Set Membership identification of nonlinear systems

In the paper the problem of identifying nonlinear dynamic systems, described in nonlinear regression form, is considered, using finite and noise-corrupted measurements. Most methods in the literature are based on the estimation of a model within a finitely parametrized model class describing the functional form of involved nonlinearities. A key problem in these methods is the proper choice of the model class, typically realized by a search, from the simplest to more complex ones (linear, bilinear, polynomial, neural networks, etc.). In this paper an alternative approach, based on a Set Membership framework is presented, not requiring assumptions on the functional form of the regression function describing the relations between measured input and output, but assuming only some information on its regularity, given by bounds on its gradient. In this way, the problem of considering approximate functional forms is circumvented. Moreover, noise is assumed to be bounded, in contrast with statistical methods, which rely on assumptions such as stationarity, ergodicity, uncorrelation, type of distribution, etc., whose validity may be difficult to test reliably and is lost in presence of approximate modeling. In this paper, necessary and sufficient conditions are given for the validation of the considered assumptions. An optimal interval estimate of the regression function is obtained, providing its uncertainty range for any assigned regressor values. The set estimate allows to derive an optimal identification algorithm, giving estimates with minimal guaranteed L_p error on the assigned domain of the regressors. The properties of the optimal estimate are investigated and its worst-case L_p identification error is evaluated. The presented approach is tested and compared with other nonlinear methods on the identification of a water heater, a mechanical system with input saturation and a vehicle with controlled suspensions.     

一类非线性系统的地球物理参量辨识和算法

本文讨论一类非线性分布参数系统在间断函数类中的系统辨识问题,用脉冲变分原理得 出了逐点变分梯度公式,讨论了辨识的唯一性问题,并提出了辨识系数的算法,最后给出了若 干例题.     

Boundary identification for a 3D Laplace equation using a genetic algorithm

In this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three-dimensional Laplace equation. We investigate the determination of the shape of an unknown portion of the boundary of a solution domain from Cauchy data on the remaining portion of the boundary. This problem arises in the study of quantitative non-destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion. The domain identification problem is considered as a variational problem to minimize a defect functional, which utilises some additional data on certain known parts of the boundary. A real coded genetic algorithm (RCGA) is used in order to minimise the objective functional. The unknown boundary is parameterized using B-splines. The Laplace equation is discretised using the method of fundamental solutions (MFS). Numerical results are presented and discussed for several test examples.     

The use of domain knowledge in program understanding

Program understanding is an essential part of all software maintenance and enhancement activities. As currently practiced, program understanding consists mainly of code reading. The few automated understanding tools that are actually used in industry provide helpful but relatively shallow information, such as the line numbers on which variable names occur or the calling structure possible among system components. These tools rely on analyses driven by the nature of the programming language used. As such, they are adequate to answer questions concerning implementation details, so called what questions. They are severely limited, however, when trying to relate a system to its purpose or requirements, the why questions. Application programs solve real‐world problems. The part of the world with which a particular application is concerned is that application's domain. A model of an application's domain can serve as a supplement to programming‐language‐based analysis methods and tools. A domain model carries knowledge of domain boundaries, terminology, and possible architectures. This knowledge can help an analyst set expectations for program content. Moreover, a domain model can provide information on how domain concepts are related. This article discusses the role of domain knowledge in program understanding. It presents a method by which domain models, together with the results of programming‐language‐based analyses, can be used to answers both what and why questions. Representing the results of domain‐based program understanding is also important, and a variety of representation techniques are discussed. Although domain‐based understanding can be performed manually, automated tool support can guide discovery, reduce effort, improve consistency, and provide a repository of knowledge useful for downstream activities such as documentation, reengineering, and reuse. A tools framework for domain‐based program understanding, a dowser, is presented in which a variety of tools work together to make use of domain information to facilitate understanding. Experience with domain‐based program understanding methods and tools is presented in the form of a collection of case studies. After the case studies are described, our work on domain‐based program understanding is compared with that of other researchers working in this area. The paper concludes with a discussion of the issues raised by domain‐based understanding and directions for future work. This revised version was published online in June 2006 with corrections to the Cover Date.     

Approximate H∞ identification using partial sumoperators in a disc algebra basis

H_∞ system identification using a basis in the disc algebra is presented. The approximate model is represented by a partial sum with respect to this basis. The identification problem is to estimate the expansion coefficients of this partial sum. Since the constructed basis functions cannot be represented analytically, they are approximated in order to arrive at a model in a suitable form. An algorithm is presented which calculates the model parameters from the frequency domain data set     

Design sensitivity analysis of multi-span non-linear elastic beam–columns with elastic supports

The incremental problem arising from the design perturbation of a materially non-linear elastic beam–column with intermediate supports and elastic end supports is formulated via a second variation of the potential energy functional, augmented with constraint conditions. Design variables are distributed parameters (bending stiffness and transverse load), discrete (compression force, end points dead loads and elasticity of supports) and domain (length and intermediate support points). The state variables perturbations are the solution of an incremental BVP (equilibrium differential equation, static, kinematic and jump conditions) derived from an incremental virtual work equation. A sensitivity formula is obtained by the adjoint method.     

Modeling and parameter identification of systems with multisegmentpiecewise-linear characteristics

This paper deals with the modeling and parameter identification of nonlinear systems having multi-segment piecewise-linear characteristics. The decomposition of the corresponding mapping provides a new form of multi-segment nonlinearity representation, leading to an output equation where all the parameters to be estimated are separated. Hence, an iterative method with internal variable estimation can be applied for parameter identification using input/output data records. The only required a-priori knowledge of the nonlinear characteristic represents the limits for the domain partition. The proposed model of given static nonlinearity is also incorporated into the Hammerstein model. Examples of parameter identification for static and dynamic systems with multi-segment piecewise-linear characteristics are presented     

Document analysis by processing JBIG-encoded images

Techniques are presented to directly process JBIG-encoded document images. Two experimental processing pipelines are designed to evaluate the performance of the methods from the application perspective. They are document segmentation for obtaining the global layout and the form processing system for form type identification and the form dropout. The JBIG coding context is employed to perform horizontal smearing and connected-component detection concurrently in the course of decoding the base layer of the JBIG images. It is shown that, using a simple segmentation algorithm, the global layout is identified 50 times faster compared to the case of processing the full resolution images. In addition, an original solution is presented for form type identification by use of the Hough transform of the JBIG base layer images, thus expediting it by a factor of 16 in the designed form dropout system. Advantages of the compressed domain processing include fast procedures, reduced memory requirements, and the possibility of hardware implementation. Received: 31 January 2004, Accepted: 4 January 2005, Published online: 5 April 2005     

An approach to optimization in transport logistics

A new approach to some optimization problems arising in the transport logistics was proposed. Consideration was given to the fundamental problems of the today logistics such as the problem of optimal arrangement and that of identification and segmentation of the logistic zones. They are solved using the “wave” method which relies on the analogy between the determination of the global extremum of the integral functional and propagation of light in an optically inhomogeneous medium. A numerical algorithm was developed, and the results of calculations presented.     

Relevance-based abstraction identification: technique and evaluation

When first approaching an unfamiliar domain or requirements document, it is often useful to get a quick grasp of what the essential concepts and entities in the domain are. This process is called abstraction identification, where the word abstraction refers to an entity or concept that has a particular significance in the domain. Abstraction identification has been proposed and evaluated as a useful technique in requirements engineering (RE). In this paper, we propose a new technique for automated abstraction identification called relevance-based abstraction identification (RAI), and evaluate its performance—in multiple configurations and through two refinements—compared to other tools and techniques proposed in the literature, where we find that RAI significantly outperforms previous techniques. We present an experiment measuring the effectiveness of RAI compared to human judgement, and discuss how RAI could be used to good effect in requirements engineering.     

Nonlinear automata over a finite ring

The properties of the class of information-lossless automata represented by recurrent relations over a finite ring are investigated. For these automata, the structure of classes of equivalent states is investigated, problems of parametric identification and identification of the initial state are solved, and the variation in the behavior of such automata as a result of variation of their parameters or initial states is characterized. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 29–42, November–December 2006.     

‘<Emphasis Type="Italic">if p then q</Emphasis>’ . . . and all that: Logical Elements in Reasoning and Discourse

In this paper we explore differences in use of the so-called ‘logical’ elements of language such as quantifiers and conditionals, and use this to explain differences in performance in reasoning tasks across subject groups with different educational backgrounds. It is argued that quantified sentences are difficult natural bases for reasoning, and hence more prone to elicit variation in reasoning behaviour, because they are chiefly used with a pre-determined domain in everyday speech. By contrast, it is argued that conditional sentences form natural premises because of the function they serve in everyday speech. Implications of this for the role of logic in modelling human reasoning behaviour are briefly considered.     

Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solid–liquid interfaces

Molecular dynamics (MD) simulations of nano-scale flows typically utilize fixed lattice crystal interactions between the fluid and stationary wall molecules. This approach cannot properly model interactions and thermal exchange at the wall–fluid interface. We present a new interactive thermal wall model that can properly simulate the flow and heat transfer in nano-scale channels. The new model utilizes fluid molecules freely interacting with the thermally oscillating wall molecules, which are connected to the lattice positions with “bonds”. Thermostats are applied separately to each layer of the walls to keep the wall temperature constant, while temperature of the fluid is sustained without the application of a thermostat. Two-dimensional MD simulation results for shear driven nano-channel flow shows parabolic temperature distribution within the domain, induced by viscous heating due to a constant shear rate. As a result of the Kapitza resistance, temperature profiles exhibit jumps at the fluid–wall interface. Time dependent simulation results for freezing of liquid argon in a nano-channel are also presented.     

Rainbow: A framework for analysing computer-mediated pedagogical debates

In this paper we present a framework for analysing when and how students engage in a specific form of interactive knowledge elaboration in CSCL environments: broadening and deepening understanding of a space of debate. The framework is termed “Rainbow,” as it comprises seven principal analytical categories, to each of which a colour is assigned, thus enabling informal visualisation by the analyst of the extent to which students are engaging in interaction relating to potential achievement of its pedagogical goal. The categories distinguish between activities that are part of the prescribed assignment and activities that are not, and between task-focused and non-task-focused activities. Activities focused on managing the interaction itself are distinguished from argumentative interaction. Notably, an operational definition of what it means to broaden and deepen understanding in this case is also provided here. The functional Rainbow analysis is complemented by an analysis of topics and subtopics that enables identification of one form of conceptual deepening of the question. In comparison with existing analysis techniques, Rainbow synthesises much of what is known into a single framework, with a broad theoretical base. The usability and educational relevance of the framework has been validated experimentally across a variety of collaborative learning tasks and communication media. Possible and actual extensions to the framework are discussed, with respect to additional CSCL tools, domains and tasks. The research reported here was carried out within the SCALE project (Internet-based intelligent tool to Support Collaborative Argumentation-based Learning in secondary schools, project n° IST-1999–10664, March 2001 – February 2004), funded by the European Community under the ‘Information Societies’ Technology’ (IST) Programme. Information on the project can be found at: , or     

Application of wavelet neural network in signal processing of MEMS accelerometers

A new method with wavelet neural network is described to optimize MEMS accelerometers for temperature independent sensitivity. Linear accelerations are measured and compensated by a thermocouple the fast algorithm which is used to deal with the nonlinearity error. The simulation results show that MEMS accelerometers with compensation is characterized by an excellent temperature stability of the sensitivity with less than 0.1% variation for a temperature range −40–100°C, while the variation of acceleration without compensation is 8%. The proposed algorithm can be useful for realization of high accuracy miniature gyroscope systems based on MEMS technology.     

Face identification using novel frequency-domain representation of facial asymmetry

Face recognition is a challenging task. This paper introduces a novel set of biometrics, defined in the frequency domain and representing a form of "facial asymmetry." A comparison with existing spatial asymmetry measures suggests that the frequency-domain representation provides an efficient approach for performing human identification in the presence of severe expressions and for expression classification. Error rates of less than 5% are observed for human identification and around 25% for expression classification on a database of 55 individuals. Feature analysis indicates that asymmetry of the different face parts helps in these two apparently conflicting classification problems. An interesting connection between asymmetry and the Fourier domain phase spectra is then established. Finally, a compact one-bit frequency-domain representation of asymmetry is introduced, and a simplistic Hamming distance classifier is shown to be more efficient than traditional classifiers from storage and the computation point of view, while producing equivalent human identification results. In addition, the application of these compact measures to verification and a statistical analysis are presented.     

Piezoresistive device optimization using topological derivative concepts

A piezoresistive sensor is composed of a piezoresistive membrane attached to a flexible plate. The piezoresistive material is anisotropic, and its electrical properties change when subjected to mechanical stresses. In this work, the topology design of a piezoresistive pressure sensor is addressed. More specifically, an optimization technique based on topological sensitivity analysis is proposed in order to obtain the optimized distribution of piezoresistive material over the plate. In most of the works regarding topological sensitivity analysis, isotropic materials are considered. However, the problem of conductivity in an anisotropic non-homogeneous domain has been recently addressed, and a closed form for the topological derivative associated to the energy shape functional has been presented. In this work, on the other hand, a closed form for the topological derivative associated with a multi-objective shape functional related to the steady-state anisotropic current density diffusion problem is presented. To illustrate the applicability of the closed formula and the proposed optimization procedure, numerical examples regarding the conceptual design of piezoresistive sensors, considering distinct optimization parameters and boundary conditions in the conductivity problem, are presented.     

Numerical study of dynamic processes in a continuous medium with a crack initiated by a near-surface disturbance by means of the grid-characteristic method

The purpose of this work is to study the problem of the near-surface disturbance propagation in a massive rock containing various heterogeneities, i.e., empty or filled cracks. Numerical solutions have been obtained for problems of wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock that can be manifested in the vicinity of a seismic gap or a well bore. All kinds of elastic and elastoplastic waves are analyzed resulting from the propagation of the initial disturbance and the waves arising from the reflection from the cracks and from the boundaries of the integration domain. An investigation was carried out of wave identification by means of seismograms obtained at the receiver located near the ground surface. In this study, the grid-characteristic method is employed using computational grids with triangular meshes and boundary conditions formulated at the interface between the rock and the crack, and on free surfaces in an explicit form. The proposed numerical method is extremely general and is suitable for investigations of the processes of seismic waves’ interaction with heterogeneous inclusions because it ensures the construction of the most correct computational algorithms at the boundaries of the integration domain and at the medium’s interface.     

Optimal sensor location for parameter estimation of distributed processes

The problem under consideration is to plan sensor movements in prescribed feasible regions in such a way as to maximize the accuracy of parameter identification of a distributed system defined in a two-dimensional spatial domain. A general functional defined on the Fisher information matrix is used as the design criterion. Central to the approach is the formulation of the problem as an optimal control one, possibly with state inequality constraints. Its solution is obtained numerically with the use of a method of successive linearizations which is capable of handling various constraints imposed on the sensors' motions. Simple numerical examples are included which clearly demonstrate the ideas and trends presented in the paper.     

A general approach to approximate solutions of nonlinear differential equations using particle swarm optimization

A general algorithm is presented to approximately solve a great variety of linear and nonlinear ordinary differential equations (ODEs) independent of their form, order, and given conditions. The ODEs are formulated as optimization problem. Some basic fundamentals from different areas of mathematics are coupled with each other to effectively cope with the propounded problem. The Fourier series expansion, calculus of variation, and particle swarm optimization (PSO) are employed in the formulation of the problem. Both boundary value problems (BVPs) and initial value problems (IVPs) are treated in the same way. Boundary and initial conditions are both modeled as constraints of the optimization problem. The constraints are imposed through the penalty function strategy. The penalty function in cooperation with weighted-residual functional constitutes fitness function which is central concept in evolutionary algorithms. The robust metaheuristic optimization technique of the PSO is employed to find the solution of the extended variational problem. Finally, illustrative examples demonstrate practicality and efficiency of the presented algorithm as well as its wide operational domain.