Initial Guess Values Research Articles

Identification of Armax Models With Time Dependent Coefficients

A method that uses input/output measurements is developed for the estimation of the coefficients of stochastic Time-varying AutoRegressive Moving Average with eXogeneous imputs (TARMAX) models. The TARMAX coefficients are expressed as linear combinations of a set of pre-selected functions. The model coefficients estimation method is fully based on linear operations, does not require initial guess values and is suitable for micro-computer implementation. The good performance of the estimation method is verified through numerical examples. A TARMAX model is also used to capture the dynamics of a detailed highly nonlinear model of an automobile hydraulic active suspension system. The TARMAX model is used to relate a desired force provided by a corner processor to the actual force generated by the hydraulic actuator. The TARMAX model is shown to provide good signal prediction ability.

Joint inversion of induction/lateral/normal logs, case studies at Shenli field site, China

The behavior of local convergence and nonunique solutions in electric-logging inversion problems make logging interpretation difficult. These negative effects are improved by joint inversion of induction- and galvanic-logging measurements. A two-dimensional joint inversion algorithm is suggested for the simultaneous estimation of formation resistivity, invasion depth and invasion-zone resistivity from field data containing a combination of induction array, lateral and normal devices. Compared with single-log inversion of lateral and normal logs, the joint inversion not only improves the unfavorable local convergence of single inversion, but also constrains the range of possible solutions. Even if the initial guess values vary within a wide region, the joint inversion is fast to converge close to true values; it weakens the dependence of inversion results on initial guesses. In addition, these nonunique solutions are constrained in a limited domain by the present joint inversion technique, thus, the inconsistent interpretations that are usually caused by traditional single-log approach can be avoided. Case studies also illustrate that the present joint inversion of induction/lateral/normal logs provides a reasonable and efficient algorithm that allows for improving the accuracy of the results, enhancing the reliability of formation parameter estimation, and in most cases reducing the uncertainty of hydrocarbon saturation.

Determination of Lamb mode eigenvalues.

An original method is presented to determine the complex Lamb wave spectrum by using a numerical spectral method applied to the elasticity equations. This method presents the advantage to directly determine complex wave numbers for a given frequency via a classical matricial eigenvalue problem, and allows the wave numbers to be determined at relatively high frequencies (i.e., corresponding to many propagating modes). It does not need initial guess values for the wave numbers, contrary to the usual method of root finding of the Rayleigh-Lamb frequency equations (dispersion relation) in the complex plane. Results are presented and the method is discussed.

傾斜坑井デザインにおける生産システムの最適化

In the design of deviated well trajectories, the minimization of torque and drag has conventionally been one of the most important factors to be considered. Once the well starts production, however, thetrajectories of the deviated wells become strongly influential on the vertical pressure loss performance intubings. Well trajectories, therefore, need to be well-optimized using production engineering-basedevaluations for minimizing the pressure loss in the vertical flow in tubings and hence for maximizing the production rate from the reservoir.In this paper, well trajectories and tubing parameters of deviated wells were optimized in terms of profit-based objective functions. The net present values from the well production operations, after discounting the well drilling costs, were defined as the objective function for optimization. In the optimization process, Newton-type methods, the polytope method and Genetic Algorithms were applied and their efficiency and stability in optimization calculations were investigated.Among the optimization calculations, Newton-type methods showed poor optimization performance due to the lack of robustness to avoid the convergence to local maximum/minimum on the objective function surfaces. Genetic Algorithms showed the best performance in finding optimum well trajectory and tubing parameters. In some cases, the polytope method performed well, though the performances of the polytope method were dependent on initial guess values for the iteration.With the appropriate application of production optimization methods in deviated well designs, more profitable and realistic well design would be enabled for the future reservoir development.

LDA measurements and CFD simulations of flow generated by impellers in mechanically agitated reactors

The turbulent flow produced by various designs of axial flow impellers in a stirred vessel was measured using a laser Doppler anemometer (LDA). Flat-bottomed cylindrical vessels of diameters 0.3 m and 0.5 m provided with 4 baffles ofT/10 width were used as the reactors. The standard two-equation (k-e) turbulence model was used to numerically simulate the flow (both 2D and 3D). Three numerical schemes, namely upwind scheme, hybrid scheme and power-law scheme, were used to evaluate the competitiveness of the various schemes. The effects of the initial guess values of the flow variables, the under-relaxation parameters and internal iterations etc. on the rate of convergence were analysed for both 2D and 3D models. The effect of grid size was also studied in both the cases. The 2D and 3D predictions were compared and it was observed that the 2D predictions were not good enough to give the details of the flow. So, the sensitivity of the model parameters on the flow characteristics was investigated thoroughly in the case of 3D models. It was observed that no single set of model parameters could yield even reasonable agreement between the model predictions and the experimental observations throughout the vessel. Therefore, the concept of zonal modelling was introduced for ther-z plane. It was observed that with the introduction of zonal modelling the predicted values of flow variables were in good agreement with experimental data even close to the top surface of the tank. The same could not be obtained with a standard set of parameters and single zone.

NUMERICAL ESTIMATION OF THERMAL CONDUCTIVITY FROM BOUNDARY TEMPERATURE MEASUREMENTS

A numerical algorithm is proposed to estimate the thermal conductivity of a homogeneous material from boundary temperature measurements. In this inverse analysis the homogeneous material is divided into several subdomains, and the thermal conductivity in each individual subdomain is assumed to be a linear function of temperature. A hybrid numerical scheme involving the combination of the Laplace transform technique and the control volume method is used to solve the pertinent nonlinear equations. The estimated thermal conductivity of the material is taken as a combination of estimated values of those subdomains. The accuracy of the predicted results is examined from an illustrated case using simulated transient boundary temperature data with measurement errors. Results show that good estimations on the thermal conductivity can be obtained with arbitrary initial guess values. The present study found that the thermal conductivity can be determined without measuring temperature data inside the material.

The absolute instability of boundary-layer flow over viscoelastic walls

The linear stability of boundary-layer flow over a viscoelastic-layer wall is considered. A companion matrix technique is used to formulate the stability problem as a linear matrix eigenvalue problem for complex frequency and all the eigenvalues may be determined without any initial guess values. The eigenvalues are compared with those obtained with an accurate shooting method. The instability character of the boundary-layer flow is further investigated with the purpose of finding the conditions under which the instability of the flow could become absolute. The mapping technique of Kupferet al. (1987) is used to identify the occurrence of absolute instability eigenvalues. Absolute instabilities are discovered for cases of soft damped wall over certain ranges of Reynolds number. The effects of wall material stiffness, damping coefficient, thickness of layer, and Reynolds number on the occurrence of absolute instability are examined and presented.

MODELLING OF SLOPE FAILURE USING A GLOBAL OPTIMIZATION TECHNIQUE

This paper deals with modelling of slope failure of natural slopes using the RST-2 algorithm, a random search global optimization technique. The factor of safety equation for a given slope based on Janbu's method of slices has been used in the analysis, using the co-ordinates of the slip surface. By the RST-2 algorithm the critical non-circular slip surface is located by determining the unique combination of the co-ordinates of the slip surface which minimize the factor of safety. Although any optimization technique could be used for the analysis, the RST-2 algorithm has been particularly selected since (1) it attempts to determine the global rather than the local optimal solution;(2) it does not require any continuity and differentiability conditions of the functions appearing in the optimization problem (in this case the objective function is a discontinuous function); (3) it does not require any initial guess value of the slip surface to initiate the algorithm, but requires an approximate lower and upper bound of the co-ordinates of the slip domain; (4) it is easy to programme, and can be applicable to a wide variety of problems. The model developed has been successfully applied to three original case studies. A comparison of the results between Bishop's method (circular), and Janbu's method (non-circular) using the hit and trial approach for the location of the critical slip surface and the RST-2 algorithm as a numerical technique for global optimization has been made. It can be concluded that the RST-2 algorithm is a very efficient, accurate and convenient algorithm to use for determining the critical failure surface and its corresponding minimum factor of safety. Moreover, the failure surface is not assumed but is arrived at by only providing the domain of the failure surface as the input

The uniqueness of the local minimum for power economic dispatch problems

Abstract The functions of the cost curve and transmission losses are nonlinear and simultaneously subject to equality and inequality constraints in the economic power dispatch problem. Mathematically, the solution of the nonlinear equations of the economic power dispatch problem may result in multiple solutions. Conventional methods may fail to find all the multiple solutions if the initial guess values are not appropriately located within the region of convergency. To overcome this difficulty, the homotopy method is suggested for the solution technique. Concurrently, the properties of the convex function are applied to analyze the intersection equation of the objective equation and the equality constraints equation. Hence we can demonstrate that only one local minimum exists in the augmented cost function, so that the local minimum is the optimal solution of the economic power dispatch problem.

Simulation of Flow in Stirred Vessels with Axial Flow Impellers: Effects of Various Numerical Schemes and Turbulence Model Parameters

The standard two-equation (k-e) turbulence model has been used to numerically simulate the flow in an agitated baffled cylindrical vessel with axial flow impellers. Three numerical schemes, namely, upwind scheme, hybrid scheme, and power-law scheme, were used to evaluate the competitiveness of the various schemes. The solutions were obtained by using the SIMPLE algorithm. The effects of initial guess values of the flow variables, the underrelaxation parameters, internal iterations, etc., on the rate of convergence were analyzed. The sensitivity of the model parameters on the flow characteristics was investigated thoroughly. Further, the effects of global grid sizes and near-wall grid sizes on the solution were also investigated. The boundary conditions in the impeller region for the velocities and turbulent kinetic energy were provided from the experimental data. However, for the energy dissipation rate, as iterative process was adopted taking the local information into account. Computations were carried out for six different impeller designs. It was found that the predicted values were qualitatively in good agreement with the experimental data.

Selection method of initial guess values for surface temperature estimation from the satellite data

Abstract For the estimation of sea surface temperature on the basis of linearized inversion of the radiative transfer equation (Rodgers method), the selection method of the initial guess values of sea surface temperature and atmospheric condition is proposed. The selection method uses the temporal statistics of air temperature profile and precipitable water profiles as an atmospheric models. The satellite observed brightness temperature is calculated from the atmospheric models and some surface models, and the atmospheric model and surface model which makes the difference between the calculated and the observed radiance minimize is selected as the initial guess values. The sea surface temperature estimation from MOS-1/VTIR data shows a good correspondence to the sea truth data.

Measurement of Neutron Activation Cross Sections for Energies up to 40 MeV for Natural Samples of Mg, Si, Ca, V, Cr, Cu and Zn

The cross section measurements of 17 neutron induced reactions using an intense semi-monoenergetic neutron field were recently reported. Neutrons for energies up to 40 MeV were produced by a simple Be target system bombarded by protons of 9 different energies between 20 and 40 MeV. Successively in this neutron field, we measured the cross sections of 15 reactions of natMg(n, Xnp) 24Na, natSi(n, Xn2p) 27Mg, natSi(n, Xnp) 28Al, natSi(n, Xnp) 29Al, natCa(n, Xnp) 42K, natCa(n, Xnp) 43K, nat (n, Xn2p) 46Sc, natV(n, Xn2p) 47Sc, natCr(n, Xnp,) V52V, natCr(n, Xnp) 53V, natCu(n, Xn2p) 62mCo (T 1/2=14 min), natZn(n, Xn2p) 65Ni, natZn(n, Xnp)Cu,64Cu, natZn(n, Xnp)Cu,66Cu and natZn(n, Xnp) 68mCu ( T,1/2=3.8 min) by irradiating natural samples of Mg, Si, Ca, V, Cr, Cu and Zn. The excitation functions of these reactions were obtained by using the least- squares fitting (LSF) of the cross-section values calculated with the ALICE/LIVERMORE82 code, and also by using the SAND-II and the NEUPAC unfolding codes with the initial guess values derived from the LSF results and empirical reference data.

An equation decoupling technique for identification of unstable aircraft with unsteady aerodynamic modelling

AbstractA simplified trailing vortex concept has been used to model unsteady aerodynamic effects onto the mathematical model for an augmented unstable aircraft. An output error method with, and without, an equation decoupling technique in the frequency domain has been used for the estimation of parameters. The two approaches of estimation are compared for the cases where unsteady effects are included or excluded from the estimation model. It is shown that the incorporation of the equation decoupling technique makes the estimation algorithm robust with respect to initial guess values of the parameters. Finally, the inclusion of unsteady aerodynamics is shown to reduce the variation in the parameter estimates due to different control input forms.

Maximum life spur gear design

Optimization procedures allow one to design a spur gear reduction for maximum life and other end use criteria. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial guess values. The optimization algorithm is described, and the models for gear life and performance are presented. The algorithm is compact and has been programmed for execution on a desk top computer. Two examples are presented to illustrate the method and its application.

Measurement of Neutron Activation Cross Sections of Energy up to 40 MeV Using Semimonoenergetic p-Be Neutrons

An intense semimonoenergetic neutron field was made using a simple beryllium target system bombarded by protons of nine different energies between 20 and 40 MeV. Natural sodium, aluminum, vanadium, chromium, manganese, copper, zinc, and gold samples were irradiated at this field, and gamma rays from the samples were observed by a germanium detector. The production rates of 17 radionuclides were obtained for the nine different neutron fields, and the excitation functions of these 17 reaction channels of 23Na(n,2n)22Na, 27Al(n, α)24Na, 51V(n, α)48Sc, 51V(n,p)51Ti, 50Cr(n,3n)48Cr, 50Cr(n,2n)49Cr, 55Mn(n,4n)51Ti, 55Mn(n,4n)52Mn, 55Mn(n,2n)54Mn, 63Cu(n,3n) Cu, 63Cu(n,2n)62Cu, 65Cu(n,p)65Ni, 64Zn(n,t)62 Cu, 64Zn(n,3n)62Zn, 64Zn(n,2n)63Zn, 197Au(n,4n)194Au, and 197Au(n,2n)196Au were obtained for neutron energies up to 40 MeV by using the SAND-II and the NEUPAC unfolding codes and also least-squares fitting. The initial guess value for these methods was obtained primarily from calculations of the ALICE/LIVERMORE82 code.

Impedance analysis method for painted and unpainted metals

An interactive computer analysis program, Z_CALC, is described for the analysis of electrochemical impedance data obtained from both unpainted and painted metal/solution interfaces. This program consists of two main subprograms, AUTOGUESS and CURVEFIT. The subprogram AUTOGUESS is used to obtain initial guess values for parameters of the model chosen to represent the unpainted or painted metal/solution interface. It is a semi-automatic routine requiring only a little operator iteration to identify impedance data belonging to a semicircle. AUTOGUESS is based on a non-iterative linear least squares curve fitting procedure for a Nyquist depressed semicircle, and on the method of subtraction. Subprogram CURVEFIT uses the initial guess values from AUTOGUESS and improves their accuracy using an iterative, complex, non-linear least squares method. Three such non-linear least squares algorithms (Gauss-Newton, Levenberg-Marquardt, Modified Gauss-Newton), are compared, using corrupted theoretical data, for their ability to converge and speed of execution. Z_CALC is also compared with two commercially available impedance analysis programs—EUQIVCRT and LEVM. These comparisons indicate what computers the programs run on, the ability of each program to provide parameter initial guess values, the types of equivalent circuit models available, curve fitting ability (convergence properties and number of iterations) and user-friendliness. Examples are given of the application of the Z_CALC program for the analysis of impedance data from unpainted (a 55%Al-Zn Atmospheric Corrosion Monitor with 0.5 mm water films exposed to laboratory air containing 0.05 ppm [SO 2]) and painted (silicone modified polyester painted ZINCALUME (55%Al-Zn alloy coating on a steel substrate) immersed in 5% NaCl solution at 50°C) metals.

System Identification of Multivariate Systems With Feedback

System identification of linear stochastic systems has been the concern of many scientists and engineers. The same system can be described in many ways and consequently many different models have been proposed. However, the complexity of the systems and computational difficulty, especially under the presence of feedback and external disturbances, have rendered identification a difficult task. This paper deals with a general modeling procedure that can be used for identification of feedback systems. First, a brief discussion on the joint input-output process models is given, followed by the discussion on the canonical representation of the model. A simplified model is derived from the general vector model. This will lead to the validity of using the Modified Autoregressive Moving Average Vector (MARMAV) model in the identification of the general multivariate system with open-loop and closed-loop dynamics. Next, an estimation procedure is explained. The estimation is pursued to reach a maximum likelihood model by nonlinear iterative calculations. Since initial values are required to start the procedure which are critical to the estimation, two methods for the initial guess value estimation are provided in the appendices.

A method to calculate the structure and motion parameters from line correspondences

In this paper a new scheme is introduced for the estimation of structure and motion parameters in an image sequence. The proposed method consists of two steps. In the first step, using the correspondences of two straight lines over four frames, a set of nonlinear equations in terms of the structure and motion parameters is established. In order to solve the simultaneous equations numerically, a good initial guess is required, thus the second step uses a new technique to obtain initial guess values of the parameters from the existing solutions for planar surfaces.

Optimal Parameter Estimation for Hydro-Plant Performance Models in Economic Operation Studies

Optimal Economic Operational schedules in hydro-thermal electric power systems are obtained on the basis of models of the various subsystems involved. In this paper we are concerned with models of hydro-plant performance characteristics. Due to the diversity of plant types and installations, a number of models have been proposed in developing optimal operational strategies over the years. Here we choose four commonly used models. The problem of finding optimal estimates of model parameters is investigated for the Glimn-Kirchmayer model, the Hildebrand model, the Hamilton-Lamont model and the Arvanitidis-Rosing model. We develop the optimal estimator equations for each model using the weighted-least-squares approach. The result for three of the models is a set of nonlinear equations in the unknown parameters. We adopt Newton's method for actually implementing the optimal estimators. Due to the sensitivity of the algorithm's convergence characteristics to the initial guess of the unknowns, we explore and present procedures for generating initial guess values to improve the procedure's performance. Computational experience with the techniques is given in the paper to confirm its feasibility using test data from existing hydro-plants. The paper proposes and examines some extensions to the classical models to improve the accuracy of the modeling process.

Application of the homotopy method to load flow solution-finding all the multiple solutions

Mathematically, the solution of the non-linear equations of load flow problems may result in multiple solutions. Conventional methods may fail to find all the multiple solutions if the initial guess values are not appropriately located within the convergency region. To overcome this difficulty, the homotopy method is suggested for the solution technique. In this paper, the mathematical performance of the homotopy theorem is discussed and its application to the load flow solution method is approached. By the proposed method, the ‘approach load flow solution’ can be obtained more systematically using no strict rules to determine the initial guess values. Utilization of the Newton-Raphson method with the approach load flow solutions guarantees all the multiple solutions. In the solution method, extra computation time and additional storage requirements result from the additional step. Nevertheless, the proposed method is highly recommended.