Form Of Transfer Function Research Articles

Early experience in the use of quantitative image quality measurements for the quality assurance of full field digital mammography x-ray systems

Quantitative image quality results in the form of the modulation transfer function (MTF), normalized noise power spectrum (NNPS) and detective quantum efficiency (DQE) are presented for nine full field digital mammography (FFDM) systems. These parameters are routinely measured as part of the quality assurance (QA) programme for the seven FFDM units covered by our centre. Just one additional image is required compared to the standard FFDM protocol; this is the image of an edge, from which the MTF is calculated. A variance image is formed from one of the flood images used to measure the detector response and this provides useful information on the condition of the detector with respect to artefacts. Finally, the NNPS is calculated from the flood image acquired at a target detector air kerma (DAK) of 100 µGy. DQE is then estimated from these data; however, no correction is currently made for effects of detector cover transmission on DQE. The coefficient of variation (cov) of the 50% point of the MTF for five successive MTF results was 1%, while the cov for the 50% MTF point for an a-Se system over a period of 17 months was approximately 3%. For four a-Se based systems, the cov for the NNPS at 1 mm−1 for a target DAK of 100 µGy was approximately 4%; the same result was found for four CsI based FFDM units. With regard to the stability of NNPS over time, the cov for four NNPS results acquired over a period of 12 months was also approximately 4%. The effect of acquisition geometry on NNPS was also assessed for a CsI based system. NNPS data acquired with the antiscatter grid in place showed increased noise at low spatial frequency; this effect was more severe as DAK increased. DQE results for the three detector types (a-Se, CsI and CR) are presented as a function of DAK. Some reduction in DQE was found for both the a-Se and CsI based systems at a target DAK of 12.5 µGy when compared to DQE data acquired at 100 µGy. For the CsI based systems, DQE at 1 mm−1 fell from 0.49 at 100 µGy to 0.38 at 12.5 µGy. For the a-Se units, there was a slightly greater reduction in average DQE at 1 mm−1, from 0.53 at 100 µGy to 0.31 at 12.5 µGy. Somewhat different behaviour was seen for the CR unit; DQE (at 1 mm−1) increased from 0.40 at 100 µGy to 0.49 at 12.5 µGy; however, DQE fell to 0.30 at 420 µGy. DQE stability over time was assessed using the cov of DQE at 1 mm−1 and a target DAK of 100 µGy; the cov for data acquired over a period of 17 months for an a-Se system was approximately 7%. For comparison with conventional testing methods, the cov was calculated for contrast-detail (cd) data acquired over the same period of time for this unit. The cov for the threshold contrast results (averaged for disc diameters between 0.1 mm and 2 mm) was 6%, indicating similar stability.

Providing stability maps for milling operations

This article presents a new stability prediction tool. The method is based on the dynamic behaviour of both milling tool and workpiece, computed using finite element method. Dynamic behaviour is expressed under the form of transfer functions and used to predict stability lobes at each tool position. The unconditionally stable depth of cut is then stored and displayed on a graphic representation of the machined surface under the form of colour axis, named stability map. An application of the method on a Renault cylinder block is presented as an illustration.

New Transfer Functions for Simulation of Naturally Fractured Reservoirs With Dual-Porosity Models

SummaryThis paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual-porosity models. Most of the existing dual-porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudosteady-state flow. More importantly, a direct generalization of single-phase flow equations is used to model multiphase flow, which can lead to significant inaccuracies in multiphase flow-behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs.First, combining the differential form of the single-phase transfer function with analytical solutions of the pressure-diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudosteady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Also, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e., non-orthogonal fractures) is proposed. This technique also accounts for both transient and pseudosteady-state pressure behavior. The results were verified against fine-grid single-porosity models and were found to be in excellent agreement.Second, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting-phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine-grid single-porosity models are used to verify the validity of the new transfer function. The results from single-block dual-porosity models and the corresponding single-porosity fine-grid models were in good agreement.

DATA-BASED MECHANISTIC MODELLING AND RIVER FLOW FORECASTING

The paper briefly reviews the topic of rainfall-flow modelling and the inductive, Data-Based Mechanistic (DBM) approach to modelling stochastic, dynamic systems. It then uses DBM modelling methods to investigate the nonlinear relationship between daily rainfall and flow in the Leaf River, Mississippi, USA. Initially, recursive State-Dependent Parameter (SDP) estimation is used to identify, in non-parametric (graphical) terms, the location and nature of the 'effective rainfall' nonlinearity. Parameterization of this nonlinearity and optimization of a constrained version of the resulting model allow for its interpretation in a hydrologically meaningful State-Dependent Parameter Transfer Function (SDTF) form. Finally, the model its used as the basis for the design of a realtime flow forecasting using an optimized SDP Kalman Filter (SDPKF) forecasting engine that includes a model of the heteroscedastic measurement noise.

LATEST DEVELOPMENTS FOR THE MATLAB CONTSID TOOLBOX

This paper describes the latest developments for the CONtinuous-Time System IDentification (CONTSID) toolbox to be run with Matlab which includes time-domain identification methods for estimating continuous-time transfer function or state-space models directly from sampled data. The main additions to the new version aim at extending the optimal instrumental variable method to handle wider practical situations in order to enhance the application field of the CONTSID toolbox. The toolbox now includes: (1) a recursive version of the optimal instrumental variable method, (2) a version for multiple input system identification where the denominators of the transfer functions associated with each input are not constrained to be identical, (3) a version for identifying hybrid models of the general Box-Jenkins transfer function form, where a continuous-time plant model with a discrete-time noise model is estimated.

Application of linear and nonlinear techniques in river flow forecasting in the Kilombero River basin, Tanzania / Application de techniques linéaires et non-linéaires à la prévision des débits dans le bassin de la Rivière Kilombero, en Tanzanie

Modelling of the rainfall–runoff transformation process and routing of river flows in the Kilombero River basin and its five sub-catchments within the Rufiji River basin in Tanzania was undertaken using three system (black-box) models—a simple linear model, a linear perturbation model and a linear varying gain factor model—in their linear transfer function forms. A lumped conceptual model—the soil moisture accounting and routing model—was also applied to the sub-catchments and the basin. The HEC-HMS model, which is a distributed model, was applied only to the entire Kilombero River basin. River discharge, rainfall and potential evaporation data were used as inputs to the appropriate models and it was observed that sometimes the system models performed better than complex hydrological models, especially in large catchments, illustrating the usefulness of using simple black-box models in datascarce situations.

Optical image processing by means of acousto-optic spatial filtration

Results are presented of a theoretical and experimental study of a new method of optical image processing based on two-dimensional acousto-optic filtration of the spatial spectrum of images. Most attention is concentrated on the analysis of the acousto-optic cell transfer function form and its dependence on crystal cut, geometry of acousto-optic interaction and ultrasound frequency. Results of computer simulation of acousto-optic spatial filtering are illustrated by the example of an object in the form of an amplitude grating. Experiments investigating the transfer functions of acousto-optic cells with collinear and tangential geometry of acousto-optic interaction are described. Acousto-optic image processing is demonstrated experimentally using the example of the edge enhancement effect for some elementary images.

EXACT PARAMETER ESTIMATION USING RELAY FEEDBACK CONTROL

Obtaining the parameters for PID controllers based on limit cycle information from the process in a relay controlled feedback loop is, in many cases, an acceptable practical procedure. If the form of the plant transfer function is known, exact expressions for the limit cycle frequency and amplitude can be derived in terms of the plant parameters, so that their measurements, assumed error free, can be used to calculate two unknown plant parameter values. In the literature to date the solutions have been considered for stable or unstable first order plus dead time (FOPDT) or second order plus dead time (SOPDT) plant transfer functions. This paper reports on exact parameter estimation for an SOPDT plant transfer function with the further addition of a, stable or unstable, zero by a single relay feedback test.

Novel Ideas for Fast Muscle Action Potential Simulations Using the Line Source Model

Using a signal processing approach, we analyze the line source model for muscle action potential (AP) modeling. We show that the original model presents a tradeoff between violating the Nyquist criterion on one hand and using a discretization frequency that is unnecessarily high with respect to the bandwidth of the generated AP on the other. Here, we present an improved line source model that, compared to the original, allows a lower discretization frequency while retaining the accuracy by simply introducing a continuous-time anti-aliasing filter. Moreover, a transfer function form of the transmembrane current is presented that promote the use of sophisticated signal processing methods on these type of signals. Both continuous-time and discrete-time models are presented. We also address and analyze the implications of the finite length of the muscle fibers. Including this in the model is straightforward, owing to the convolutional form of the line source model, and is manifested by a simple transformation of the associated weighting function. AP modeling is discussed for the three different electrode models: the concentric needle electrode, the single fiber electrode, and the macro electrode. The presented model is suitable for modeling large motor units, where both accuracy and computational efficiency are important factors. To simplify the selection of the discretization interval, we derive what we call the cumulative cutoff frequency that provides an estimate of the required Nyquist frequency.

AN INDUSTRIAL REHEATING FURNACE WITH FLUE GAS RECIRCULATION MODELED BY LINEAR TRANSFER FUNCTIONS

To design an effective active combustion control system, it is important to have detailed knowledge about the dynamic relationships of the furnace from its inputs to its outputs. A novel approach has been proposed to construct a set of dynamic models in the form of transfer functions for an industrial furnace with flue gas recirculation (FGR) based on the computational fluid dynamics (CFD) simulation results. The inputs to the furnace are the flow rate of the combustion air, the temperature of the combustion air, and the pressure head of the FGR fan. The outputs are nitric oxide (NO) and oxygen (O2) concentrations. Therefore, the furnace has been represented by a three-input and two-output system. The model construction relies on the CFD simulations of the combustion process and NO formation in the furnace as well as frequency domain system identification techniques. Low-amplitude sinusoidal signals of different frequencies have been administered at the furnace inputs around a designed furnace operating condition. The dynamic relationships among the furnace inputs and outputs at these frequencies are first established in terms of frequency responses. These frequency responses are further processed by a least-squares-based system identification technique to convert them to a set of parametric models. These models are validated against the results obtained from the CFD simulations.

A Finite-Dimensional Modeling of Heat Conduction Systems with State Distribution Error Bounds

In this paper we present finite-dimensional modeling of heat conduction systems with frequency and space-dependent error bounds where the eigenstruc-tures of the systems are only partially known. It is shown that steady state analysis for dc input of a system is used effectively in reduced order modeling and bounding errors for the whole spatial distribution of temperature. A class of nominal models is clarified with tight additive error bounds, and the nominal models as well as the uncertainty weights are explicitly described as simple real rational form of transfer functions. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in copper rod.

FAVORABLE CHARACTERISTICS OF INTELLIGENT MACHINE COOPERATING WITH INSTRUCTIONS BY FINGER MOVEMENTS

When intelligent machines coexist with humans, it is important that the intelligent machine's movement in response to human instruction is acceptable by the human state of mind. When a human instructs an intelligent machine with his or her finger, we focus on a simple and easy interface via which conversion of the finger indication to intelligent machine motion is realized by a transfer function. In this paper, we evaluate relations between the transfer functions and human feelings using Semantic Differential method. The results of the SD method show that there are typical forms of transfer functions and parameters to generate comfortable motion for humans. Desirable transfer functions are the first-order or the second-order delay elements in which the parameters must be chosen so that the maximum velocity of generated intelligent machine motion exists in the range of 71-77% of the maximum velocity of instruction movement. In addition, human feelings to the intelligent machine motion generated by human instructions are represented by the factors of “lively”, “mild”, and “interest”.

Elementary linear filtering tasks using CNNs with minimum-size templates

In this paper we investigate the linear filtering capabilities of the standard cellular neural network in the general case of non-symmetric templates. We approached here systematically the CNNs with minimum-size templates (1x3), analyzing in detail their filtering capabilities in the one-dimensional case. Starting from a general form of the spatial transfer function, we emphasize some useful filtering functions that can be obtained. For each filter type, we derive the relations which give the template parameter values, in order to design a given CNN filter with specified characteristics-like central frequency, bandwidth, selectivity etc. Filters with symmetric templates are treated as a particular case. For each type of filtering the characteristics are shown and simulation results are presented as well. Some of these results are then extended to 2-D CNNs and several simulations of useful filtering tasks are presented on real images.

SHAKING TABLE DYNAMICS: RESULTS FROM A TEST-ANALYSIS COMPARISON STUDY

This paper presents the results of a comprehensive comparison study between the analytically predicted and experimentally identified dynamics of the shaking table system built recently in the Structural Engineering Laboratory at Rice University in Houston, Texas. The primary objectives of the research presented here are two-fold: (1) to shed light into the dynamic performance of asmall-tc-medium size, uni-axial, servo-hydraulic, displacement-controlled shaking table system, and (2) to validate a linearised dynamic model of the system (in the form of the total shaking table transfer function) developed earlier by the authors from basic principles. The analytical model incorporates the inherent dynamic characteristics of the various components of the shaking table system (i.e. controller, servovalve, actuator, test specimen, and reaction mass) and their dynamic interaction. The test-analysis correlation study performed over a wide range of operating and payload conditions provides useful information on the sensitivity of the shaking table transfer function to control gain parameters and how it can be used to tune the shaking table controller for optimum performance under various payload conditions. The good test-analysis correlation results obtained validate the analytical shaking table model, show its robustness, and provide keen insight into the underlying coupled dynamics of a shaking table system. In order to achieve this good test-analysis correlation, it was crucial to include a time delay in the analytical model of the shaking table system (innovative feature of the model to account for the time lag in the response of the servovalve-actuator system). The expected significant dynamic interaction between payload and shaking table is also confirmed by this study.

Non-interacting control design for multivariable industrial processes

Abstract In this paper, a systematic method is proposed for the design of general multivariable controller for complex processes to achieve the goal of fast loop responses with acceptable overshoots and minimum loop interaction while maintaining low complexity of the feedback controller. The design of general transfer function type controller is based on the fundamental relations under decoupling of a multivariable process, and the characterization of the unavoidable time delays and non-minimum phase zeros that are inherent in the decoupled loops. The objective loop transfer functions are then suitably specified to achieve fast loop response taking into account the performance limitation imposed by those non-minimum phase zeros and time delays. The ideal controller is then obtained which is in general a complicated irrational transfer matrix, for which model reduction with recursive least squares is applied in the frequency domain to obtain a much simpler transfer matrix with its elements in the form of rational transfer function plus delay. Simulations show that very satisfactory control performance is achieved.

Structural interpretation of matched pole–zero discretisation

Deals with matched pole-zero discretisation, which has been used in practice for hand calculations in the digital redesign of continuous-time systems but available only in the transfer-function form. Since this form is inconvenient for characterising the time-domain properties of sampled-data loops and for computerising the design of such systems, a state-space formulation is developed. Under the new interpretation, the matched pole-zero model is shown to be structurally identical to a hold-equivalent discrete-time model, where the generalised hold takes integral part, thus unifying the most widely used discretisation approaches. An algorithm for obtaining the generalised hold function is presented. The hold-equivalent structure of the matched pole-zero model clarifies several discrete-time system properties, such as controllability and observability, and their preservation or loss with a matched pole-zero discretisation. With the proposed formulation, the matched pole-zero, hold-equivalent, and mapping models can now all be constructed with a single schematic model.

Minimum variance control and performance assessment of time-variant processes

Abstract This paper is concerned with (1) an explicit solution of a minimum variance control law for linear time-variant (LTV) processes in the transfer function form, and (2) performance assessment of LTV processes using minimum variance control as the benchmark. It is shown that there exists a time-variant, absolute lower bound of process variance that is achievable under LTV minimum variance control and can be estimated from routine operating data. This lower bound can subsequently be used to assess the benefit of implementing LTV control such as adaptive control. The proposed methods are illustrated through simulated examples and an industrial case study.

Solution of Some One- and Two-Dimensional Master Equation Models for Thermal Dissociation: The Dissociation of Methane in the Low-Pressure Limit

Using three formulations of the master equation (ME), we have investigated theoretically the dissociation of methane in the low-pressure limit. The three forms of the ME are as follows: (1) A one-dimensional model in which E, the total energy, is the independent variable (the E model). (2) The two-dimensional strong-collision-in-J model of Smith and Gilbert (Int. J. Chem. Kinet. 1988, 20, 307−329) in which ε, the energy in the active degrees of freedom, and J, the total angular momentum quantum number, are the independent variables (the ε,J model). (3) A two-dimensional variant of the ε,J model in which E and J are the independent variables (the E,J model). The third form of the ME is the most physically realistic, and for this model we investigate the dependence of values of the energy transfer moments (〈ΔEd〉, −〈ΔE〉, and 〈ΔE2〉1/2) deduced from experiment on assumed forms of the energy transfer function, P(E,E‘), and on temperature. All three moments increase as the temperature rises; −〈ΔE〉 increases from 20−25 cm-1 at 300 K to 110−120 cm-1 at 4000 K. The variation in the energy transfer moments with the form of P(E,E‘) depends on the particular moment and the temperature, but generally the variation is not greater than 25%. For the same input to the models, the E and E,J models give similar values of the rate coefficient at high temperature, implying that the rotational degrees of freedom behave increasingly as if they are active as temperature is increased. For T > 3000 K, the dissociation perturbs the equilibrium energy distribution of the molecule so much that the detailed-balance condition begins to fail; i.e., k0(T)/kr(T) ≠ Keq(T), where k0(T) and kr(T) are the dissociation and recombination rate coefficients and Keq(T) is the equilibrium constant.

Criterions for detectability and strong detectability of faults in linear systems

A fault is (strongly) detectable if it is possible to construct a residual generator that is sensitive to the (constant) fault while decoupling all disturbances. Existing fault detectability criterions are reviewed and in two cases, improved versions are derived. For strong fault detectability, three new criterions are presented. To prove all criterions, a framework of polynomial bases is utilized. With these new and improved criterions, there exists now a criterion for models given both on transfer function form and state-space form, and for both fault detectability and strong fault detectability investigations. Recommendations are given on what criterion to use in different situations.

RESIDUAL GENERATION FOR FAULT DIAGNOSIS OF SYSTEMS DESCRIBED BY GENERAL LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

An algorithm for designing linear residual generators is presented. A main result is that the algorithm is able to design residual generators for any model described by general linear differential-algebraic equations. Previous algorithms have been restricted to models on transfer function, state space, or descriptor form. The presented algorithm can handle all these types of models, but also more general model descriptions not handled by previous algorithms. This is important since more general linear differential-algebraic equations models are often the result of object-oriented equation-based modeling. Also included is an extension to the stochastic case. Since the algorithm is based on well studied algebraic manipulations of polynomial matrices, it will have good numerical performance. The algorithm is demonstrated on a linearized model of a three-link robot.