Numerical identification of a nonlinear diffusion coefficient by discrete mollification

The discrete mollification method is a convolution-based filtering procedure suitable for the regularization of ill-posed problems. Combined with explicit space-marching finite difference schemes, it provides stability and convergence for a variety of coefficient identification problems in linear parabolic equations. In this paper, we extend such a technique to identify some nonlinear diffusion coefficients depending on an unknown space dependent function in one dimensional parabolic models. For the coefficient recovery process, we present detailed error estimates and to illustrate the performance of the algorithms, several numerical examples are included.     

Dynamical systems identification using Gaussian process models with incorporated local models

Gaussian process (GP) models form an emerging methodology for modelling nonlinear dynamic systems which tries to overcome certain limitations inherent to traditional methods such as e.g. neural networks (ANN) or local model networks (LMN).The GP model seems promising for three reasons. First, less training parameters are needed to parameterize the model. Second, the variance of the model's output depending on data positioning is obtained. Third, prior knowledge, e.g. in the form of linear local models can be included into the model. In this paper the focus is on GP with incorporated local models as the approach which could replace local models network.Much of the effort up to now has been spent on the development of the methodology of the GP model with included local models, while no application and practical validation has yet been carried out. The aim of this paper is therefore twofold. The first aim is to present the methodology of the GP model identification with emphasis on the inclusion of the prior knowledge in the form of linear local models. The second aim is to demonstrate practically the use of the method on two higher order dynamical systems, one based on simulation and one based on measurement data.     

An experimental study on the applicability of evolutionary algorithms to craniofacial superimposition in forensic identification

Photographic supra-projection is a forensic process that aims to identify a missing person from a photograph and a skull found. One of the crucial tasks throughout all this process is the craniofacial superimposition which tries to find a good fit between a 3D model of the skull and the 2D photo of the face. This photographic supra-projection stage is usually carried out manually by forensic anthropologists. It is thus very time consuming and presents several difficulties. In this paper, we aim to demonstrate that real-coded evolutionary algorithms are suitable approaches to tackle craniofacial superimposition. To do so, we first formulate this complex task in forensic identification as a numerical optimization problem. Then, we adapt three different evolutionary algorithms to solve it: two variants of a real-coded genetic algorithm and the state of the art evolution strategy CMA-ES. We also consider an existing binary-coded genetic algorithm as a baseline. Results on several superimposition problems of real-world identification cases solved by the Physical Anthropology lab at the University of Granada (Spain) are considered to test our proposals.     

Space and time localization for the estimation of distributed parameters in a finite element model

In this paper we study the problem of estimating the possibly non-homogeneous material coefficients inside a physical system, from transient excitations and measurements made in a few points on the boundary. We assume there is available an adequate Finite Element (FEM) model of the system, whose distributed physical parameters must be estimated from the experimental data.We propose a space–time localization approach that gives a better conditioned estimation problem, without the need of an expensive regularization. Some experimental results obtained on an elastic system with random coefficients are given.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.     

Parameter identification of periodical signals: Application to measurement and analysis of ocean wave forces

This article presents an approach based on state observers to identify the parameters of an unknown periodic force exerted on a mechanical system. This approach comprises two stages and can be executed in real time by using only displacement measurements. The first stage goal is the estimation of the coefficients of a Fourier series that approximates the periodic force. From the estimated coefficients, the phase and the amplitude of the signal can be simultaneously computed; and from the estimated force, in a second stage, the frequencies of the signal can be estimated. To perform the tasks at each stage, two state observers were designed. To show the applicability of the proposed approach, the reconstruction of a wave force affecting a marine structure as well as the computation of the amplitude and phase of its spectral components was taken as case of study. The performance of the state observer was examined by means of simulations and off-line tests carried out with experimental data. Such data were obtained by executing laboratory tests and measuring waves in the Caribbean sea.     

Time-local formulation and identification of implicit Volterra models by use of diffusive representation

We present a time-continuous identification method for nonlinear dynamic Volterra models of the form HX=f(u,X)+v with H, a causal convolution operator. It is mainly based on a suitable parameterization of H deduced from the so-called diffusive representation, which is devoted to state representations of integral operators. Following this approach, the complex dynamic nature of H can be summarized by a few numerical parameters on which the identification of the dynamic part of the model will focus. The method is validated on a physical numerical example.     

Stochastic system transformation using generalized orthonormal basis functions with applications to continuous-time system identification

This paper studies the system transformation using generalized orthonormal basis functions that include the Laguerre basis as a special case. The transformation of the deterministic systems is studied in the literature, which is called the Hambo transform. The aim of the paper is to develop a transformation theory for stochastic systems. The paper establishes the equivalence of continuous and transformed-discrete-time stochastic systems in terms of solutions. The method is applied to the continuous-time system identification problem. It is shown that using the transformed signals the PO-MOESP subspace identification algorithm yields consistent estimates for system matrices. An example is included to illustrate the efficacy of the proposed identification method, and to make a comparison with the method using the Laguerre filter.     

蒙古文整词计算机生成理论研究

采用面向对象方法,模拟传统蒙古文整词各种形式构成机理,提出了几种蒙古语整词计算机生成数据模型。文章主要依据整词计算机生成三种模型,探讨了传统蒙古文整词计算机最优化生成理论所涉及的精确度、时间复杂度、空间复杂度三项基本要素以及最优化生成必须考虑的整词复杂特征载荷与一体化合一计算知识表示方法和计算结构,证明了“B - J - T= W”数据模型是传统蒙古文整词计算与生成最优化对象模型。     

Prediction-based Iterative Learning Control (PILC) for Uncertain Dynamic Nonlinear Systems Using System Identification Technique

Prediction-based Iterative Learning Control (PILC) is proposed in this paper for a class of time varying nonlinear uncertain systems. Convergence of PILC is analyzed and the uniform boundedness of tracking error is obtained in the presence of uncertainty and disturbances. It is shown that the learning algorithm not only guarantees the robustness, but also improves the learning rate despite the presence of disturbances and slowly varying desired trajectories in succeeding iterations. The effectiveness of the proposed PILC is presented by simulations.