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We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the solution of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the... 

Laser Powder Deposition technique is an advanced production method with many applications. Despite this fact, reliable and accurate control schemes have not yet fully developed for this method. This article presents method for in time identification of the process for modeling and adaptation of proper control strategy. ARMAX structure is chosen for system model. Recursive least square method and Kalman Filter methods are adopted for system identification, and their performance are compared. Experimental data was used for system identification, and proper filtering schemes are devised here for noise elimination and increased estimation results. It was concluded that although both methods... 

The choice of technology to transport passengers in large metropolitan areas is an important issue everywhere. There are many factors involved in this choice. This paper deals with the possibility of the objective use of available information in the analysis of the suitability of a rail public transport system for a city. A database has been made from publications on public city transportation and country level information. Logit models of choice have been calibrated by the maximum likelihood and nonlinear least square methods based on the acquired information. Each city is treated as an "individual", choosing rail or non-rail modes for its trips. Only cities with a population of more than... 

In this paper, two adaptive refinement techniques are presented for enhancing the capability of the new kind of finite volume method called meshless finite volume (MFV) method in which the moving least squares (MLS) approximation technique is employed. The proposed algorithms perform by inserting new nodes in large error regions identified using the Zienkiewicz-Zhu (Z-Z) error estimator and the T-Belytschko (TB) stress recovery scheme. In the first method referred as CV-based adaptive refinement, the new nodes are inserted at the vertices of control volumes with higher errors. The second method, referred as GA-based adaptive refinement, contains two schemes where an adaptive refinement... 

A new method for position determination of stationary targets from radio bearings, using triangulation, and based on the partial derivative analysis of bearing error has been proposed. Mathematical derivations have been carried out and a simulation illustrating the effectiveness of the method has been run. It turns out that, the method works best when the noise is excessively high and the traversed path is asymmetric. In such conditions, the method illustrates an error reduction of up to 5% with respect to the Least Square algorithm  

A new methodology has been proposed to enhance inverse dynamics applications in the process of trajectory planning and optimization in terrain following flights (TFFs). The new approach uses a least square scheme to solve a general two-dimensional (2-D) TFF in a vertical plane. In the mathematical process, Chebyshev polynomials are used to model the geographical data of the terrain in a given route in a manner suitable for the aircraft at hand. The aircraft then follows the modeled terrain with sufficient clearance. In this approach the terrain following (TF) problem is effectively converted to an optimal tracking problem. Results show that this method provides a flexible approach to solve... 

An application of the multiple models adaptive control based on switching and tuning to a flexible transmission system will be presented. This approach has been considered in order to assure high control performance in the presence of large load variation on the system. The advantages of the multiple models adaptive control system with respect to the classical adaptive control will be illustrated via the experimental results. It will also be shown that the robustness of the adaptive control system can be improved with the appropriate shaping of a sensitivity function. The use of a recently developed parameter estimation algorithm based on the minimization of the closed-loop output error in... 

Response surfaces express the behavior of responses and can be used for both single and multi-response problems. A common approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Although there are many methods available in the literature for multiple response optimizations, there are a few studies in model building especially robust models. Assuming correlated responses, in this paper, a robust coefficient estimation method is proposed for multi response problem based on M-estimators. In order to illustrate the performance of the... 

The laser powder deposition (LPD) process is an advanced material processing technique with many applications. Despite this fact, reliable and accurate control schemes have not yet been fully developed for the process. In this paper, identification of the LPD process is examined to find a more accurate model to predict and control the height of clad in real time. The model is adaptive single inputsingle output (SISO) and its structure is very similar to the Hammerstein model when the effective power (a function of laser power and velocity) is selected as the input and the clad height as the output. Weighted extended recursive least square (WERLS) is adopted to simultaneously estimate the... 

The mechanism of flow around a pier structure is so complicated that it is difficult to establish a general empirical model to provide accurate estimation for scour. Interestingly, each of the proposed empirical formula yields good results for a particular data set. Hence, in this study, alternative approaches, artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS), are proposed to estimate the equilibrium and time-dependent scour depth with numerous reliable data base. Two ANN models, multi-layer perception using back-propagation algorithm (MLP/BP) and radial basis using orthogonal least-squares algorithm (RBF/OLS), were used. The equilibrium scour depth was... 

Early detection of structural damage is an important goal of any structural health monitoring system. Among numerous data analysis techniques, those which are used for online damage detection have received considerable attention recently, although the problem of online detection in continuous structures, for example beams, is quite challenging. In this paper, it is shown how the type, the size and the location of breathing cracks are identified online with the use of the records which are gathered from a continuous beam. For determining the existence of a breathing crack in a beam, its vibrating behavior is simulated. The algorithm of the least square estimation with the use of adaptive... 

A simple and systematic approach is developed for modeling and adaptive control of an unknown (or uncertain) chaotic system of the form x(n) = f(X) + g(X)u, using only input-output data obtained from the underlying dynamic system. Two different fuzzy identification methods, i.e. least-squares and gradient descent, are used for identifying the unknown functions f (X) and g (X). Based on the fuzzy modeling, an adaptive controller is devised, which works through sliding mode method. The presented procedure is illustrated by using the chaotic system-modified Duffing's equation as an example, on which simulation results demonstrate the effectiveness of the proposed adaptive algorithm. Copyright ©... 

In this paper the combined optimal feedback-adaptive feedforward controller proposed to attain better performance of active vibration suppression of flexible structures subjected to different type of disturbances. The structure considered here is a cantilever beam actuated with a PZT patch actuator. The proposed controller consists of two individual parts, a filtered-x controller as a feedforward part and an optimal linear controller as a feedback part. Recursive Least Square algorithm (RLS) is used for the adaptive filtering scheme in Filtered-x adaptive feedforward controller. LQG optimal controller is also used in the feedback part of the controller. This research investigates the... 

In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of unsteady incompressible flows, governed by the Navier-Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based only on a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction eq. (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Moving Least Square approximation (MLS) is employed in shape... 

This paper presents a low-order and accurate method for the design of FIR fractional delay (FD) filters with complex coefficients. This method employs least square technique in Hilbert space to approximate the ideal FD transfer function with a FIR filter and to calculate its coefficients. The main advantages of the resulting filter are: very good response at all frequencies compared to other FD filter design methods and a good method to create very small delay. Design examples are presented to illustrate the effectiveness of this new design approach. © World Scientific Publishing Company  

To estimate the parameters of fuzzy linear regression models with fuzzy output and crisp inputs, we develop a mathematical programming model in this paper. The method is constructed on the basis of minimizing the square of the total difference between observed and estimated spread values or in other words minimizing the least square errors. The advantage of the proposed approach is its simplicity in programming and computation as well as its performance. To compare the performance of the proposed approach with the other methods, two examples are presented. © 2004 Elsevier Inc. All rights reserved  

This is a theoretical study that extends a classical method of treating the convection heat transfer in complex geometries to gaseous slip flow forced convection in microchannels with H1 thermal boundary condition. Through this line, the momentum and energy equations in cylindrical coordinates are made dimensionless. Afterward, solutions are presented that exactly satisfy the dimensionless differential equations along with the symmetry condition and finiteness of the flow parameter at the origin. The first-order slip boundary conditions are then applied to the solution utilizing the least squares matching method. Though the method is general enough to be applied to almost any arbitrary cross... 

We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition that a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for the uniqueness of the approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some... 

A method for two dimensional position finding of stationary targets whose bearing measurements suffers from indeterminable bias and random noise has been proposed. The algorithm uses convex optimization to minimize an error function which has been calculated based on circular as well as linear loci of error. Taking into account a number of observations, certain modifications have been applied to the initial crude method so as to arrive at a faster, more accurate method. Simulation results of the method illustrate up to 30% increase in accuracy compared with the well-known least square filter