Constant Sampling Rate Research Articles

Effects of position quantization and sampling rate on virtual-wall passivity

The "virtual wall" is the most common building block used in constructing haptic virtual environments. A virtual wall is typically based on a simple spring model, with unilateral constraints that allow the user to make and break contact with a surface. There are a number of factors (sample-and-hold, device dynamics, sensor quantization, etc.) that cause virtual walls to demonstrate active (nonpassive) behavior, destroying the illusion of reality. In this paper, we find an explicit upper bound on virtual wall stiffness that is a necessary and sufficient condition for virtual wall passivity. We consider a haptic display that can be modeled as a mass with Coulomb-plus-viscous friction, being acted upon by two external forces: an actuator and a human user. The system is equipped with only one sensor, an optical encoder measuring the position of the mass. We explicitly model the effects of position resolution, which has not been done in previous work. We make no assumptions about the human user, and we consider arbitrary constant sampling rates. The main result of our analysis is a necessary and sufficient condition for passivity that relies on the Coulomb friction in the haptic device, as well as the encoder resolution. We experimentally verify our results with a one-degree-of-freedom haptic display, and find that the system can display nonpassive behavior in two decoupled modes that are predicted by the necessary and sufficient condition. One mode represents instability, while the other mode results in active tactile sensations.

SAODR: sequence analysis for outlier data rejection

In automatic data acquisition, a sample is generally made up of several instrumental readings. A series of readings is generally reduced to a single value by simple methods, such as averaging. However, outlying values can affect the series. The paper introduces an algorithm, named ‘sequence-analysis outlier data rejection’ (SAODR), which takes into account one of the most common problems affecting the measurand during the acquisition, i.e. a nonlinear drift with embedded sequences of outliers due to pulse-noise peaks. The algorithm uses a time-ordering procedure and the ‘distances’ between successive readings. The frequent case of constant sampling rate is discussed. The reported tests show the results obtained with Fortran 77 and MATLAB® implementations of the algorithm. A rejection efficiency higher than 99% was obtained.

Modified CSP-C Continuous Sampling Plan for Consumer Protection

Dodge (1943) introduced a single level attribute continuous sampling plan designated as CSP-1 for the application of continuous production processes. Govindaraju & Kandasamy (2000) developed a new single level continuous sampling plan whose sampling inspection phase is characterized by a maximum allowable number of non-conforming units c, and a constant sampling rate f and was designated as CSP-C. In this paper, a modification is proposed on the CSP-C continuous sampling plan. In this modified plan, sampling inspection is continued until the occurrence of c+1 non-conforming units, provided the first m sampled units have been found conforming during the sampling phase. Using a Markov chain model, expressions for the performance measures of the modified CSP-C plan are derived. The main advantage of the modified plan is that it is possible to lower the average outgoing quality limit.

Chirp-Z analysis for sol–gel transition monitoring

Gelation is a complex reaction that transforms a liquid medium into a solid one: the gel. In gel state, some gel materials (DMAP) have the singular property to ring in an audible frequency range when a pulse is applied. Before the gelation point, there is no transmission of slow waves observed; after the gelation point, the speed of sound in the gel rapidly increases from 0.1 to 10 m/s. The time evolution of the speed of sound can be measured, in frequency domain, by following the frequency spacing of the resonance peaks from the Synchronous Detection (SD) measurement method. Unfortunately, due to a constant frequency sampling rate, the relative error for low speeds (0.1 m/s) is 100%. In order to maintain a low constant relative error, in the whole speed time evolution range, Chirp-Z Transform (CZT) is used. This operation transforms a time variant signal to a time invariant one using only a time dependant stretching factor ( S). In the frequency domain, the CZT enables us to stretch each collected spectrum from time signals. The blind identification of the S factor gives us the complete time evolution law of the speed of sound. Moreover, this method proves that the frequency bandwidth follows the same time law. These results point out that the minimum wavelength stays constant and that it only depends on the gel.

Issues regarding artificial neural network modeling for reactors and fermenters

In recent years researchers in many areas have used artificial neural networks (ANNs) to model a variety of physical relationships. While in many cases this selection appears sound and reasonable, one must remember than ANN modeling is an empirical modeling technique (based on data) and is subject to the limitations of such techniques. Poor prediction occurs when the training data set does not contain adequate “information” to model a dynamic process. Using data from a simulated continuous-stirred tank reactor, this paper illustrates four scenarios: (1) steady state, (2) large process time constant, (3) infrequent sampling, and (4) variable sampling rate. The first scenario is typical of simulation studies while the other three incorporate attributes found in real plant data. For the cases in which ANNs predicted well, linear regression (LR), one of the oldest empirical modeling techniques, predicted equally well, and when LR failed to accurately model/predict the data, ANNs predicted poorly. Since real plant data would resemble a combination of situations (2), (3), and (4), it is important to understand that empirical models are not necessarily appropriate for predictively modeling dynamic processes in practice.

Estimation of Angular Velocity and Acceleration from Shaft-Encoder Measurements

This paper suggests a Kalman-filter approach to the estimation of angular velocity and acceleration from (quantized) shaft-encoder measurements. Finite-difference estimates deteriorate as sampling rates are increased. For small sampling periods, we show that the filtering problem is the dual of the cheap control problem, and we jus tify the use of all-integrator models. We investigate Kalman filtering with constant sampling rate, and also with measurements triggered by encoder pulses. Simulation and experimental results are given.

Fast estimators of time delay and Doppler stretch based on discrete-time methods

Estimation of the time delay and the Doppler stretch of a signal is required in several signal processing applications, This paper is focused on the joint fine estimation of these two parameters by a fast interpolation of the estimated ambiguity function. Four discrete-time methods (viz. multirate, piecewise scaling, linear scaling, and indirect estimators), based on an orthogonal model, are introduced. Their mean square error is mathematically derived for random signals corrupted by additive random noises. The obtained expressions have been evaluated for some typical parameter sets in the reference case of Gaussian signals and noises. The numerical results, compared with the accuracy of a continuous-time estimator, show the near efficiency of the multirate estimator for a wide range of SNRs. In fact, the adjustable multirate estimator can operate under near optimal conditions, unlike the approximate (i.e., piecewise and linear) scaling and the indirect methods based on constant sampling rates.

Effect of resolution on the apparent fractal dimension of jagged force-displacement relationships and other irregular signatures

The apparent fractal dimension of computer simulated and experimental jagged force-displacement curves was determined using the Richardson and Kolmogorov algorithms. The curves analyzed had a wide range of amplitudes and a variety of temporal resolutions. Despite the fact that curves whose points are uniformly spaced (i.e. recorded at a constant sampling rate) are not truly fractal, both algorithms could be successfully employed, as judged by the linearity of their corresponding plots. The apparent Kolmogorov dimension of the simulated curves was generally smaller than that calculated from the Richardson plot. There was however a good agreement between the two in the experimental curves. Both dimensions increased in unison with the curve fluctuation's amplitude and resolution, indicating that the apparent fractal dimension is a consistent measure of jaggedness. In all the cases, the relationship between the apparent fractal dimension and the resolution could be described by simple empirical models which could be used interchangeably to calculate the asymptotic apparent fractal dimension at infinite resolution. Consequently, the record of real instruments with a finite resolution determined by technical and physical considerations could be used to estimate the ‘ultimate jaggedness’ of the force-displacement relationship or any other digitized signature. The same method can be used, through interpolation, to estimate the curve's jaggedness at any desired resolution for the sake of comparison. Without such an adjustment, the jaggedness of different curves when expressed in terms of their apparent dimension is meaningful only if they have been recorded at the same resolution.

High Uptake Rate Radial Diffusive Sampler Suitable for Both Solvent and Thermal Desorption

A new diffusive sampler with radically changed diffusive path geometry was developed. The small cylinder has a height greater than its radius; the diffusive surface is the external cylindrical one, and the adsorber is a coaxial inner cylindrical cartridge. Due to the high value of diffusive area-path length ratio and to the high loading capacity of the adsorber (up to 80 mg for ethyl acetate), this original geometry allows high and constant sampling rates in a wide range of concentrations and exposure times. The cylindrical shape of the cartridge enables both thermal and solvent desorbing as well as active sampling. Using activated charcoal, exposure time can range from 30 minutes to 24 hours, thus allowing monitoring both in the workplace and in the outdoor environment. As an example, the 80 cm3/min uptake rate of benzene assures a detection limit as low as 2 µg/m3 after 24-hour exposure time. The uptake rate for 32 organics was measured experimentally, and results were found to be highly reproducible and unaffected by wind speed and airborne mixture composition.

Validation and verification of continuous plants operating modes using multivariate statistical methods

A method to identify and monitor the operating modes of continuos plants, is presented and discussed. The criterion uses principal component analysis (PCA) to remove the collinearity and to reduce the dimensionality of the original data set. Typical data sets consist of several variables measured on-line at a constant sampling rate. The reduction in dimension is obtained by the projection of the data set onto a smaller subspace defined by the principal components (PC). In the PC subspace, clusters are identified, and each cluster represents a particular steady-state. Later measurements, if taken while the plant operates at any of these steady-states, lie on the relevant cluster. Such clusters provide the basis for a process validation method. While using the cluster directly would be cumbersome and not intuitive, we propose the use of statistical process control (SPC) charts. An example is given using CUSUM plots. SPC charts are applied to a derived measure. This is the Euclidean distance of the sample from the center of the cluster on the principal component subspace. The definition of the derived measure and its usage are discussed using a multicomponent distillation unit. The method allows the engineer to identify whether the plant operates at the steady state and, possibly at which steady-state among the known ones. Deviations from steady state are easily detected as well as dynamic transients between different steady-states. This approach is particularly suitable for monitoring applications as it allows faster and easier detection than by monitoring individual physical variables. Typical applications of the method are discussed along with future extensions and refinements.

Application of Repetitive Control to a Peristaltic Pump

The aim of this paper is to study angular velocity control of a rotating axis, a peristaltic pump where the disturbance is associated with certain angular positions. The use of constant sampling rate then implies varying disturbance period. A discrete repetitive control scheme based on a reduced order disturbance model tuned to the setpoint of the angular velocity is shown to reject the modeled disturbance with asymptotically zero error. With axis angle synchronization of sampling, the plant model is time-varying but it gives a static discrete disturbance model independent of the angular velocity. If the deviation from the nominal working point is not too large this is to prefer while it gives faster convergence.

A New Look at Warning and Action Lines of Surveillance Schemes

Abstract Some authors have suggested an efficient dynamic monitoring procedure for detection of a change in the drift of a Brownian motion. Their procedure can be described as a sequence of extremely short sequential probability ratio tests (SPRT's) done in zero time with infinitesimal time between consecutive SPRT's. The drawbacks of this procedure are that it can be described only as a limit of practical procedures and it does not take into account the cost of initiating a test. In this article, we suggest a procedure that takes both sampling and overhead costs into account and that can reasonably be carried out in practice. In this procedure the process is monitored continuously with a constant sampling rate. The accumulated data are analyzed by the standard cumulative sum (CUSUM) statistics. Whenever the CUSUM procedure raises an alarm, data are accumulated as fast as possible until either the alarm is relaxed or the process is stopped.

Development of an Indoor Air Sampler for Polycyclic Aromatic Compounds

We have developed a new air sampler for collecting parriculate and gas phase polycyclic aromatic compounds (PAC). This sampler was designed to collect a 25 m3 volume of air at a constant sampling rate of 34 l/min over a 12-hour sampling penod. The 25 m3 sample volume is necessary to achieve the desired nglm3 detection limit for PAC. The 34 l/min sampling rate is estimated to cause less than a 5% reduction in the indoor contaminant concentrations. The sampler pump is a I/4 horsepower vacuum pump in an acoustically shielded fan-cooled enclosure and is relatively quiet. The pump draws air through a 47 mm teflon impregnated glass fibre filter for collection of particulate-phase PAC followed by a cartridge containing XAD-4 resin in front and back sections (2.5 g each) for collection of gas-phase PAC. In a pilot field study the mean breakthrough from the front sorbent section to the back section was less than 1% for each of 14 species of gas phase PAC except biphenyl which had a mean breakthrough of 3.7%. The pressure drop increase across the filter is linear up to a loading of 6 mg and causes less than a 10% reduction in the sample flow rate. The sampler was successfully demonstrated in a pilot field test with air temperatures as high as 30°C.

Evaluation tests and applications of a double-layer tube-type passive sampler

Validation tests on a thermally desorbable tube-type passive sampler filled with two different graphitized carbon blacks were conducted in order to determine the influence of air velocity and direction, concentration and sampling time on sampling rate. A specially made apparatus was used to study the behaviour of the passive sampler in dynamic artificial atmospheres. This apparatus permits the simultaneous sampling of 48 tubes at two different air velocities, minimizing errors due to random variations of the operating conditions during a prolonged sampling time, which allows a better stochastic analysis of data to be performed. The results were in agreement with those obtained by actively sampling the same test-tubes. The results of laboratory and field tests showed that the behaviour of tube-type devices having a small cross-section is independent of the environmental parameters checked over a wide range of operating conditions. The constant sampling rate with these samplers in the range from 30 min up to more than 12 h and the high sensitivity of thermal desorption methods allow the determination of organic species down to the ppb level. A field experiment on the evaluation of the indoor pollution in a domestic environment is also described. The use of a double-layer tube-type passive sampler, with the adsorbent of lower specific surface area positioned at the exposed side of the device, allows a better desorption efficiency.

Spectral analysis algorithms for the laser velocimeter - A comparative study

Conventional methods of computing spectra require constant sampling rates and therefore must be modified to accommodate the randomly sampled data from the laser yelocimeter. Four approaches that provide estimates of the power spectra from randomly sampled data are evaluated with respect to accuracy and computational speed. Simulated data of varying spectral content are used as input. An estimate of the correlation function that resolves the random time distribution into equidistant time intervals provides the best compromise between computational speed and accuracy for laser velocimeter data.

Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media

From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time. To enhance the resolution of the seismic reflection method, we must investigate these variations in more detail. We present quantitative results of theoretical studies on propagation of plane waves for normal incidence, through perfectly elastic multilayered media. As wavelet shapes, we use zero‐phase cosine wavelets modulated by a Gaussian envelope and the corresponding complex wavelets. A finite set of such wavelets, for an appropriate sampling of the frequency domain, may be taken as the basic wavelets for a Gabor expansion of any signal or trace in a two‐dimensional (2-D) domain (time and frequency). We can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals. These results appear as complex 2-D functions of time and frequency, i.e., as “instantaneous frequency spectra.” Choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces. For this purpose, we developed a Gabor expansion involving basic wavelets with a constant time duration/mean period ratio. For layered media, as found in sedimentary basins, we can distinguish two main types of series: (1) progressive series, and (2) cyclic or quasi‐cyclic series. The second type is of high interest in hydrocarbon exploration. Progressive series do not involve noticeable distortions of the seismic signal. We studied, therefore, the wave propagation in cyclic series and, first, simple models made up of two components (binary media). Such periodic structures have a spatial period. We present synthetic traces computed in the time domain using the Goupillaud‐Kunetz model of propagation for one‐dimensional (1-D) synthetic seismograms. Three different cases appear for signal scattering, depending upon the value of the ratio wavelength of the signal/spatial period of the medium. (1) Large wavelengths The composite medium is fully transparent, but phase delaying. It acts like an homogeneous medium, with an “effective velocity” and an “effective impedance.” (2) Short wavelengths For wavelengths close to twice the spatial period of the medium, the composite medium strongly attenuates the transmission, and superreflectivity occurs as counterpart. (3) Intermediate wavelengths For intermediate values of the frequency, velocity dispersion versus frequency appears. All these phenomena are studied in the frequency domain, by analytic formulation of the transfer functions of the composite media for transmission and reflection. Such phenomena are similar to Bloch waves in crystal lattices as studied in solid state physics, with only a difference in scale, and we checked their conformity with laboratory measurements. Such models give us an easy way to introduce the use of effective velocities and impedances which are frequency dependent, i.e., complex. They will be helpful for further developments of “complex deconvolution.” The above results can be extended to quasi‐cyclic media made up of a random distribution of double layers. For signal transmission, quasi‐cyclic series act as a high cut filter with possible time delay, velocity dispersion, and “constant Q” type of law for attenuation. For signal reflection they act as a low cut filter, with possible superreflections. These studies could be extended to three‐dimensional (3-D) binary models (grains and pores in a porous reservoir), in agreement with well‐known acoustic properties of gas reservoirs (theory of bright spots). We present some applications to real well data.

Graphs, Tables and Discussion to Aid in the Design and Evaluation of an Acceptance Sampling Procedure Based on Cumulative Sums

An acceptance sampling procedure for attributes inspection proposed by Beattie seems well suited for situations when production is continuous, sampling is destructive, a constant sampling rate is required, and discrimination between two quality levels i..

Development of a freeze-out technique and constant sampling rate for the portable unijet air sampler.

(1960). Development of a Freeze-out Technique and Constant Sampling Rate for the Portable Uni-Jet Air Sampler. American Industrial Hygiene Association Journal: Vol. 21, No. 4, pp. 325-329.