Function Of Sampling Rate Research Articles

Numerical Analysis of Error From Sampling of Alternatives in Logit-Based Demand Forecasting Models with Massive Choice Sets

Use of the multinomial logit (MNL) functional form is widespread in transportation and land use demand modeling. As the state-of-the-art evolves away from aggregate forecasting and toward activity-based models and microsimulation, MNL models are being asked to accommodate increasingly large choice sets. Different strategies exist to address the challenge of estimating models with very large choice sets, but perhaps none is as commonly employed as sampling of alternatives. The effect of sampling of alternatives on parameter estimation has received considerable attention in the scientific literature. Yet comparatively little quantitative research exists that examines the issues that arise when the same sampling strategies are applied in the context of forecasting. In this study we conducted an analysis of the effect of sampling of alternatives in discrete choice models for disaggregate location choice forecasting. First, a novel measure of forecast error was defined and then used to quantify the extent of the problem as a function of sample rate, model error, and size of the universe of alternatives. Finally, we explored the potential for strategic sampling techniques to reduce the error observed under simple random sampling. In general, we found that the proportion of aggregate demand that was misallocated owing to sampling of alternatives was actually reduced as the size of the universe of alternatives increased. Additionally, simple random sampling was shown to outperform importance sampling in most scenarios. These findings suggest that error resulting from random sampling of alternatives is less of a problem for logit-based microsimulation models than previously assumed.

Root Locus of Zeros of Discrete Time Systems as a Function of Sample Rate

Root locus plots are one of the basic design tools in classical control. They help the designer tune control gains which appear linearly in the coefficients of the closed loop characteristic polynomial. And they give considerable intuition to the designer, based on the simple rules that root loci must follow. When designing a control system, one wants to know where the zeros are, but when designing a digital control system new issues appear. The original zero locations when mapped to discrete time are functions of the new parameter, the sample time T (as well as the pole locations). In addition, new zeros are usually introduced by the discretization process. The purpose of this paper is to give a general understanding of the nature of root loci of discrete time transfer function zeros as a function of this parameter T. We consider the complete range of values from T equal zero to infinity to understand the full plot. Reasonable sample rates will only use part of the plots. The characteristic polynomial coefficients are nonlinear functions of T so the usual root locus rules do not apply. One can be amazed at how the usual root locus rules are repeatedly violated, and what new kinds of unexpected behavior can be observed.

SU‐C‐207A‐02: Proton Radiography Using Pencil Beam Scanning and a Novel, Low‐Cost Range Telescope

Purpose:While the energy of therapeutic proton beams can be adjusted to penetrate to any given depth in water, range uncertainties arise in patients due in part to imprecise knowledge of the stopping power of protons in human tissues [1]. Proton radiography is one approach to reduce the beam range uncertainty [2], thereby allowing for a reduction in treatment margins and dose escalation.Methods:The authors have adapted a novel detector technology based on Micromesh Gaseous Structure (“Micromegas”) for proton therapy beams and have demonstrated fine spatial and time resolution of magnetically scanned proton pencil beams, as well as wide dynamic range for dosimetry [3]. The authors have constructed a prototype imaging system comprised of 5 Micromegas layers. Proton radiographs were obtained downstream of solid water assemblies. The position‐sensitive monitor chambers in the IBA proton delivery nozzle provide the beam entrance position.Results:Our technique achieves spatial resolution as low as 300 µm and water‐equivalent thickness (WET) resolution as good as 0.02% (60 µm out of 31 cm total thickness). The dose delivered to the patient is kept below 2 cGy. The spatial resolution as a function of sample rate and number of delivered protons is found to be near the theoretical Cramer‐Rao lower bound. By extrapolating the CR bound, we argue that the imaging dose could be further lowered to 1 mGy, while still achieving submillimeter spatial resolution, by achievable instrumentation and beam delivery modifications.Conclusion:For proton radiography, high spatial and WET resolution can be achieved, with minimal additional dose to patient, by using magnetically scanned proton pencil beams and Micromegas detectors.

WE‐EF‐303‐08: Proton Radiography Using Pencil Beam Scanning and Novel Micromegas Detectors

Purpose:While the energy of therapeutic proton beams can be adjusted to penetrate to any given depth in water, range uncertainties arise in patients due in part to imprecise knowledge of the stopping power of protons in human tissues. Proton radiography is one approach to reduce the beam range uncertainty, thereby allowing for a reduction in treatment margins and dose escalation.Methods:The authors have adapted a novel detector technology based on Micromesh Gaseous Structure (“Micromegas”) for proton therapy beams and have demonstrated fine spatial and time resolution of magnetically scanned proton pencil beams, as well as wide dynamic range for dosimetry. In this work, proton radiographs were obtained using Micromegas 2D planes positioned downstream of solid water assemblies. The position‐sensitive monitor chambers in the IBA proton delivery nozzle provide the beam entrance position.Results:Radiography with Micromegas detectors and actively scanned beams provide spatial resolution of up to 300 µm and water‐equivalent thickness (WET) resolution as good as 0.02% (60 µm out of 31 cm total thickness), with the dose delivered to the patient kept below 2 cGy. The spatial resolution as a function of sample rate and number of delivered protons is found to be near the theoretical Cramer‐Rao lower bound. Using the CR bound, we argue that the imaging dose could be further lowered to 1 mGy, while still achieving sub‐mm spatial resolution, by relatively simple instrumentation upgrades and beam delivery modifications.Conclusion:For proton radiography, high spatial and WET resolution can be achieved, with minimal additional dose to patient, by using magnetically scanned proton pencil beams and Micromegas detectors.

Development of methodology to optimize management of failed fuels in light water reactors

Fuel cladding is one of the key components in a fission reactor that confines radioactive materials inside a fuel tube. During reactor operation, however, cladding is sometimes breached, and radioactive materials leak from the fuel pellet into the coolant water through the breach. The primary coolant water is therefore monitored so that any leak is quickly detected; coolant water is periodically sampled, and the concentration of radioactive iodine 131 (I-131), for example, is measured. Depending on the measured leakage concentration, the faulty fuel assembly with leaking rod is removed from the reactor and replaced immediately or at the next refueling. In the present study, an effort has been made to develop a methodology to optimize the management for replacement of faulty fuel assemblies due to cladding failures using measured leakage concentration. A model numerical equation is proposed to describe the time evolution of an increase in I-131 concentration due to cladding failures and is then solved using the Monte Carlo method as a function of sampling rate. Our results indicate that, to achieve rationalized management of failed fuels, higher resolution to detect a small amount of I-131 is not necessarily required, but more frequent sampling is favorable.

Performance Evaluation of Displacement Estimators for Real-Time Ultrasonic Strain and Blood Flow Imaging With Improved Spatial Resolution

Ultrasonic strain and blood flow imaging has great potential to improve early tumor detection. Both methods have the same task of estimating echo signal displacements. To be able to resolve tissue stiffness and vascularity of tumors while they are still small, spatial resolution must be improved. Moreover, ultrasonic real-time imaging is vital in clinical practice. In this paper, we evaluate the estimation performances of one novel and several established displacement estimators with real-time capability and compare these with results from cross-correlation-based standard estimators when echo signals that are typically available with a commercial ultrasound scanner set to yield the highest spatial resolution are used. Estimation errors are investigated as a function of sampling rate, signal-to-noise ratio, displacement and strain magnitudes, and frequency-dependent tissue attenuation. Results are from simulations using the FIELD II program to generate ultrasonic echo signals and tissue-mimicking phantom experiments using a Voluson 730 medical ultrasound scanner (GE medical systems Kretztechnik, Austria) that is equipped with a digital research interface that enables the export of beam-formed radio frequency echo data.

Fade Dynamics on Earth-Space Paths at Ku-Band in Fukuoka, Japan Fade-Slope Evaluation, Comparison, and Model

Using an efficient approach for data analysis, we discuss the evaluation of the fade slope as a function of sampling rate. From our analysis, we found that the standard deviation of the fade slope, as a function of attenuation, has a maximum and does not match the model recommended in ITU-R P.1623. Based on this observation, an improved fade-slope model is proposed.

Flux observer for induction machine control. Part I - Sensitivity analysis as a function of sampling rate and parameters variations

In the last decades, many vector control techniques have been developed for induction machine to increase their dynamic performances. But they are based on an accurate estimation of flux variables, which are not measurable in conventional induction machines. So, observer strategies are used in induction machine controls. Complex algorithms have been developed, but their long calculation time does not allow a simple implementation in digital form. For this reason, reduced-order observers are often used when a real-time estimation is implemented. If these structures lead to better flux estimations than in the case of an open-loop model, their convergence gains have to be determined and they are sensitive to the parameters value. The authors present a new analytical method to elaborate a reduced-order observer. The influence of the sampling rate is taken into account and the paper investigates the optimal gain, which minimise the sensitivity to the parameters value. In order to measure the observer robustness, the authors define two criteria, which are computed in steady state: the orientation error and the modulus error of the rotor flux. Some examples illustrate the theory and their calculation results are presented.

Bark and ERB bilinear transforms

Use of a bilinear conformal map to achieve a frequency warping nearly identical to that of the Bark frequency scale is described. Because the map takes the unit circle to itself, its form is that of the transfer function of a first-order allpass filter. Since it is a first-order map, it preserves the model order of rational systems, making it a valuable frequency warping technique for use in audio filter design. A closed-form weighted-equation-error method is derived that computes the optimal mapping coefficient as a function of sampling rate, and the solution is shown to be generally indistinguishable from the optimal least-squares solution. The optimal Chebyshev mapping is also found to be essentially identical to the optimal least-squares solution. The expression 0.8517[arctan(0.06583fs)]/sup 1/2/-0.916 is shown to accurately approximate the optimal allpass coefficient as a function of sampling rate f/sub s/ in kHz for sampling rates greater than 1 kHz. A filter design example is included that illustrates improvements due to carrying out the design over a Bark scale. Corresponding results are also given and compared for approximating the related "equivalent rectangular bandwidth (ERB) scale" of Moore and Glasberg (ACTA Acustica, vo.82, p.335-45, 1996) using a first-order allpass transformation. Due to the higher frequency resolution called for by the ERB scale, particularly at low frequencies, the first-order conformal map is less able to follow the desired mapping, and the error is two to three times greater than the Bark-scale case, depending on the sampling rate.

Scales of Variability in the Equatorial Pacific Inferred form Tropical Atmosphere-Ocean Buoy Array

Abstract The highly temporally resolved time series from the Tropical Atmosphere-Ocean moored buoy array are used to evaluate the scales of thermal variability in the upper equatorial Pacific. The TAO array consists of nearly 70 deep-ocean moorings arranged nominally 15° longitude and 2°–3° latitude apart across the equatorial Pacific. The bulk of the data from the array consists of daily averages telemetered in real time, with some records up to 15 years long. However, at several sites more finely resolved data exist, in some cases with resolution of 1 minute. These data form the basis for spectral decomposition spanning virtually all scales of variability from the Brunt-Vaiala frequency to the El Nino-Southern Oscillation timescale. The spectra are used to define the signal to noise ratio as a function of sample rate and frequency, and to investigate the effects of aliasing that results from sparser sampling, such as ship-based observational techniques. The results show that the signal to noise ratio is...

Flowrate associated variation in air sampling of low concentrations of benzene in charcoal tubes

The relative recovery of low level atmospheric benzene vapor from standard activated charcoal sampling tubes was studied as a function of sampling rate, vapor concentration, and sample quantity. The study indicated significant losses at the lower flowrates, while losses due to variations in tube loading and vapor concentrations were found insignificant at the 0.01 confidence level.

Flowrate associated variation in air sampling of low concentrations of benzene in charcoal tubes

The relative recovery of low level atmospheric benzene vapor from standard activated charcoal sampling tubes was studied as a function of sampling rate, vapor concentration, and sample quantity. The study indicated significant losses at the lower flowrates, while losses due to variations in tube loading and vapor concentrations were found insignificant at the 0.01 confidence level.

Optical-mechanical line-scan imaging process: its information capacity and efficiency

An expression for the information capacity of the optical-mechanical line-scan imaging process is derived, which includes the effects of blurring of spatial detail, photosensor noise, aliasing, and quantization. Both the information capacity for a fixed data density and the information efficiency (i.e., the ratio of information capacity to data density) exhibit a distinct single maximum when displayed as a function of sampling rate, and the location of this maximum is determined by the system frequency response shape, SNR, and quantization interval.

Digital Data Combinations for Low Frequency Radio Navigation

The accuracy with which an airborne receiver of a low frequency radio navigation system can be located in real time can be improved considerably by combining the position information from the receiver with velocity information from a velocity sensor such as a Doppler radar. Since aircraft maneuvers and hence the dynamics of the aircraft position and velocity are not known apriori, it is advantageous to combine position and velocity in a filter having a distortionless constraint, that is, a filter whose output has no position error resulting from the dynamics of the inputs. The theory of optimization of such distortionless filters, which are by definition analog filters, has been described in the literature. However, the long range and inherently high accuracy of a low frequency radio navigation system dictate a digital filter combination. In this paper, optimum digital filters combining position and velocity information under an approximate distortionless constraint are synthesized. Four types of digital filters are analyzed and compared: filters having a single sample rate and containing zero order or first order integrators, and filters having a dual sampling rate and containing zero order or first order integrators. These filters are optimized for minimum variance in their position outputs in response to band-limited Gaussian noise in their position and velocity inputs. Position error resulting from random noise and aircraft maneuvers are derived as a function of sample rate. Curves of position error versus sampling rate for a typical low frequency radio navigation system are presented.

Sampling Rates and Appearance of Stationary Gaussian Processes

The expected number of maxima and level crossings of a continuous stationary Gaussian process and the discrete process obtained by sampling the continuous one are evaluated and compared. The ratio of these two values as a function of sampling rate for two classes of spectra is calculated. It is shown that the rule of thumb of sampling at twice the Nyquist frequency is a good one.

Digitalization of continuous control systems

This paper deals with the development of methods for analysis, and derivation of computer programs, for digitalizing continuous control systems. More spe cifically, given a continuous control system, we wish to determine an "equivalent" computer program to take the place of some analog shaping network in the system. An equivalent program is one for which the response of the digital system approximates the response of the continuous system in the time do main. Time and frequency comparisons between the responses of continuous and digitalized systems to step inputs are given. Equivalent computer programs for various standard shaping networks are derived. Revised programs are determined, where use is made of prediction and extrapolation techniques to com pensate for digital computation delay time. Finally, the feedback network in a missile control system containing an unstable aerodynamic airframe is digitalized, and the simulated system is run on an analog-digital hybrid computer system. Results are given, indicating system performance as a function of sampling rate, computation delay, and system gains.