Initial Guess Values Research Articles

Solution of the Blasius and Sakiadis equation by generalized iterative differential quadrature method

The Blasius and Sakiadis equation was solved earlier with different numerical methods. In this study, it was solved by using the generalized iterative differential quadrature method (GIDQM). And more than one condition are imposed at the same point without using any higher-order polynomial or δ-point approximation in GIDQM although it is one of the most important drawbacks in the differential quadrature method (DQM). Procedure is started with an initial guess value and true results are obtained by iterations. More grid points are used. Hence, the solution of the Blasius equation is calculated precisely and showed good agreements when compared with other works. Copyright © 2009 John Wiley & Sons, Ltd.

Genetic algorithms based robust frequency estimation of sinusoidal signals with stationary errors

In this paper, we consider the fundamental problem of frequency estimation of multiple sinusoidal signals with stationary errors. We propose genetic algorithm and outlier-insensitive criterion function based technique for the frequency estimation problem. In the simulation studies and real life data analysis, it is observed that the proposed genetic algorithm based robust frequency estimators are able to resolve frequencies of the sinusoidal model with high degree of accuracy. Among the proposed methods, the genetic algorithm based least squares estimator, in the no-outlier scenario, provides efficient estimates, in the sense that their mean square errors attain the corresponding Cramér-Rao lower bounds. In the presence of outliers, the proposed robust methods perform quite well and seem to have a fairly high breakdown point with respect to level of outlier contamination. The proposed methods significantly do not depend on the initial guess values required for other iterative frequency estimation methods.

5143 Resource-based data availability for erbB2-driven breast cancer in Asian women: experts' opinion

In this study, simplex search method (SSM) and a differential evolution (DE) based inverse algorithm are applied to estimate fuel flow rate (FFR), boiler pressure (BP) and steam turbine (ST) inlet temperature (STIT) of a ST based power cycle. First a theoretical model simulates the cycle performance in terms of net power, efficiency (energy and exergy) and total irreversibility at various FFRs, BPs and STITs. The forward model based results show that the net power increases linearly with FFR while also producing more irreversible losses at higher FFR. The cycle performance also improves at higher BP and STIT. The inverse analysis shows that the DE based method is more appropriate than the SSM where the searching range of parameters is specified and parameter estimation is done from the range of specified parameter values. In SSM, the estimation depends upon the chosen initial guess values and convergence criterion sometimes is not fulfilled with some guessed values of the parameters. Both the inverse methods, however give multiple combinations of parameters and thus provides sufficient scope at the hands of the designer to select the appropriate combinations of parameters required for meeting a particular power requirement.

Optimal Design of Multichannel Fiber Bragg Grating Filters With Small Dispersion and Low Index Modulation

We have proposed an effective method to synthesize and optimize multichannel fiber Bragg grating filters (MCFBGFs). The novel method contains two steps, i.e., the discrete layer peeling algorithm generates the excellent initial guess values and, successively, the nonlinear least squares method reconstructs and optimizes the expected fiber Bragg grating parameters from the initial guess in the previous step. Design examples demonstrate that the proposed method has unique merits to optimize the reflectivity and dispersion of MCFBGFs and effectively reduce their index modulation simultaneously.

Indirect fitting procedure to separate the effects of mobility degradation and source-and-drain resistance in MOSFET parameter extraction

A new procedure is presented to separate the effects of source-and-drain series resistance and mobility degradation factor in the extraction of MOSFET model parameters. It requires only a single test device and it is based on fitting the I D ( V GS , V DS ) equation to the measured characteristics. Two types of bidimensional fitting are explored: direct fitting to the drain current and indirect fitting to the measured source-to-drain resistance. The indirect fitting is shown to be advantageous in terms of fewer number of iterations needed and wider extent of initial guess values range.

Estimation of heat flux and thermal stresses in multilayer gun barrel with thermal contact resistance

In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown time-dependent heat flux at the inner surface of gun barrel, in which the interlayer thermal contact resistance between the steel cylinder and the chrome coating is taken into account in the boundary conditions. While knowing the temperature history at the measuring position, no prior information is needed on the functional form of the unknown heat flux. The temperature data calculated from the direct problem are used to simulate the temperature measurement. The influence of measurement errors and initial guess values upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent heat flux, temperature distributions, and thermal stresses can be obtained for the case considered in this study.

Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method

For most parallel manipulators, the inverse kinematics is straightforward, while the direct kinematics is challenging. The latter requires the solution of a system of nonlinear equations. In this paper we use the homotopy continuation method to solve the forward and inverse kinematic problems of an offset 3-UPU translational parallel manipulator. The homotopy continuation method is a novel method which alleviates drawbacks of the traditional numerical techniques, namely; the acquirement of good initial guess values, the problem of convergence and computing time. The direct kinematics problem of the manipulator leads to 16 real solutions.

LOAD FLOW SOLUTION FOR ILL-CONDITIONED BY HOMOTOPY CONTINUATION METHOD

Although the Newton-Raphson method possesses very powerful convergence characteristics, this algorithm can not have a guarantee for finding load flow solutions if the power system is ill-conditioned. In this paper, the application of the homotopy method to solve the ill-conditioned system is proposed and discussed. This method merits attention to the flexibility of choosing the initial guess values. To present this superiority, different cases of ill-conditioned power systems are tested. Numerical convergence is discussed for each particular case. It is ideally suitable for finding load flow solutions of ill-conditioned power systems.

Estimation of thermal contact resistance and thermally induced optical effects in single-coated optical fibers

In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown time-dependent thermal contact resistance in a single-coated optical fiber, which is subjected to transient thermal loading. While knowing the temperature history at the measuring position, no prior information is needed on the functional form of the unknown contact resistance. The temperature data obtained from the direct problem are used to simulate the temperature measurement. The influence of measurement errors, initial guess values, and measurement locations upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent thermal contact resistance, temperature distributions, thermally induced microbending loss, and refractive index changes can be obtained for the case considered in this study.

Comparison of the Luus−Jaakola Optimization and Gauss−Newton Methods for Parameter Estimation in Ordinary Differential Equation Models

The direct search optimization method of Luus and Jaakola (LJ) and the Gauss−Newton (GN) method are employed to solve four parameter optimization problems for chemical and biochemical processes described by ordinary differential equation models. A comparison of the solution methods was thus carried out. It was found that the impact of initial guess values is minimal on the optimal parameters and the optimum. Gauss−Newton, however, was found to be sensitive to the initial guess. Moreover, GN encountered convergence problems which were alleviated by the use of the Marquardt−Levenberg approach.

Optimal Grade Transition in Polymerization Reactors: A Comparative Case Study

A detailed study of grade transitions, as encountered in polymerization reactors, is presented. We explore various issues such as the nonconvexity of the associated dynamic optimization problem and study its impact on the optimal policies when the widely used sequential quadratic programming (SQP) solvers are applied. The results underscore the need for global optimization algorithms to fully realize the benefits of grade transition that are typically nonconvex, because of the nonlinear dynamics of the process. A study of the structure of the objective function used in optimization of grade transitions indicates that opportunities exist for varying the degree of nonconvexity using a priori knowledge of the new grade and appropriate choice of weight matrices in the objective function. For comparison with the SQP solution, we use a nongradient, parallel search stochastic method, namely differential evolution (DE). Our simulations indicate that, although the DE solution is highly dependent on the algorithm parameters and mutation strategy, the SQP solution is dependent on the initial guess value and consistently provides faster convergence. However, if the objective function is modified using the a priori knowledge of the new grade and appropriate choice of the weight matrices, transition policies based on SQP become less dependent on the initial guess value and identical to the best DE solution while retaining its benefits of faster convergence. Finally, we also explore the issue of explicit minimization of the grade changeover time. We also present a study exhibiting sensitivity of the DE algorithm to its parameters. All of the aforementioned issues have been demonstrated for the grade transition of polymethyl methacrylate (PMMA) in a nonisothermal continuous stirred tank reactor (CSTR).

Frequency estimation of undamped exponential signals using genetic algorithms

In this paper, we consider the problem of frequency estimation of undamped superimposed exponential signals model. We propose two iterative techniques of frequency estimation using genetic algorithms. The proposed methods use an elitism based generational genetic algorithm for obtaining the least squares and the approximate least squares estimates. In the simulation studies, it is observed that the proposed methods give nearly efficient estimates, having mean square error almost attaining the corresponding Cramér–Rao lower bound. The proposed methods significantly do not depend on the initial guess values otherwise required for other iterative methods of frequency estimation. It is also observed that the proposed methods have fairly high breakdown point with respect to different types of outliers present in the data. Outlier robustness and accuracy of the proposed methods are compared with the classical approaches for this problem.

OPTIMAL GRADE TRANSITION IN POLYMERIZATION REACTORS: A COMPARATIVE CASE STUDY

A study of grade transitions as encountered in polymerization reactors is presented. The results underscore the need for global optimization algorithms to fully realize the benefits of grade transition that are necessarily non-convex. For comparison purposes we use a non-gradient, parallel search, stochastic method, namely differential evolution (DE). Our simulations indicate that while the DE solution is highly dependent on the algorithm parameters and mutation strategy, the SQP solution depends on the initial guess value and consistently provides faster convergence. Finally, we also explore the issue of evaluating the optimal grade changeover time. All of the above issues have been demonstrated for the grade transition of polymethyl methacrylate (PMMA) in a non-isothermal CSTR.

Improved closed loop identification of transfer function model for unstable systems

The method of identifying first order plus time delay transfer function model proposed for unstable systems by Ananth and Chidambaram [Closed loop identification to transfer function model for unstable systems, J. Franklin Inst. 336 (1999) 1055–1061] is modified to avoid the stability problems [Cheres, Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication] of the method. Two modifications are proposed. In the first modification of the method, the under-determined algebraic equations problem is converted into an optimization problem for calculation of the three parameters of the first order plus time delay (FOPTD) model. A simple method is given for the initial guess values of the model parameters. In the second approach, from the definition of Laplace transform of the output response, a third equation is formulated. The resulted three equations, in terms of the three parameters of the transfer function model, are then numerically solved. Simulation results are given for the second order plus time delay transfer function considered by Cheres 2005 [Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication]. The responses of the identified models with the same PID controllers are compared with that of the actual system. PID controllers are designed based on the identified models. The closed loop responses of the controllers on the original system are evaluated and compared. The present methods give better control performances.

An effect iteration algorithm for numerical solution of discrete hamilton-jacobi-bellman equations

An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution, then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.

A study of convergence on the Newton-homotopy continuation method

The traditional Newton method is a well-known and popular method for solving non-linear equation. It has high efficient in the convergence speed. However, we always need to guess the initial value in the iteration process. Good initial guess value can solve the equation quickly. Bad initial guess value usually will yield divergence. Homotopy continuation method is a kind of perturbation method. It can guarantee the answer by a certain path if we choose the auxiliary homotopy function, or call start system, well. This paper presents some useful rules for the choice of the auxiliary homotopy function to avoid the problem of divergence of traditional Newton method.

Estimation of initial conditions and parameters of a chaotic evolution process from a short time series

Tracing back to the initial state of a time-evolutionary process using a segment of historical time series may lead to many meaningful applications. In this paper, we present an estimation method that can detect the initial conditions, unobserved time-varying states and parameters of a dynamical (chaotic) system using a short scalar time series that may be contaminated by noise. The technique based on the Newton-Raphson method and the least-squares algorithm is tolerant to large mismatch between the initial guess and actual values. The feasibility and robustness of this method are illustrated via the numerical examples based on the Lorenz system and Rossler system corrupted with Gaussian noise.

Study on the adjoint method in data assimilation and the related problems

It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observedM 2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulateM 2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. the satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.

Aquifer parameter identification using the extended Kalman filter

An approach using the extended Kalman filter (EKF) and cubic spline is proposed to identify the aquifer parameters in both confined and unconfined aquifer systems. The cubic spline applied to the observation data can generate interpolated data with uniform time intervals and facilitates the implementation of EKF. The EKF combined with the Theis solution or Neuman's model, using the interpolated drawdown data produced by cubic spline, can optimally determine the parameters through the recursive process. The proposed approach can quickly identify the parameters, using only part of observed drawdown data, and the obtained parameters are shown to have good accuracy. Thus length of time of pumping tests may be shortened. Comparisons of results from nonlinear least squares combined with finite difference Newton's method (NLN) and EKF show that the EKF allows a wider range of initial guess values than NLN and have the accuracy of the results on the same order of magnitude as that of NLN. When determining the aquifer parameters, the identification process of specific yield reflects the effect of gravity drainage on the drawdown curve and conforms to the physical nature of an unconfined aquifer. Furthermore, this study shows that EKF can be successfully applied to analyze the drawdown data even with white noises or temporally correlated noises.

Chaos-regularization hybrid algorithm for nonlinear two-dimensional inverse heat conduction problem

A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature. Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model. The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.