Transfer Function Parameters Research Articles

Repeatability of Measurements Obtained with a Ray Tracing Aberrometer

To evaluate the repeatability of ocular aberrometry at distance and near vision conditions provided by the latest version of a ray tracing aberrometer. A total of 22 healthy eyes of 22 patients with ages ranging from 21 to 65 years were included in this study. All eyes achieved a best spectacle corrected visual acuity of 20/20, and had not undergone previous ocular surgeries. Three consecutive aberrometric measurements were obtained with the iTrace system (Tracey Technologies) by an experienced examiner at distance (5 m) and near (40 cm). Low values of within-subject standard deviation (Sw) were found for sphere and cylinder at distance and near and for the power vector components of refraction. However, a more pronounced variability was observed for the coefficients associated with higher order aberrations, with the poorest repeatability for the vertical coma at near, Sw of 0.011 μm for a mean value of 0.018 μm. Additionally, Sw for vertical coma was significantly larger at near (p = 0.01). No significant differences between the distance and near values of Sw for the power vector components of refraction were found (p ≥ 0.08). The Sw values for the distance and near modulation transfer function parameters were low when compared with their corresponding mean values. The iTrace system provides repeatable measurements of the spherocylindrical refraction at near and distance, but consistency of aberrometric and optical quality measurements seems to be limited.

Assessing preferential flow through an unsaturated waste rock pile using spectral analysis

Waste rock piles are an outcome of open pit and underground mining operations. Unprocessed low‐grade rock is disposed of in piles from several meters high to 100 m+ high. Waste rock piles may still contain sufficient concentrations of metals to be a potential source of pollution. The evaluation of the potential risk involves properly characterizing flow through these piles under unsaturated conditions. The main flow characteristic of the piles is the presence of a large range of grain and pore sizes. Based on data from an instrumented rock pile located in Saskatchewan Canada, unsaturated flow through the pile is modeled as a linear system after separating a fast and a slow component. Water reaching the base of the pile is monitored by 16 contiguous zero‐tension lysimeters. The fast component, flowing through macropores, is assumed to be released instantaneously, while the slow component is simulated using a linear‐reservoir model that assumes the presence of an interconnected porous matrix. An empirical transfer function (TF) is computed as the ratio of the spectra of signals between the output (basal outflow) and the input (rainfall time series). Determination of a parametric transfer function model provides information on the characteristic time of water storage in the matrix and on the fraction of the water within each subsection of the experimental pile that is channeled through the macropores. An analysis of the output signal at different support scales is performed, indicating the nonlinearity of the macropore fraction scaling processes.

Application of transfer functions to model water injection in hydrocarbon reservoir

Water flooding is one of the most economical methods to increase oil recovery. In order to improve the ultimate oil recovery during waterflooding, it is essential to provide an accurate forecast of reservoir performance. Hence, various methods have been utilized to simulate reservoirs. Although grid-based simulation is the most common and accurate method, time-consuming computation and the demand for large quantities of data restrict the use of this method. Sometimes, a quick overview of reservoir performance is sufficient or all required data are not accessible. Therefore, in this study a fast simulator is introduced to provide a quick overview with the minimum amount of data. A new method is presented to forecast the performance of water injection based on Transfer Function (TF). In this approach, it is assumed that a reservoir consists of a combination of TFs. The order and arrangement of TFs are chosen based on the physical conditions of the reservoir which are ascertained by examining several cases. The selected arrangement and orders can be extended to any other reservoirs. Injection and production rates act as input and output signals to these TFs, respectively. After analyzing input and output signals, the unknown parameters of TFs are calculated. Subsequently, it is possible to predict reservoir performance. Four different cases are employed to validate the derived equation. The results reveal a good agreement with those obtained from the common grid-based simulators. In addition, it has been demonstrated that the TF parameters depend on the characteristics and the pattern of different sections of the reservoir. This approach is a quick way to forecast waterflooding performance and can be a new window for the future of fast simulators. It provides the prediction with higher certainty in comparison with the other fast simulators. Furthermore, the only requirements for the method are injection and production rates. The analytical solution of the method enables its utilization in finding optimum rates for water injection in a short period of time. The method also presents some key parameters such as well connectivity. The use of the model is limited to situations when a rapid estimation is looked for and/or adequate data is not accessible.

Identification of a thermal system using continuous linear parameter-varying fractional modelling

In this study, the authors present an identification procedure of a non-linear thermal system that exhibits a diffusive interface. Indeed, the system deals with heat conduction in a homogeneous material through a wall. Heating front face temperature dynamics when random heat flux is applied to the wall's front face area are considered. If the thermophysical properties of the material depend on the temperature, the heat equation is not linear anymore. Hence, in order to explicitly take into account the dependence of the system dynamics on the temperature, a fractional continuous linear parameter-varying model is used and determined thanks to a local approach composed of two steps. First, the authors show that for small heating temperature variations, the heat diffusion can be modelled with the help of a local fractional model based on a fractional integrator operator of order (1/2), which acts only over a limited spectral band. The transfer function parameters of this model are estimated thanks to an output-error technique at different initial temperature-operating points. Secondly, the transfer function parameters dependence with respect to the initial temperature of the material is obtained by direct polynomial interpolation. Simulations using ARMCO iron are used to demonstrate the performances of the proposed local approach.

Identification of 5-Axis Machine Tools Feed Drive Systems for Contouring Simulation

An identification technique is introduced for identifying closed loop transfer function of machine tool’s feed drive systems to be used in simulation of the tracking and contouring performance of Computer Numerical Controlled (CNC) machine tools. The identification is performed from air-cutting tests utilizing only standard G-codes containing linear motion commands. A general transfer function model is derived for representing the closed loop tracking response of the feed drive system. The model considers the drive to be controlled by commonly used controller schemes such as P-PI Cascade, PID or the Sliding Mode Controller (SMC) with feed-forward dynamic and friction compensation. The parameters of the model transfer function are fitted tominimize the discrepancy between the actual and predicted axis position on the axis. In order to guarantee the stability of the identified model transfer function, bounds on the pole locations are imposed. The resultant constrained non-linear optimization problem is solved efficiently using the Particle Swarm Optimization (PSO) method. For achieving reliable convergence of the stochastic PSO algorithm, a parameter tuning strategy is presented. Simulation and experimental studies show that the identified feed drive model captures the fundamental dynamics of the drives system accurately for simulating their closed loop response. Combined with the kinematics of the machine, contouring errors of 5-axis CNC machine tools during simultaneous multi-axis motion are predicted.

Parameter identification of continuous-time systems using iterative learning control

This paper presents a system identification technique for continuous-time state-space system using the iterative learning control. The transfer function parameters are regarded as functions with respect to the state-space parameters which will be identified. The relationship between the state-space parameters and the response error is explicitly derived. An update law of the state-space parameters is proposed so as to improve the convergence speed. The effectiveness of the proposed identification technique is demonstrated by numerical examples.

Improved (non-)parametric identification of dynamic systems excited by periodic signals—The multivariate case

Recently [1] a method has been developed to suppress nonparametrically the noise (and system) transients (leakage errors) in frequency response function and noise (co-)variance estimates of single-input, single-output systems excited by periodic signals. This paper extends the results of [1] to multiple-input, multiple-output systems where all inputs and outputs are disturbed by noise (i.e. an errors-in-variables framework). Two methods are presented: the first starts from multiple experiments with uncorrelated sets of inputs, and makes no assumption about the frequency response matrix (FRM); while the second only requires one single experiment, but assumes that the FRM can locally be approximated by a polynomial. Both methods estimate simultaneously the FRM, the noise level, and the level of the nonlinear distortions. For lightly damped systems, the proposed methods either significantly reduce the experiment duration or, for a given measurement time, significantly increase the frequency resolution of the FRM estimate. If the noise (and/or system) transients are the dominant error sources, then the proposed methods also significantly reduce the covariance matrix of the FRM estimates. The use of the nonparametric noise covariance estimates for parametric transfer function modelling is also discussed in detail.

Visibility Histograms and Visibility-Driven Transfer Functions

Direct volume rendering is an important tool for visualizing complex data sets. However, in the process of generating 2D images from 3D data, information is lost in the form of attenuation and occlusion. The lack of a feedback mechanism to quantify the loss of information in the rendering process makes the design of good transfer functions a difficult and time consuming task. In this paper, we present the general notion of visibility histograms, which are multidimensional graphical representations of the distribution of visibility in a volume-rendered image. In this paper, we explore the 1D and 2D transfer functions that result from intensity values and gradient magnitude. With the help of these histograms, users can manage a complex set of transfer function parameters that maximize the visibility of the intervals of interest and provide high quality images of volume data. We present a semiautomated method for generating transfer functions, which progressively explores the transfer function space toward the goal of maximizing visibility of important structures. Our methodology can be easily deployed in most visualization systems and can be used together with traditional 1D and 2D opacity transfer functions based on scalar values, as well as with other more sophisticated rendering algorithms.

Nonlinear Multiple Model Predictive Control of Solution Polymerization of Methyl Methacrylate

A sequential linearized model based predictive controller is designed using the DMC algorithm to control the temperature of a batch MMA polymerization process. Using the mechanistic model of the polymerization, a parametric transfer function is derived to relate the reactor temperature to the power of the heaters. Then, a multiple model predictive control approach is taken in to track a desired temperature trajectory.The coefficients of the multiple transfer functions are calculated along the selected temperature trajectory by sequential linearization and the model is validated experimentally. The controller performance is studied on a small scale batch reactor.

Simulation of added inductive coil influence onto the digital servo system with DC motor

This paper describes a simulation of a real electrical servo drive with a digital equalizer. The whole system is simulated in the simulation toolkit of the LabView package. Real transfer functions are simulated (the transfer functions of the motor and the current and angular velocity gauges), as well as the nonlinearities of the motor and the gears. Clasical mathematical methods for modeling servosistems are used. The method for determining transfer function parameters is also used. The influence of neglecting the electrical time constant is analyzed.

Morphology and structure of lipoproteins revealed by an optimized negative-staining protocol of electron microscopy

Plasma lipoprotein levels are predictors of risk for coronary artery disease. Lipoprotein structure-function relationships provide important clues that help identify the role of lipoproteins in cardiovascular disease. The compositional and conformational heterogeneity of lipoproteins are major barriers to the identification of their structures, as discovered using traditional approaches. Although electron microscopy (EM) is an alternative approach, conventional negative staining (NS) produces rouleau artifacts. In a previous study of apolipoprotein (apo)E4-containing reconstituted HDL (rHDL) particles, we optimized the NS method in a way that eliminated rouleaux. Here we report that phosphotungstic acid at high buffer salt concentrations plays a key role in rouleau formation. We also validate our protocol for analyzing the major plasma lipoprotein classes HDL, LDL, IDL, and VLDL, as well as homogeneously prepared apoA-I-containing rHDL. High-contrast EM images revealed morphology and detailed structures of lipoproteins, especially apoA-I-containing rHDL, that are amenable to three-dimensional reconstruction by single-particle analysis and electron tomography.

Non-Asymptotic Confidence Sets for the Parameters of Linear Transfer Functions

We consider the problem of constructing confidence sets for the parameters of input-output transfer functions based on observed data. The assumptions on the noise affecting the system are reduced to a minimum; the noise can virtually be anything, but in return the user must be able to select the input signal. In this paper a procedure for solving this problem is developed in the general framework of leave-out sign-dominant confidence regions. The procedure returns confidence regions that are guaranteed to contain the true transfer function with a user-chosen probability for any finite data set.

The effect of urbanization on stream hydrology in hillslope watersheds in central Texas

AbstractThis study examined the effect of urbanization on stream hydrology in hillslope watersheds. Ten streams (seven in hillslope and three in gentle slope watersheds) around Austin, Texas were selected for analysis. For each stream, we compared parameters of transfer function (TF) models estimated from daily rainfall and streamflow data collected in two study periods (October 1988–September 1992 and October 2004–September 2008) representing different degrees of watershed urbanization. As expected, the streams became more intermittent as the watersheds were more urbanized in all the study streams. However, the effect of urbanization on peakflow differs between hillslope and gentle slope watersheds. After watershed urbanization, peakflow increased in gentle slope watersheds, but decreased in hillslope watersheds. Based on the results of the TF models, we found that urbanization made stream not flashier but drier in hillslope watersheds. Overpumpage of aquifer has been recognized as a problem that leads to the stream dryness in the study area. However, the overpumpage alone cannot explain the differences in hydrological changes between the two types of watersheds. We attributed the reduced peakflow and stream dryness in the hillslope watersheds to land grading for construction forming stair‐stepped or terraced landscape. Compared with natural hillslope, a stair‐stepped landscape could infiltrate more stormwater by slowing down surface runoff on tread portions of the stair. Our findings suggest that a watershed management scheme should take into account local hydrogeologic conditions to mitigate the stream dryness resulting from urbanization in hillslope watersheds. Copyright © 2010 John Wiley & Sons, Ltd.

Stable LPV Realization of Parametric Transfer Functions and Its Application to Gain-Scheduling Control Design

The paper deals with the stabilizability of linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on the plant parameters and internally stabilizing the closed-loop control system when the plant parameters are constant, can be realized in such a way that the closed-loop asymptotic stability is guaranteed under arbitrary parameter variations. To this purpose, it is preliminarily proved that any transfer function that is stable for all constant parameters values admits a realization that is stable under arbitrary parameter variations (linear parameter-varying (LPV) stability). Then, the Youla-Kucera parametrization of all stabilizing compensators is exploited; precisely, closed-loop LPV stability can be ensured by taking an LPV stable realization of the Youla-Kucera parameter. To find one such realization, a reasonably simple and general algorithm based on Lyapunov equations and Cholesky's factorization is provided. These results can be exploited to apply linear time-invarient design to LPV systems, thus achieving both pointwise optimality (or pole placement) and LPV stability. Some potential applications in adaptive control and online tuning are pointed out.

Using the Fredholm resolvent for computing the ℋ2-norm of linear periodic systems

This article presents a method for the ℋ2-norm computation of single-loop finite-dimensional linear continuous periodic systems, which is based on the parametric transfer function concept and the calculus of Fredholm integral equations of the second kind. General formulae for the computation of the mean output variance are provided as relations of two integral functions of an auxiliary parameter. On the basis of the general solution, an approximate computation method is derived, and the deviation of the approximate solution is estimated. In principle, this approach allows one to perform the computation with any desired accuracy.

Guaranteed performance for sampled-data systems with generalized higher-order hold

The paper investigates the digital control of continuous-time processes, where continuous stochastic disturbances act directly on the continuous part of the system, which is typical for motion control of marine vehicles. Instead of zero-order hold, which is normally used, the digital computer and the continuous process are connected by hold elements of arbitrary order. On basis of the parametric transfer function concept, the paper presents a rigorous description of this class of sampled-data system. This description allows to find optimal controllers by using polynomial and numerical methods. For the practically relevant problem, where the disturbances are only known to belong to a certain class, a minimax solution is presented, which guarantees a certain performance for any admissible disturbances. The effect of higher-order hold is briefly discussed on basis of an examples.

Transcranial Doppler Monitoring in Parkinson’s Disease: Cerebrovascular Compensation of Orthostatic Hypotension

Despite of precipitous blood pressure falls in Parkinson’s Disease (PD) patients, they may not experience syncope or postural complaints. Can cerebral blood flow regulation explain why orthostatic hypotension (OH) has often no accompanying symptoms? In patients with PD and OH (18 asymptomatic; 8 symptomatic), arterial blood pressure (ABP) as well as Doppler-detected cerebral blood flow velocity (CBFV) in middle and posterior cerebral arteries (MCA and PCA) were monitored during head-up tilt and compared with 25 controls and eight non-PD-OH patients. Analysis included the transfer function between slow spontaneous pressure and flow-oscillations. ABP and CBFV were maintained at significantly higher levels in asymptomatic than symptomatic PD-OH (ABP: 85.7 ± 10.5 vs. 66.9 ± 12.5%; MCA-FV: 83.3 ± 9.3 vs. 66.1 ± 6.8%; PCA-FV: 84.4 ± 12.2 vs. 65.9 ± 9.3% of supine). When orthostatic complaints occurred, CBFV depended directly on ABP changes (MCA r 2 = 0.64; PCA r 2 = 0.62; both p < 0.05). Despite of a tilt-induced blood pressure instability in PD-OH, the transfer function parameters did not differ from normal [phase: MCA: 46.6 ± 20.5°; PCA 39.2 ± 28.8°, gain: MCA 2.0 ± 0.7; PCA 2.9 ± 1.6)]. Results showed a normal autoregulatory response to downward blood pressure shifts in PD. Moreover, orthostatic blood pressure instability is compensated equally sufficient in anterior and posterior parts of cerebral circulation. Whether in PD patients, OH becomes symptomatic rather seems to depend on blood pressure falling below the autoregulated range. (E-mail: Christina.Haubrich@t-online.de)

The Rijke Tube: A Green's Function Approach in the Frequency Domain

The stability behaviour of a Rijke tube is studied by a Green's function approach in the frequency domain. The tube is open at both ends. It contains an acoustically compact flame holder that blocks the acoustic motions; there is also a jump in cross-sectional area and in mean temperature. The oscillating part of the rate of heat release is modelled by a flame transfer function, i.e. the frequency-domain ratio of heat release rate to acoustic velocity. An equation for the complex eigenfrequencies is derived. Its solutions give the frequencies and growth rates of the acoustic modes in the tube. The approach is then used to study the effect of several flame transfer functions on the stability behaviour of the Rijke tube. The role of several parameters in these flame transfer functions is examined. Finally, the possibility is discussed whether one can discriminate between these transfer functions from measurements of the stability behaviour and frequencies in a simple Rijke tube set-up.

GA-Based Model Evolutionary Identification for Yaw Channel of Small-scale Unmanned Helicopter

This paper analyzes the model structure of small-scale unmanned helicopter's yaw channel.The parameter transfer function model using the alterable fractional form is established.Subsequently,a genetic algorithm(GA) based method is designed to identify the established model structure,and the system model structure and the parameters can be obtained simultaneously.Based on safety and convenience,a kind of ground stand is produced,and the experimental data used for identification and validation is collected and pre-treated.The results are used to explain the feasibility of the proposed identification algorithm.

Parametric Transfer Matrix and Statistical Analysis of Sampled-data Systems with Delay

This paper considers the statistical analysis problem for multivariable stable sampled-data systems, where various delays are located in different parts of the control loop. The analysis is based on the parametric transfer function concept. Apart from closed expressions for the parametric transfer matrix of the system, the paper provides a constructive method for calculating the output variance as a function of continuous time.