Search results for: differential algebraic equations

Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

Abstract:

This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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Authors: Amit Goyal, Alka, Rama Gupta, C. Nagaraja Kumar

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We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some cases, the BF equations could be solved for arbitrary timedependent coefficient of convection term.

Keywords: Solitary wave solution, Variable coefficient Burgers- Fisher equation, Auxiliary equation method.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: Ameleh Aghajanloo, Moharam Dolatshahi Pirouz, Masoud Montazeri Namin

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In this paper, a two-dimensional (2D) numerical model for the tidal currents simulation in Persian Gulf is presented. The model is based on the depth averaged equations of shallow water which consider hydrostatic pressure distribution. The continuity equation and two momentum equations including the effects of bed friction, the Coriolis effects and wind stress have been solved. To integrate the 2D equations, the Alternative Direction Implicit (ADI) technique has been used. The base of equations discritization was finite volume method applied on rectangular mesh. To evaluate the model validation, a dam break case study including analytical solution is selected and the comparison is done. After that, the capability of the model in simulation of tidal current in a real field is represented by modeling the current behavior in Persian Gulf. The tidal fluctuations in Hormuz Strait have caused the tidal currents in the area of study. Therefore, the water surface oscillations data at Hengam Island on Hormoz Strait are used as the model input data. The check point of the model is measured water surface elevations at Assaluye port. The comparison between the results and the acceptable agreement of them showed the model ability for modeling marine hydrodynamic.

Keywords: Persian Gulf, Tidal Currents, Shallow Water Equations, Finite Volumes

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Authors: Tae Yun Chung, Jungho Moon, Tae Kwon Ha

Abstract:

Al/Cu clad sheet has been fabricated by using differential speed rolling (DSR) process, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100 and 150oC with speed ratios from 1.4 to 2.2, in which the total thickness reduction was in the range between 14 and 46%. Interfacial microstructure and mechanical properties of Al/Cu clad were investigated by scanning electron microscope equipped with energy dispersive X-ray detector, and tension tests. The DSR process was very effective to provide a good interface for atoms diffusion during subsequent annealing. The strength of bonding was higher with the increasing speed ratio. Post heat treatment enhanced the mechanical properties of clad sheet by forming intermetallic compounds in the interface area. 

Keywords: Aluminum/Copper clad sheet, Differential speed rolling, Interface microstructure, Annealing, Tensile test.

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Authors: S.H. Mirtalaie, M.A. Hajabasi

Abstract:

In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.

Keywords: Free vibration, laminated composite beam, material coupling, state space.

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Authors: G. Sarojamma, K. Vendabai

Abstract:

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: Casson nanofluid, Boundary layer flow, Internal heat generation/absorption, Exponentially stretching cylinder, Heat transfer, Brownian motion, Thermophoresis.

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Authors: Vineet K. Srivastava, Mukesh K. Awasthi, Mohammad Tamsir

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A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.

Keywords: Burgers’ equation, Implicit Finite-difference method, Newton’s method, Gauss elimination with partial pivoting.

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Authors: Abhijit Chandra, Sudipta Chattopadhyay

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In this communication, we have made an attempt to design multiplier-less low-pass finite impulse response (FIR) filter with the aid of various mutation strategies of Differential Evolution (DE) algorithm. Impulse response coefficient of the designed FIR filter has been represented as sums or differences of powers of two. Performance of the proposed filter has been evaluated in terms of its frequency response and associated hardware cost. Supremacy of our approach has been substantiated by comparing our result with many of the existing multiplier-less filter design algorithms of recent interest. It has also been demonstrated that DE-optimized filter outperforms Genetic Algorithm (GA) based design by a large margin.  Hardware efficiency of our algorithm has further been validated by implementing those filters on a Field Programmable Gate Array (FPGA) chip.

Keywords: Convergence speed, Differential Evolution (DE), error histogram, finite impulse response (FIR) filter, total power of two (TPT), zero-valued filter coefficient (ZFC).

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Authors: Nurul Zahirah M.A., N. Zainul Abidin

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Green buildings have been commonly cited to be more expensive than conventional buildings. However, limited research has been conducted to clearly identify elements that contribute to this cost differential. The construction cost of buildings can be typically divided into “hard" costs and “soft" cost elements. Using a review analysis of existing literature, the study identified six main elements in green buildings that contribute to the general cost elements that are “soft" in nature. The six elements found are insurance, developer-s experience, design cost, certification, commissioning and energy modeling. Out of the six elements, most literatures have highlighted the increase in design cost for green design as compared to conventional design due to additional architectural and engineering costs, eco-charettes, extra design time, and the further need for a green consultant. The study concluded that these elements of soft cost contribute to the green premium or cost differential of green buildings.

Keywords: Green building, cost differential, soft cost, intangible cost.

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Authors: I. Naeem, R. Naz

Abstract:

The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.

Keywords: Two-dimensional jets, radial jets, group invariant solution.

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Authors: Y. V. Kim

Abstract:

This article presents an approach with regards to the Functional Testing of Space System (SS) that could be a space vehicle (spacecraft-S/C) and/or its equipment and components – S/C subsystems. This test should finalize the Space Qualification Tests (SQT) campaign. It could be considered as a generic test and used for a wide class of SS that, from the point of view of System Dynamics and Control Theory, may be described by the ordinary differential equations. The suggested methodology is based on using semi-natural experiment laboratory stand that does not require complicated, precise and expensive technological control-verification equipment. However, it allows for testing totally assembled system during Assembling, Integration and Testing (AIT) activities at the final phase of SQT, involving system hardware (HW) and software (SW). The test physically activates system input (sensors) and output (actuators) and requires recording their outputs in real time. The data are then inserted in a laboratory computer, where it is post-experiment processed by the MATLAB/Simulink Identification Toolbox. It allows for estimating the system dynamics in the form of estimation of its differential equation coefficients through the verification experimental test and comparing them with expected mathematical model, prematurely verified by mathematical simulation during the design process. Mathematical simulation results presented in the article show that this approach could be applicable and helpful in SQT practice. Further semi-natural experiments should specify detail requirements for the test laboratory equipment and test-procedures.

Keywords: system dynamics, space system ground tests, space qualification, system dynamics identification, satellite attitude control, assembling integration and testing

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

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In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper presents a differential evolution algorithm to design a robust PI and PID controllers for Load Frequency Control (LFC) of nonlinear interconnected power systems considering the boiler dynamics, Governor Dead Band (GDB), Generation Rate Constraint (GRC). Differential evolution algorithm is employed to search for the optimal controller parameters. The proposed method easily copes of with nonlinear constraints. Further the proposed controller is simple, effective and can ensure the desirable overall system performance. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic controller for the same power systems. The comparison is done using various performance measures like overshoot, settling time and standard error criteria of frequency and tie-line power deviation following a 1% step load perturbation in hydro area. It is noticed that, the dynamic performance of proposed controller is better than fuzzy logic controller. Furthermore, it is also seen that the proposed system is robust and is not affected by change in the system parameters.

Keywords: Automatic Generation control (AGC), Generation Rate Constraint (GRC), Governor Dead Band (GDB), Differential Evolution (DE)

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Authors: S. Behnia, S. Fathizadeh

Abstract:

Conductivity properties of DNA molecule is investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. This model is a tight-binding linear nanoscale chain. We have tried to study the electrical current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: Charge transfer in DNA, Chaos theory, Molecular electronics, Negative Differential resistance.

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Authors: Kittipong Tripetch

Abstract:

This paper proposes a study of input impedance of 2 types of CMOS active inductors. It derives 2 input impedance formulas. The first formula is the input impedance of the grounded active inductor. The second formula is the input impedance of the floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of the fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption. 

Keywords: Grounded active inductor, floating active inductor, Fully differential bandpass amplifier.

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: Bonded rubber, quasi-static test, shape factor, apparent Young’s modulus.

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Authors: T. Messikh, S. Mekhilef, N. A. Rahim

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This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.

Keywords: Adaptive notch filter, Active power filter, harmonic filtering, Time varying frequency.

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

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This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: Convection flow, internal heat generation, similarity, spectral method, numerical analysis, Williamson nanofluid.

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Authors: Changzhao Li, Juan Zhang

Abstract:

In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.

Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.

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Authors: Sanaz Haddadian, Rahele Hedayati

Abstract:

A 10bit, 40 MSps, sample and hold, implemented in 0.18-μm CMOS technology with 3.3V supply, is presented for application in the front-end stage of an analog-to-digital converter. Topology selection, biasing, compensation and common mode feedback are discussed. Cascode technique has been used to increase the dc gain. The proposed opamp provides 149MHz unity-gain bandwidth (wu), 80 degree phase margin and a differential peak to peak output swing more than 2.5v. The circuit has 55db Total Harmonic Distortion (THD), using the improved fully differential two stage operational amplifier of 91.7dB gain. The power dissipation of the designed sample and hold is 4.7mw. The designed system demonstrates relatively suitable response in different process, temperature and supply corners (PVT corners).

Keywords: Analog Integrated Circuit Design, Sample & Hold Amplifier and CMOS Technology.

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial or non-inertial reference frame.

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Authors: O. Miraliyari

Abstract:

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

Keywords: Thermal buckling, functionally graded beam, piezoelectric layer, various boundary conditions.

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Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Randhir Singh Baghel, Govind Shay Sharma

Abstract:

In this paper, we explore an ecosystem that contains a three-species food chain. The first and second species are in competition with one another for resources. However, the third species plays an important role in providing non-linear Crowley-Martin functional support for the first species. Additionally, the third species consumes the second species in a linear fashion, taking advantage of the available resources. This intricate balance ensures the survival of all three species in the ecosystem. A set of non-linear isolated first-order differential equations establish this model. We examine the system's stability at all potential equilibrium locations using the perturbed technique. Furthermore, by spending a lot of time observing the species in their natural habitat, the numerical illustrations at suitable parameter values for the model are shown.

Keywords: Competition, predator, response function, local stability, numerical simulations.

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Authors: V. Tawiwat, T. Amornthep, P. Pnop

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Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper considers the indirect minimum Jerk method for higher order differential equation in dynamics optimization proposes a simple yet very interesting indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This case considers the linear equation of a simple system, for instance, mass, spring and damping. The simple system uses two mass connected together by springs. The boundary initial is defined the fix end time and end point. The higher differential order is solved by Galerkin-s methods weight residual. As the result, the 6th higher differential order shows the faster solving time.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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