Time-averaged Estimates Research Articles

Optimization of Rotor Tip Cavity Shapes for Mitigating Aerodynamic Tip Leakage Losses

Rotor blade tip leakage loss influences turbine stage efficiency. A parametric optimization method based on five design variables combined with Non-Linear Programming by Quadratic Lagrangian to optimize the turbine efficiency estimated from computational fluid dynamics analysis has been used to obtain estimates of the optimal cavity depth and split rib location within the tip cavity, which appears to improve the stage efficiency by 1.5%. Besides the design point, the influence of the optimized tip cavity shape impacts the performance of the rotor at different rotational speeds and pressure ratios. In this study, by comparing different tip cavity shapes, it is shown that a dual-cavity shape on the rotor blade tip with a stream-direction split rib can effectively control the air flow bending angle inside the tip clearance and improve the aerodynamic performance. The compressible unsteady Reynolds-averaged Navier–Stokes model is used to verify the adaptability of the optimized tip cavity shape to periodic wake disturbances, and the results demonstrate that the time-averaged estimate of the efficiency can be improved by 1.3% compared to that of the flat rotor tip.

Time-averaged concentration estimation of uraemic toxins with different removal kinetics: a novel approach based on intradialytic spent dialysate measurements.

Kt/Vurea is the most used marker to estimate dialysis adequacy; however, it does not reflect the removal of many other uraemic toxins, and a new approach is needed. We have assessed the feasibility of estimating intradialytic serum time-averaged concentration (TAC) of various uraemic toxins from their spent dialysate concentrations that can be estimated non-invasively online with optical methods. Serum and spent dialysate levels and total removed solute (TRS) of urea, uric acid (UA), indoxyl sulphate (IS) and β2-microglobulin (β2M) were evaluated with laboratory methods during 312 haemodialysis sessions in 78 patients with four different dialysis treatment settings. TAC was calculated from serum concentrations and evaluated from TRS and logarithmic mean concentrations of spent dialysate (MlnD). Mean (± standard deviation) intradialytic serum TAC values of urea, UA, β2M and IS were 10.4±3.8mmol/L, 191.6±48.1µmol/L, 13.3±4.3mg/L and 82.9±43.3µmol/L, respectively. These serum TAC values were similar and highly correlated with those estimated from TRS [10.5±3.6mmol/L (R 2=0.92), 191.5±42.8µmol/L (R 2=0.79), 13.0±3.2mg/L (R 2=0.59) and 82.7±40.0µmol/L (R 2=0.85)] and from MlnD [10.7±3.7mmol/L (R 2=0.92), 191.6±43.8µmol/L (R 2=0.80), 12.9±3.2mg/L (R 2=0.63) and 82.2±38.6µmol/L (R 2=0.84)], respectively. Intradialytic serum TAC of different uraemic toxins can be estimated non-invasively from their concentration in spent dialysate. This sets the stage for TAC estimation from online optical monitoring of spent dialysate concentrations of diverse solutes and for further optimization of estimation models for each uraemic toxin.

Development of a Flow Phantom for Transcranial Doppler Ultrasound Quality Assurance.

Anecdotal evidence was recently brought to our attention suggesting a potential difference in velocity estimates between transcranial Doppler (TCD) systems when measuring high velocities (∼200 cm/s) close to the threshold for sickle cell disease stroke prevention. As we were unable to identify a suitable commercial TCD phantom, a middle cerebral artery (MCA) flow phantom was developed to evaluate velocity estimates from different devices under controlled conditions. Time-averaged velocity estimates were obtained using two TCD devices: a Spencer Technologies ST3 Doppler system (ST3 PMD150, Spencer Technologies, Seattle, WA, USA) and a DWL Dopplerbox (DWL Compumedics, SN-300947, Singen, Germany). These were compared with velocity estimates obtained using a Zonare duplex scanner (Zonare Medical Systems, Mountain View, CA, USA), with timed collection of fluid as the gold standard. Bland-Altman analysis was performed to compare measurements between devices. Our tests confirmed that velocities measured with the DWL TCD system were +4.1 cm/s (+3.7%; limits of agreement [LoA]: 2%, 5%; p=0.03) higher than the Spencer system when measuring a velocity 110 cm/s and +12 cm/s higher (+5.7 %; LoA: 4.8%, 6.6%; p=0.03) when measuring velocities of 210 cm/s, close to the diagnostic threshold for stroke intervention. We found our MCA phantom to be a valuable tool for systematically quantifying differences in TCD velocity estimates between devices, confirming that the DWL system gave consistently higher readings than the Spencer ST3 system. Differences become more pronounced at high velocities, which explains why they were not identified earlier. Our findings have clinical implications for centers using TCD to monitor patients with sickle cell disease, as extra care may be needed to adjust for bias between manufacturers when making treatment decisions about children with sickle cell with velocities close to the diagnostic threshold.

Beach Profile, Water Level, and Wave Runup Measurements Using a Standalone Line-Scanning, Low-Cost (LLC) LiDAR System

A prototype rapidly deployable, Line-scanning, Low-Cost (LLC) LiDAR system (USD 400 per unit; 2020) was developed to measure coastal hydro-morphodynamic processes. A pilot field study was conducted at the U.S. Army Corps of Engineers, Field Research Facility (FRF) in Duck, North Carolina, USA to evaluate the efficacy of the LLC LiDAR in measuring beach morphology, wave runup, and free-surface elevations against proven approaches. A prototype LLC LiDAR collected continuous cross-shore line scans for 25 min of every half hour, at ~7 revolutions/s and ~1.3° angular resolution, at two locations (one day at each location), spanning 12 m (i) on the backshore berm (35 scans; Series B) and (ii) in the swash/inner surf zone (28 scans; Series C). LLC LiDAR time-averaged beach profiles and wave runup estimates were compared with the same quantities derived from the continuously sampling terrestrial LiDAR scanner installed atop the dune at the FRF (DUNE LiDAR). The average root-mean-square difference (RMSD) between 17 (6) time-averaged LLC and DUNE LiDAR beach profiles was 0.045 m (0.031 m) with a standard deviation of 0.004 m (0.002 m) during Series B (Series C). Small-scale (cm) swash zone bed level changes were resolved over 5-min increments with the LLC LiDAR. The RMSD between LLC- and DUNE LiDAR-derived wave runup excursions over two 25-min segments was 0.542 m (cross-shore) and 0.039 m (elevation) during the rising tide and 0.366 m (cross-shore) and 0.032 m (elevation) during the falling tide. Between 72–79% of the LLC LiDAR wave runup data were more accurate than the RMSD values, thereby demonstrating the LLC LiDAR is an effective, low-cost instrument for measuring wave runup and morphodynamic processes. Co-located water levels were measured with a continuously sampling (16 Hz) RBRsolo3 D|wave16 pressure logger during Series C. LLC LiDAR free-surface elevations at the nadir during one high tide (4.5 h) compared well with pressure-derived free-surface elevations (RMSD = 0.024 m, R2 = 0.85).

Optimal Transmission-Constrained Scheduling of Spatio-Temporally Dependent Observations Using Age-of-Information

This paper proposes an optimal scheduling policy for broadcasting spatio-temporally dependent observations to two remote estimators over a finite time horizon. The system comprises a scheduler that can broadcast one observation from one out of two spatio-temporally dependent processes at each time instant. Since the number of broadcasting instants for each sensor is constrained, the scheduler must plan the broadcasting that minimizes the time-averaged estimation error. As the scheduler cannot observe the measurements, it determines the expected estimation error based on the age-of information (AoI). Using AoI as a state variable, we derive a set of optimal scheduling policies that minimizes the average mean squared error (MSE) for any given time horizon. The policies provide the optimal number of transmission instances for each sensor and time-varying AoI thresholds for when to be scheduled. By studying how the MSE evolves with respect to the AoI generated by a given scheduling sequence, we can obtain an optimal policy using a low-complexity numerical method. Numerical results validate the theory and demonstrate how utilizing spatio-temporal dependencies together with AoI can enhance the estimation accuracy in a communication-constrained sensor network.

Time-averaged low-density lipoprotein cholesterol lowering with evolocumab: Pooled analysis of phase 2 trials

LDL-C is the pivotal risk factor for atherosclerotic cardiovascular disease, and the benefit from LDL-C lowering is proportional to the magnitude of reduction. Clinical trials demonstrate that evolocumab reduces LDL-C levels by approximately 60% when measured at the trough of drug effect, which may underestimate cumulative LDL-C reduction. We obtained a time-averaged estimate of LDL-C lowering that included both peaks and troughs. Pooled analysis of 5 phase 2 trials included patients with hypercholesterolemia who received placebo or evolocumab (140 mg every 2 weeks [Q2W] or 420 mg monthly [QM]). Percent changes from baseline LDL-C and free serum PCSK9 were averaged across weeks 9–12. In 372 patients, time-averaged percent reduction from baseline in LDL-C with evolocumab vs placebo was 67.6% (95% CI: 63.9–71.3) with Q2W dosing and 65.0% (95% CI: 60.7–69.3) with QM dosing. The time-averaged measure yielded LDL-C reductions for evolocumab that exceeded measurements at the end of dosing intervals and may provide a better estimate of cardiovascular benefit during long-term therapy.

Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations.

We present a method to facilitate Monte Carlo simulations in the grand canonical ensemble given a target mean particle number. The method imposes a fictitious dynamics on the chemical potential, to be run concurrently with the Monte Carlo sampling of the physical system. Corrections to the chemical potential are made according to time-averaged estimates of the mean and variance of the particle number, with the latter being proportional to thermodynamic compressibility. We perform a variety of tests, and in all cases find rapid convergence of the chemical potential-inexactness of the tuning algorithm contributes only a minor part of the total measurement error for realistic simulations.

Normalization in dynamic speckle analysis for non-destructive monitoring of speed of processes

The paper is dedicated to analysis of normalized intensity-based pointwise algorithms for processing dynamic speckle images with spatially varying speckle statistics in non-destructive visualization of regions of faster or slower changes across an object. Both existing and newly proposed algorithms are analyzed. Extraction of speed of changes is done by acquiring correlated in time speckle images formed on the object surface under laser illumination. The studied algorithms have been applied to simulated low and high contrast speckle data. Their performance has been compared to processing of binary patterns as another approach for dealing with varying speckle statistics in the acquired images. The efficiency of the algorithms have been checked on the experimental data, including data in a compressed format. We have proven that the algorithms with normalization at successive instants by a sum of two intensities or a single intensity outperform as a whole the algorithms which apply the time-averaged estimates of the mean value and the variance of speckle intensity.

A Variable Step‐Size Leaky LMS Algorithm

The leaky LMS algorithm has been extensively studied because of its control of parameter drift. This unexpected parameter drift is linked to the inadequacy of excitation in the input sequence. And generally leaky LMS algorithms use fixed step size to force the performance of compromise between the fast convergence rate and small steady‐state misalignment. In this paper, variable step‐size (VSS) leaky LMS algorithm is proposed. And the variable step‐size method combines the time average estimation of the error and the time average estimation of the normalized quantity. Variable step‐size method proposed incorporating with leaky LMS algorithm can effectively eliminate noise interference and make the early convergence, and final small misalignments are obtained together. Simulation results demonstrate that the proposed algorithm has better performance than the existing variable step‐size algorithms in the unexcited environment. Furthermore, the proposed algorithm is comparable in performance to other variable step‐size algorithms under the adequacy of excitation.

Quantifying dispersal variability among nearshore marine populations.

Dispersal drives diverse processes from population persistence to community dynamics. However, the amount of temporal variation in dispersal and its consequences for metapopulation dynamics is largely unknown for organisms with environmentally driven dispersal (e.g., many marine larvae, arthropods and plant seeds). Here, we used genetic parentage analysis to detect larval dispersal events in a common coral reef fish, Amphiprion clarkii, along 30km of coastline consisting of 19 reef patches in Ormoc Bay, Leyte, Philippines. We quantified variation in the dispersal kernel across seven years (2012-2018) and monsoon seasons with 71 parentage assignments from 791 recruits and 1,729 adults. Connectivity patterns differed significantly among years and seasons in the scale and shape but not in the direction of dispersal. This interannual variation in dispersal kernels introduced positive temporal covariance among dispersal routes that theory predicts is likely to reduce stochastic metapopulation growth rates below the growth rates expected from only a single or a time-averaged connectivity estimate. The extent of variation in mean dispersal distance observed here among years is comparable in magnitude to the differences across reef fish species. Considering dispersal variation will be an important avenue for further metapopulation and metacommunity research across diverse taxa.

The impact of temporal variability in light-climate on time-averaged primary production and a phytoplankton bloom in a well-mixed estuary

Phytoplankton primary production (PP) in turbid estuaries is often limited by light-availability. Two important factors altering light-climate are solar irradiance at the water surface and exponential light-extinction coefficient within the water column. Additionally, the depth of the water body changes the light-climate and corresponding PP by altering the ratio of the euphotic and mixing depth in a well-mixed estuary. These three parameters are highly variable yet are often assumed to be constant by both experimental scientists and modelers because of a lack of data or to reduce complexity. Because assuming constant parameters introduces an error, we utilize an idealized model of depth-integrated primary production to analyze the (individual) impact of temporal variability in these three parameters. We only consider the main tidal and solar constituents in temporal variability of the forcings and apply a second-order moment approximation to analyze the bias introduced to time-averaged PP estimates by neglecting temporal fluctuations. We demonstrate that the sign and magnitude of this bias are system-specific and depend on two non-dimensional parameters that characterize the system. The first is equivalent to the ratio of mixing and photic depth. The second accounts for typical incident irradiance and the photosynthetic parameters of the phytoplankton population present. To demonstrate the applicability of our approach, we apply the model to two cases in the Scheldt estuary (Belgium) in the brackish and freshwater part. In the first application, we study the impact of fluctuations on phytoplankton in dynamic equilibrium, where biomass is assumed to be constant. We show that variability in solar irradiance has the largest impact on time-averaged PP in dynamic equilibrium, resulting in a 30 percent decrease compared to time-invariant forcing. By comparing with a numerical integrator, we show that a second-order moment approximation correctly predicts the order of magnitude of the impact of temporal variability of the individual parameters. In the second application, we study the impact of fluctuations on unbounded exponential phytoplankton growth. Also here, fluctuations in solar irradiance have the largest impact and lead to a significant decrease in exponential growth. In this case study, we show that temporal fluctuations delay the onset of the biomass by two weeks and decrease the biomass by a factor 14 after two weeks compared to time invariant forcing. Additionally, we show that the temporal fluctuations induce low-frequency variability in phytoplankton biomass with similar periodicity as the spring-neap cycle, making it difficult to observe these phenomena in real-world time series.

Numerical study of extreme mechanical force exerted by a turbulent flow on a bluff body by direct and rare-event sampling techniques

This study investigates, by means of numerical simulations, extreme mechanical force exerted by a turbulent flow impinging on a bluff body, and examines the relevance of two distinct rare-event algorithms to efficiently sample these events. The drag experienced by a square obstacle placed in a turbulent channel flow (in two dimensions) is taken as a representative case study. Direct sampling shows that extreme fluctuations are closely related to the presence of a strong vortex blocked in the near wake of the obstacle. This vortex is responsible for a significant pressure drop between the forebody and the base of the obstacle, thus yielding a very high value of the drag. Two algorithms are then considered to speed up the sampling of such flow scenarii, namely the AMS and the GKTL algorithms. The general idea behind these algorithms is to replace a long simulation by a set of much shorter ones, running in parallel, with dynamics that are replicated or pruned, according to some specific rules designed to sample large-amplitude events more frequently. These algorithms have been shown to be relevant for a wide range of problems in statistical physics, computer science, biochemistry. The present study is the first application to a fluid-structure interaction problem. Practical evidence is given that the fast sweeping time of turbulent fluid structures past the obstacle has a strong influence on the efficiency of the rare-event algorithm. While the AMS algorithm does not yield significant run-time savings as compared to direct sampling, the GKTL algorithm appears to be effective to sample very efficiently extreme fluctuations of the time-averaged drag and estimate related statistics such as return times.

Radiation energy losses in a single chamber three phase plasma torch with rod electrodes

The paper deals with the results of the study of the plasma energy loss in a chamber of the three phase alternating current arc plasma torch at pressures above atmospheric. It is shown that the loss due to radiation takes the main share. A time-averaged estimation of the radiation power per unit length of the arcs and its dependence on pressure was obtained based on the results of calorimetric measurements of the heat flux into the end part of the plasma torch. The dependence of the fraction of energy loss by radiation versus the total loss in the plasma torch chamber depending on the pressure and gas flow rate are presented. The dependence of the efficiency of the plasma torch versus the gas flow rate and pressure is also given. Studies were conducted on a plasma torch over the power range from 50 to 200 kW. The working gas was nitrogen.

Incorporating two coupling noises into a nonlinear competitive system with saturation effect

In this paper, a novel stochastic two-species competitive system with saturation effect is formulated, in which there exist two noise resources and their coupling mode is relatively complex and every noise source has effect on the intrinsic growth rates of both species. With the help of some suitable Lyapunov functions, sufficient conditions for stochastic permanence are established as exponential extinction, extinction, permanence in time average and asymptotic pathwise estimation of system. The effect of coupling noise on the asymptotic behaviors of the populations is shown.

Continuous, Near-Bed Current Velocity Estimation Using Pressure and Inertial Sensing

The near-bed velocity is a key physical parameter in hydrological, ecological and geomorphological studies. Considering climate change, measurement methods capable of providing continuous observations are needed to assess and predict the effects of increasing uncertainty. Therefore, a technology gap remains for continuous near-bed measurements. To address this gap, we have developed a multimodal flow measurement device, the hydromast. The hydromast uses a combination of pressure and inertial sensing to measure the near-bed (< 30 cm) velocity. We have previously shown that the device can be used to classify river hydromorphological units. Encouraged by these results, we now show that the same device is also capable of continuously measuring the near-bed velocity in rivers. Ten hydromast prototypes were built and calibrated over the range of 0.01 – 2 m/s in a large-scale laboratory tow tank and validated under natural conditions (0.35 – 1.2 m/s) using 118 turbulent flow measurements in a river. It was found that the streamwise, time-averaged velocity mean estimation error from the hydromast in continuous tests with different methods was 0.095 m/s, as compared with a state-of-the-art acoustic Doppler velocimeter. The contribution of this study is a new method for continuous near-bed velocity measurements, verified with turbulent field data from a river.

The dynamics of passive feathering rotation in hovering flight of bumblebees

The fluid–structure interaction problem of the flapping wings of bumblebees is considered, with focus on the action of elastic joints between wings and body. Morphological measurements and kinematic reconstruction of the wing motion using synchronized high-speed video recordings are described. They provide the necessary input data for numerical modeling. In particular, for the first time, the moments of inertia of bumblebee’s wing are determined using realistic mass distribution. A computational fluid dynamics solver is combined with a dynamical model that describes the wing motion. The model consists of the wings approximated as flat plates, connected with the body by elastic hinges. The results of high-resolution numerical simulations are presented. The hinged plate model produces realistic feathering motion and accurate time-average estimates of the aerodynamic performance in hover, despite some discrepancy in the instantaneous values of aerodynamic forces compared with the fully prescribed model. A parameter sweep reveals that the hinge is not exactly tuned to maximum efficiency during hovering flight, but slightly offset away from the maximum.

Power-tracking control for cross-flow turbines

For economic reasons, above a certain water speed, it is desirable for current turbines to maintain a constant power output. This requires a control strategy to shed power. Here, such a strategy is evaluated through simulation and laboratory experiment for a helically bladed turbine with four blades and a straight-bladed turbine with two blades. These are contrasting cases because hydrodynamic torque produced by the straight-bladed turbine has a substantially more azimuthal phase variability than the helically bladed turbine. For practical implementation, a control algorithm is desired that requires only a time-average characteristic performance curve and estimates of angular velocity and control torque. Additionally, the transition between power maximizing and power tracking regimes should be smooth and automatic. The controller can be further constrained to only apply a resistive torque to the turbine. A control strategy satisfying these constraints is shown experimentally to achieve these objectives for both types of turbines at a variety of power set points. The power-tracking error (&amp;lt;3%) is primarily at the blade passage frequency for the straight-bladed turbine and at the rate of turbine rotation for the helical turbine. While partially a consequence of how the generator drive is tuned, comparison to simulation indicates that perfect power-tracking is not generally possible even under ideal conditions for a fixed-pitch, cross-flow turbine using purely resistive torque control.

Time average estimation in the fraction-of-time probability framework

Abstract The problem of time average estimation is addressed in the fraction-of-time probability framework. In this approach, the observed signal is modeled as a single function of time rather than as a sample path of a stochastic process. Under mild regularity assumptions on temporal cumulants of the signal, a central limit theorem (CLT) is proved for the normalized error of the time average estimate, where the normalizing factor is the square root of the observation interval length. This rate of convergence is the same as that obtained in the classical stochastic approach, but is derived here without resorting to mixing assumptions. That is, no ergodicity hypothesis is needed. Examples of functions of interest in communications are provided whose time average estimate satisfies the CLT. For the class of the almost-periodic functions, a non normal limit distribution for the normalized error of the time average estimate can be obtained when the normalizing factor equals the observation interval length. The limit distribution, nevertheless, depends on the sequence adopted to perform the limit, a result that cannot be obtained in the classical stochastic approach. Numerical examples illustrate the theoretical results and an application to test the presence of a nonzero-mean cyclostationary signal is presented.

Weak and Strong Solutions of the 3D Navier–Stokes Equations and Their Relation to a Chessboard of Convergent Inverse Length Scales

Using the scale invariance of the Navier-Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the $3D$ Navier-Stokes equations, an infinite `chessboard' of estimates for these inverse length scales is displayed in terms of labels $(n,\,m)$ corresponding to $n$ derivatives of the velocity field in $L^{2m}$. The $(1,\,1)$ position corresponds to the inverse Kolmogorov length $Re^{3/4}$. These estimates ultimately converge to a finite limit, $Re^3$, as $n,\,m\to \infty$, although this limit is too large to lie within the physical validity of the equations for realistically large Reynolds numbers. Moreover, all the known time-averaged estimates for weak solutions can be rolled into one single estimate, labelled by $(n,\,m)$. In contrast, those required for strong solutions to exist can be written in another single estimate, also labelled by $(n,\,m)$, the only difference being a factor of 2 in the exponent. This appears to be a generalisation of the Prodi-Serrin conditions for $n\geq 1$.

Radiative cooling of swept-up gas in AGN-driven galactic winds and its implications for molecular outflows

We recently used hydro-chemical simulations to demonstrate that molecular outflows observed in luminous quasars can be explained by molecule formation within the AGN wind. However, these simulations cover a limited parameter space, due to their computational cost. We have therefore developed an analytic model to follow cooling in the shocked ISM layer of an AGN wind. We explore different ambient densities ($1-10^{4} \, \rm{cm}^{-3}$), density profile slopes ($0-1.5$), AGN luminosities ($10^{44}-10^{47} \, \rm{erg} \, \rm{s}^{-1}$), and metallicities ($0.1-3 \rm{Z}_{\odot}$). The swept up gas mostly cools within ~1 Myr. Based on our previous simulations, we predict that this gas would produce observable molecular outflows. The instantaneous momentum boost initially increases as the outflow decelerates. However, it reaches a maximum of $\approx$20, due to work done against the gravitational potential. The predicted time-averaged observational estimate of the molecular outflow momentum boost reaches a maximum of $\approx1-2$, partly due to our assumed molecular fraction, 0.2, but also because the instantaneous and observational, time-averaged definitions are not equivalent. Thus recent observational estimates of order unity momentum boosts do not necessarily rule out energy-driven outflows. Finally, we find that dust grains are likely to re-form by accretion of metals after the shocked ISM layer has cooled, assuming that a small fraction of dust grains swept up after this layer has cooled are able to mix into the cool phase, and assuming that grain growth remains efficient in the presence of the strong AGN radiation field. This would enable rapid molecule formation, as assumed in our models.