of a prototypical implementation.

A Low-Power High-Linear Time-to-Digital Converter for Measuring R-R Intervals in ECG Signal Optimized by Neural Network and TLBO Algorithm

In this paper, a two-stage time interpolation time-to-digital converter (TDC) is proposed to achieve adequate resolution and wide dynamic range for measuring R-R intervals in QRS detection. The architecture is based on a coarse counter and a couple of two-stage interpolator circuit in order to improve the conversion linearity. The proposed TDC is modeled with the neural network, while the teacher–learner-based optimization algorithm (TLBO) is used to optimize the integral nonlinearity (INL) of the proposed TDC. The proposed optimization method shows a characteristic close to the ideal output of the TDC behavior over a wide input range. Using the achieved results of the TLBO algorithm simulation results using CADENCE VIRTUOSO and standard 180[Formula: see text]nm CMOS technology shows 1.2[Formula: see text]s dynamic range, 100[Formula: see text]ns resolution, 0.19[Formula: see text]mW power consumption and area of 0.16[Formula: see text]mm2. The proposed circuit can find application in biomedical engineering systems and other fields where long and accurate time interval measurement is needed.

A space–time parallel framework for fine-scale visualization of pollen levels across the Eastern United States

ABSTRACTAllergic rhinitis (hay fever) resulting from seasonal pollen affects 15–30% of the population in the United States, and can exacerbate several related conditions, including asthma, atopic eczema, and allergic conjunctivitis. Timely monitoring, accurate prediction, and visualization of pollen levels are critical for public health prevention purposes, such as limiting outdoor exposure or physical activity. The low density of pollen detecting stations and complex movement of pollen represent a challenge for accurate prediction and modeling. In this paper, we reconstruct the dynamics of pollen variation across the Eastern United States for 2016 using space–time interpolation. Pollen levels were extracted according to a stratified spatial sampling design, augmented by additional samples in densely populated areas. These measurements were then used to estimate the space–time cross-correlation, inferring optimal spatial and temporal ranges to calibrate the space–time interpolation. Given the computational requirements of the interpolation algorithm, we implement a spatiotemporal domain decomposition algorithm, and use parallel computing to reduce the computational burden. We visualize our results in a 3D environment to identify the seasonal dynamics of pollen levels. Our approach is also portable to analyze other large space–time explicit datasets, such as air pollution, ash clouds, and precipitation.

Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification

In this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm.

Development of a Retention Time Interpolation scale (RTi) for liquid chromatography coupled to mass spectrometry in both positive and negative ionization modes

The accuracy and sensitivity of high resolution mass spectrometry (HRMS) enables the identification of candidate compounds with the use of mass spectrometric databases among other tools. However, retention time (RT) data in identification workflows has been sparingly used since it could be strongly affected by matrix or chromatographic performance. Retention Time Interpolation scaling (RTi) strategies can provide a more robust and valuable information than RT, gaining more confidence in the identification of candidate compounds in comparison to an analytical standard. Up to our knowledge, no RTi has been developed for LC-HRMS systems providing information when acquiring in either positive or negative ionization modes.In this work, an RTi strategy was developed by means of the use of 16 isotopically labelled reference standards, which can be spiked into a real sample without resulting in possible false positives or negatives. For testing the RTi performance, a mixture of several reference standards, emulating suspect analytes, were used. RTi values for these compounds were calculated both in solvent and spiked in a real matrix to assess the effect of either chromatographic parameters or matrix in different scenarios. It has been demonstrated that the variation of injection volume, chromatographic gradient and initial percentage of organic solvent injected does not considerably affect RTi calculation. Column aging and solid support of the stationary phase of the column, however, showed strong effects on the elution of several test compounds. Yet, RTi permitted the correction of elution shifts of most compounds. Furthermore, RTi was tested in 47 different matrices from food, biological, animal feeding and environmental origin. The application of RTi in both positive and negative ionization modes showed in general satisfactory results for most matrices studied.The RTi developed can be used in future LC-HRMS screening analysis giving an additional parameter, which facilitates tedious processing tasks and gain more confidence in the identification of (non)-suspect analytes.

Pemikiran Thomas Djamaluddin tentang Salat dan Puasa di Daerah Dekat Kutub

With the development of science of hisab today, the time of prayer and fasting can be calculated because the movement of the Sun is relatively fixed. This only applies to areas that have normal day and night turns. However, in extreme areas with latitudes greater than 48 (areas close to the poles), continuous twilight may occur namely continuous twilight and dawn light may even occur at late night so that early dawn and sunset to begin and break the fasting can not be determined. Responding to the issue, some argues that the practice of prayer is worshiped with people who fall asleep while fasting is replaced in other months. Another opinion suggests that to follow the time in the surrounding normal area or follow the areas where the sharia came down, namely Mecca and Medina. Those opinions have imperfect weaknesses in performing Ramadan because it can happen one full month of Ramadan that people can not carry out fasting and the prayer times between different regions vary due to the ever-moving circulation of the Sun. Meanwhile, Thomas Djamaluddin offers a time interpolation solution by taking into account the time before and after the extreme time so that the obligation of five-time prayers can still be held every day and fasting is held in Ramadan. However, this opinion has a weakness that the implementation of isya and subuh prayer and fasting is not appropriate to shari'ah because it is held in the light of twilight is still visible.Keyword: Prayer, Fasting, Areas Near The Poles.

Wave hindcast in the North Pacific area considering the propagation of surface disturbances

Ocean surface waves in the North Pacific area are affected by storm winds. It is necessary to consider the movement of storms to predict waves. The impact of a time interpolation method for winds that considers the propagation of surface disturbances on ocean wave prediction from 2005 to 2006 in the North Pacific area is demonstrated. It is possible to interpolate surface winds, even when there are multiple cyclones and anticyclones moving in different directions at different distances. This method will be useful for wind fields with increasing amounts of spatial information. The predicted wave heights and periods from the linearly interpolated winds and the winds predicted using this new method are compared with in-situ observations from several moored buoys. The predicted wave heights are also compared with those from several drifting buoys in the northwestern Pacific. The improvement of the wave height and period prediction is evident in the case where the difference in the predicted wave parameters between the linear interpolation and the present method is large. The improvement of the wave height and period prediction is statistically significant at more than 95% in most cases. It is shown that the wave height and period prediction can be improved by improving the time interpolation method; however, the improvement of the wave direction prediction is not evident.

3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.

Implementation of a Parallel GPU-Based Space-Time Kriging Framework

In the study of spatiotemporal geographical phenomena, the space–time interpolation method is widely applied, and the demands for computing speed and accuracy are increasing. For nonprofessional modelers, utilizing the space–time interpolation method quickly is a challenge. To solve this problem, the classical ordinary kriging algorithm was selected and expanded to a spatiotemporal kriging algorithm. Using the OpenCL framework to integrate central processing unit (CPU) and graphic processing unit (GPU) computing resources, a parallel spatiotemporal kriging algorithm was implemented, and three experiments were conducted in this work to verify the results. The results indicated the following: (1) when the size of the prediction point dataset is consistent, the performance of the method is robust with the increasing size of the observation point dataset; (2) the acceleration effect of the parallel method increases with an increased number of predicted points. Compared with the original sequential program, the implementation of the improved parallel framework showed a 3.23 speedup, which obviously shortens the interpolation time; (3) when cross-validating the temperature data in the Beijing Tianjin Hebei region, the space–time acceleration model provides a better fit than traditional pure space interpolation.

A 256-channel, high throughput and precision time-to-digital converter with a decomposition encoding scheme in a Kintex-7 FPGA

Field Programmable Gate Arrays (FPGAs) made with 28 nm and more advanced process technology have great potentials for implementation of high precision time-to-digital convertors (TDC), because the delay cells in the tapped delay line (TDL) used for time interpolation are getting smaller and smaller. However, the bubble problems in the TDL status are becoming more complicated, which make it difficult to achieve TDCs on these chips with a high time precision. In this paper, we are proposing a novel decomposition encoding scheme, which not only can solve the bubble problem easily, but also has a high encoding efficiency. The potential of these chips to realize TDC can be fully released with the scheme. In a Xilinx Kintex-7 FPGA chip, we implemented a TDC system with 256 TDC channels, which doubles the number of TDC channels that our previous technique could achieve. Performances of all these TDC channels are evaluated. The average RMS time precision among them is 10.23 ps in the time-interval measurement range of (0–10 ns), and their measurement throughput reaches 277 M measures per second.

An 18-ps TDC using timing adjustment and bin realignment methods in a Cyclone-IV FPGA.

The method commonly used to produce a field-programmable gate array (FPGA)-based time-to-digital converter (TDC) creates a tapped delay line (TDL) for time interpolation to yield high time precision. We conduct timing adjustment and bin realignment to implement a TDC in the Altera Cyclone-IV FPGA. The former tunes the carry look-up table (LUT) cell delay by changing the LUT's function through low-level primitives according to timing analysis results, while the latter realigns bins according to the timing result obtained by timing adjustment so as to create a uniform TDL with bins of equivalent width. The differential nonlinearity and time resolution can be improved by realigning the bins. After calibration, the TDC has a 18 ps root-mean-square timing resolution and a 45 ps least-significant bit resolution.

Research on Intelligent Control System of Manipulator Based on Multi Degree of Freedom

In order to improve the accuracy and flexibility of forestry robot mechanical arm, the mechanical arm mathematical model is constructed in this paper by Denavit–Hartenberg parameter method, and the inverse solution algorithm based on Newton iteration method is designed. On this basis, in the joint space, three times interpolation and five times interpolation algorithm are designed for path planning. Then, the hardware framework and software system of mechanical arm control system are designed, and the simulation experiment is carried out, to test the precision and error of mechanical arm. The results showed that the motor rotation error of the seven freedom mechanical arm control system is 0.025%, the position error of the mechanical arm is 5%, and the repetitive positioning error of the mechanical arm is less than 7 mm. Based on the above findings, it is concluded that the error of the end motion is within the allowable range, and the desired design requirements are completed.

A Multi-Chain Merged Tapped Delay Line for High Precision Time-to-Digital Converters in FPGAs

Field programmable gate array (FPGA)-based time-to-digital converters (TDCs) use a tapped delay line (TDL) for time interpolation to yield a sub-clock time resolution. The granularity and uniformity of delay cells in TDL determines achievable TDC time precision. To gain small delay cells in TDL, we propose a new TDL architecture by merging multiple conventional delay chains to obtain very fine intrinsic cell delays. The uniformity of these cell delays is improved by a bin decimation method so that the time interpolation with the TDL has minimum nonlinearity error. To evaluate the performance improvement using the new TDL architecture, two identical TDC channels with 1-chain, 2-chain, and 4-chain merged TDLs, respectively, were implemented in a Xilinx Kintex-7 FPGA. For time-intervals in the range from 0 to 50 ns, the average RMS precisions of these TDC pairs were measured as 8.5 ps, 5.3 ps, and 4.3 ps, respectively. The test results confirm that the proposed TDL architecture is an FPGA-independent effective method for boosting TDC precision without significant increase in hardware complexity and logic resource consumption.