Suitable Initial Values Research Articles

Efficient algorithm for estimating the parameters of two dimensional chirp signal

Two dimensional chirp signal has been used for modeling gray scale symmetric images in the statistical signal processing literature. In this paper we propose a computationally efficient algorithm for estimating different parameters of a two dimensional chirp signal model in presence of stationary noise. Starting from a suitable initial guess value, the proposed method produces estimators which are asymptotically equivalent to the corresponding least squares estimators. We also discuss how to obtain the initial estimates suitably. Some simulation experiments have been performed to see the effectiveness of the proposed method, and it is observed that the proposed estimators perform very well.

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process Xt to be fractional of order d and cofractional of order d b; that is, there exist vectorsfor which � 0 Xt is fractional of order d b: The parameters d and b satisfy either db � 1=2, d = b � 1=2, or d = d0 � b � 1=2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1=2� bdd1 for any d1� d0. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator ofis asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also …nd the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

Parabolic-trough solar thermal power plant simulation scheme, multi-objective genetic algorithm calibration and validation

Abstract The dynamic simulator design and development of a direct steam generation parabolic-trough solar thermal power plant is detailed in this paper. The dynamic simulator is not only the equation-based object-oriented model but also includes features to facilitate the simulation process. A whole simulator scheme has been developed for that purpose. This simulator scheme considers the issues of fetching and converting sensors data to model inputs and obtaining suitable initial values for the boundary condition problem in the numerical integration. The calibration and validation processes have been tackled, using Matlab as the primary tool. However, several tools were studied and tested. A multi-objective genetic algorithm approach has been chosen for calibrating the dynamic model.

Feature-based initial population generation for the optimization of job shop problems

A suitable initial value of a good (close to the optimal value) scheduling algorithm may greatly speed up the convergence rate. However, the initial population of current scheduling algorithms is randomly determined. Similar scheduling instances in the production process are not reused rationally. For this reason, we propose a method to generate the initial population of job shop problems. The scheduling model includes static and dynamic knowledge to generate the initial population of the genetic algorithm. The knowledge reflects scheduling constraints and priority rules. A scheduling strategy is implemented by matching and combining the two categories of scheduling knowledge, while the experience of dispatchers is externalized to semantic features. Feature similarity based knowledge matching is utilized to acquire the constraints that are in turn used to optimize the scheduling process. Results show that the proposed approach is feasible and effective for the job shop optimization problem.

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β′X_{t} is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d_{0}≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d_{1} for any d_{1}≥d_{0}. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β′X(t) is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d₀≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d₁ for any d₁≥d₀. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

Structure-Preserving Stabilization for Hamiltonian System and its Applications in Solar Sail

A structure-preserving controller is constructed to stabilize a hyperbolic Hamiltonian system. Bounded orbits for the planar solar sail three-body problem are generated by means of the controller. The invariant (stable, unstable, and center) manifolds of the equilibrium are used to stabilize a Hamiltonian system of 2 degrees of freedom using only position feedback. It is proved that the poles of the system can be assigned to any position on the imaginary axis by choosing the manifolds' gains properly. A new type of quasi-periodic orbit referred to as a stable Lissajous orbit is obtained. The orbit will degenerate to a periodic orbit in the case of resonance between modes and suitable initial values (Lyapunov orbit). Using the controller to solve the solar sail three-body problem yields a stable Lissajous orbit, which is quite different from the classical Lissajous orbit. We show that the sail equilibrium can be stabilized, and moreover that the orbit is bounded. The allocation law of the controller is also studied, which verifies that the controller is realizable.

Optimal Control in Networks of Pipes and Canals

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an optimal control is proved. From the analytical point of view, these results are based on the well posedness of a suitable initial boundary value problem and on techniques for quasidifferential equations in a metric space.

Design of broadband single matching networks

In general commercially available software tools are preferred, to design broadband matching networks for wireless communication systems. But they need a properly selected matching network topology with good initial element values. Therefore, in this paper a new real frequency technique is presented, to generate broadband single matching networks with suitable initial element values. In the proposed method, load impedance is written in terms of ABCD-parameters of the desired matching network and the source resistor. Then, free parameters are optimized which in turn yields the desired matching network with initial element values. It is not needed to select a circuit topology for the matching network, which is the natural consequence of the matching processes. Also, there is no need to select the desired transducer power gain level; the proposed technique naturally provides a gain curve fluctuating around the final available level. Eventually, the initial design is improved by optimizing the performance of the matched system employing the commercially available computer-aided design (CAD) packages. An algorithm and two examples are given, to illustrate the utilization of the proposed technique.

A nonlocal phase-field system with inertial term

We study a phase-field system where the energy balance equation has the standard (parabolic) form, while the kinetic equation ruling the evolution of the order parameter X is a nonlocal and nonlinear second-order ODE. The main features of the latter equation are a space convolution term which models long-range interactions of particles and a singular configuration potential that forces X to take values in (-1,1). We first prove the global existence and uniqueness of a regular solution to a suitable initial and boundary value problem associated with the system. Then, we investigate its long time behavior from the point of view of ω-limits. In particular, using a nonsmooth version of the Lojasiewicz-Simon inequality, we show that the ω-limit of any trajectory contains one and only one stationary solution, provided that the configuration potential in the kinetic equation is convex and analytic.

Coarse orientation of terrestrial laser scans in urban environments

The use of terrestrial laser scanners is becoming increasingly popular. For the acquisition of larger scenes, it is usually necessary to align all scans to a common reference frame. While there are methods using direct measurement of the orientation, due to simplicity and costs, mostly artificial targets are used. This works reliably, but usually adds a substantial amount of time to the acquisition process. Methods to align scans using the scan data itself have been known for a long time, however, being iterative, they need good initial values. In this paper, we investigate two different methods targeted at the determination of suitable initial values. The first one is based on a symbolic approach, using corresponding features to compute the orientation. The second one is based on an iterative alignment scheme originally proposed in the robotics domain. To assess the performance of both methods, a set of 20 scans has been acquired systematically along a trajectory in a downtown area. Reference orientations were obtained by a standard procedure using artificial targets. We present the results of both methods regarding convergence and accuracy, and compare their performance.

Best iterative initial values for PLS in a CSI model

According to the characters of customer satisfaction index (CSI) models, we transformed these models into common regression models, and we find suitable iterative initial values with the constraint of a unit vector for latent variables. The convergence of the new algorithm is also illustrated in this paper. Consequently, the partial least square (PLS) algorithm for CSI models is improved greatly with the best iterative initial values. The results of this paper have been embodied into the software DASC.

Parameter estimation in biochemical systems models with alternating regression.

BackgroundThe estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable.ResultsWe show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear inverse problem of estimating parameter values into iterative steps of linear regression. We show with several artificial examples that the method works well in many cases. In cases of no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations.ConclusionAlternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

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.

Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations

We study the stability of a delayed Hopfield neural network with periodic coefficients and inputs and an arbitrary and constant delay. We consider non-decreasing activation functions which may also have jump discontinuities in order to model the ideal situation where the gain of the neuron amplifiers is very high and tends to infinity. In particular, we drop the assumption of Lipschitz continuity on the activation functions, which is usually required in most of the papers. Under suitable assumptions on the interconnection matrices, we prove that the delayed neural network has a unique periodic solution which is globally exponentially stable independently of the size of the delay. The assumptions we exploit concern the theory of M-matrices and are easy to check. Due to the possible discontinuities of the activation functions, the convergence of the output of the neural network is also studied by a suitable notion of limit. The existence, uniqueness and continuability of the solution of suitable initial value problems are proved.

Analysis of a Thermomechanical Model for Shape Memory Alloys

This note addresses the mathematical study of a nonlinear model arising in the description of the macroscopic thermomechanical behavior of shape memory materials and previously introduced in [R. Peyroux, A. Chrysochoos, Ch. Licht, and M. Löbel, J. Phys. C4 Suppl., 6 (1996), pp. 347--356]. In particular, we discuss the model derivation and investigate a system of PDEs coupled with a vectorial variational inequality. We develop the analysis in both the dissipative and the nondissipative cases, providing indeed a quantitative asymptotic connection between the two regimes. Moreover, we prove the global in time well-posedness for suitable initial and boundary value problems. As a by-product of the well-posedness analysis, we address a variable time-step discretization procedure, proving indeed its convergence and providing some a priori error bounds. Finally, we deal with the asymptotic behavior of the system for large times and establish the convergence of the trajectories to the solution of a suitable stationary problem.

The Cauchy problem for non-autonomous nonlinear Schrödinger equations

In this paper we study the Cauchy problem for cubic nonlinear Schrodinger equation with space- and time-dependent coefficients on ∝m and \(\mathbb{T}^m \). By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m = 1, 2.

Pseudo-replicates in the Linear Circular Functional Relationship Model

2 Abstract: The relationship between readings on two instruments may be represented by a linear functional relationship with errors of observation in both variables. This study describes a method of fitting the relationship between the two circular variables and the replicate observations are available. Maximum likelihood estimates are used and it is shown that the closed-form expression for the estimators are not available and the estimates may be obtained iteratively by choosing a suitable initial value. The model is illustrated with an application to the analysis of the wave and wind direction data recorded by two different instruments and assuming the pseudo-replicates based on time have been obtained from this unreplicated circular data.

A path following method for box-constrained multiobjective optimization with applications to goal programming problems

We propose a path following method to find the Pareto optimal solutions of a box-constrained multiobjective optimization problem. Under the assumption that the objective functions are Lipschitz continuously differentiable we prove some necessary conditions for Pareto optimal points and we give a necessary condition for the existence of a feasible point that minimizes all given objective functions at once. We develop a method that looks for the Pareto optimal points as limit points of the trajectories solutions of suitable initial value problems for a system of ordinary differential equations. These trajectories belong to the feasible region and their computation is well suited for a parallel implementation. Moreover the method does not use any scalarization of the multiobjective optimization problem and does not require any ordering information for the components of the vector objective function. We show a numerical experience on some test problems and we apply the method to solve a goal programming problem.

開発した直流電源使用ツイン電極電解ドレッシング法の検討 ブロンズボンドダイヤモンドホイールヘの適用の可能性

With the purpose of developing the high efficient electrolytic dressing method for bronze bond diamond wheel of a coarse grain, twin electrode electrolytic dressing method using DC power source is devised and the validity of its method is examined by the experiments. In the larger initial electrolytic current value than the critical value, the electrolytic current value decreases with dressing time until a constant corresponding with dressing conditions because the oxide layer generated by the electrolytic reaction increases with dressing time. In the suitable initial electrolytic current value below the critical value, on the other hand, the electrolytic current value is independent on dressing time because the oxide layer does not increase with dressing time. In the suitable dressing conditions, the grain extrusion height from the bond surface increases efficiently in approximately proportion to dressing time beyond the height of 35μm which is about one-third of abrasive grain diameter of #140 wheel. The grinding performance of wheel dressed suitably by twin electrode method has longer dressing life interval, smaller variation of surface roughness in grinding process and larger grinding ratio than single electrode method. From the results, it is referred that the method is useful for dressing of coarse grain wheel of #140.