Riemannian and Finslerian geometry in thermodynamics

It is shown how the methods of Riemannian and Finslerian geometry may be used in thermodynamics of equilibrium and nonequilibrium states. In both cases the Riemannian structure on the spaces of thermodynamic parameters is defined by means of the relative information (entropy). Thermodynamic meaning of the Riemannian scalar curvature is then interpreted in terms of stability of the considered systems. For nonequilibrium systems the time derivative of the relative information leads to the Finslerian structure. It is shown how a homogenization procedure of Rund leads to the Finslerian metric of the Kropina type. Three types of the Finslerian curvature tensors connected with the Cartan connection are considered for two-dimensional spaces. In particular, the so-called horizontal curvature is considered in detail. It turns out that in thermodynamic spaces Cartan connection coincides with the Berwald connection. Thermodynamic meaning of the Finslerian scalar curvatures is not clear since they vanish for two-dimensional spaces.Work supported by The State Committee for Scientific Research, project KBN 2 0412 91 01.     

A convex parameterization of robustly stabilizing controllers

This paper treats synthesis of robust controllers for linear time-invariant systems. Uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial. The main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations. With the new parameterization, certain robust performance problems can be stated in terms of quasi-convex optimization     

A linguistic approach for the control of information flow in abattlefield environment

We developed three linguistic statements to describe user information desires in a battlefield information environment. These rules are based on end-user interest in each track report generated from radars across the battlefield. Along with these rules of user interest, a linguistic statement describing communications systems capabilities at each node was created. These linguistic statements were converted to fuzzy variables and these variables were used as network control devices in a simulation model. The model results show that effective communications control can be exercised by these simple rules     

Characterization of the contribution of inertial parameters to the dynamics of multibody systems

In this paper, an approach is developed for sensitivity analysis of inertial parameters. It is based on the reformed equations of motion linear in terms of the inertial parameters, which are transformed to dimensionless inertial parameters. Based on an eigenvalue analysis, directions of the parameter space are found along which maximum/minimum changes are achieved on the generalized forces, i.e., on the dynamics of the system. Directional derivatives of the generalized force vector in these directions characterize how each inertial parameter contributes to the system dynamics.     

基于LMI的非线性摄动系统鲁棒绝对稳定性判据

讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄 动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性 条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据.     

Consistent parameter estimation in multi-input multi-output discrete systems

An algebraic approach to the determination of consistent parameter estimates of multiple-input multiple-output (MIMO) discrete systems for general type input sequences is developed. It is shown that a special canonical structure for the system matrices exist such that the parameter estimation equations decouple into p independent subsystem equations. This results in a significant reduction in the dimension of the data matrix and allows simple algebraic equations to be derived relating system parameters, least-squares parameter estimates, and noise parameters. It is shown that the solution of these equations yields consistent parameter estimates which have rapid initial convergence towards the correct parameter values.     

The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation

In this paper, a formulation for a spatial sliding joint is derived using absolute nodal coordinates and non-generalized coordinate and it allows a general multibody move along a very flexible cable. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the nongeneralized coordinate, which is related to neither the inertia forces nor the external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. Hereby, the non-generalized coordinate represents the arc-length parameter. The constraint equations for the sliding joint are expressed in terms of generalized coordinate and nongeneralized coordinate. In the constraint equations for the sliding joint, one constraint equation can be systematically eliminated. There are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph-catenary systems for high speed-trains.     

Linguistic Vector Similarity Measures and Applications to Linguistic Information Classification

In this paper, we generalize the similarity degree for linguistic labels to the so‐called the linguistic similarity measure. Linguistic vector, whichcan be used to represent objects whose attributes are given in terms of linguistic labels, is defined. Some mathematical properties are stated and proved. The linguistic vector similarity measure is developed and applied to linguistic information classification. Experimental results on real data confirm the effectiveness of the proposed method.     

Parameter Identification of Recurrent Fuzzy Systems With Fuzzy Finite-State Automata Representation

This paper presents the identification of nonlinear dynamical systems by recurrent fuzzy system (RFS) models. Two types of RFS models are discussed: the Takagi-Sugeno-Kang (TSK) type and the linguistic or Mamdani type. Both models are equivalent and the latter model may be represented by a fuzzy finite-state automaton (FFA). An identification procedure is proposed based on a standard general purpose genetic algorithm (GA). First, the TSK rule parameters are estimated and, in a second step, the TSK model is converted into an equivalent linguistic model. The parameter identification is evaluated in some benchmark problems for nonlinear system identification described in literature. The results show that RFS models achieve good numerical performance while keeping the interpretability of the actual system dynamics.     

Linguistic summarization of event logs – A practical approach

The amount of data that is generated during the execution of a business process is growing. As a consequence it is increasingly hard to extract useful information from the large amount of data that is produced. Linguistic summarization helps to point business analysts in the direction of useful information, by verbalizing interesting patterns that exist in the data. In previous work we showed how linguistic summarization can be used to automatically generate diagnostic statements about event logs, such as ‘for most cases that contained the sequence ABC, the throughput time was long’. However, we also showed that our technique produced too many of these statements to be useful in a practical setting. Therefore this paper presents a novel technique for linguistic summarization of event logs, which generates linguistic summaries that are concise enough to be used in a practical setting, while at the same time enriching the summaries that are produced by also enabling conjunctive statements. The improved technique is based on pruning and clustering of linguistic summaries. We show that it can be used to reduce the number of summary statements 80–100% compared to previous work. In a survey among 51 practitioners, we found that practitioners consider linguistic summarization useful and easy to use and intend to use it if it were commercially available.     

Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics

In this paper, we provide a full instruction on how to formulate and evaluate planar frictional contact problems in the spirit of non-smooth dynamics. By stating the equations of motion as an equality of measures, frictional contact reactions are taken into account by Lagrangian multipliers. Contact kinematics is formulated in terms of gap functions, and normal and tangential relative velocities. Associated frictional contact laws are stated as inclusions, incorporating impact behavior in form of Newtonian kinematic impacts. Based on this inequality formulation, a linear complementarity problem in standard form is presented, combined with Moreau’s time stepping method for numerical integration. This approach has been applied to the woodpecker toy, of which a complete parameter list and numerical results are given in the paper.     

Self-adaptive population sizing for a tune-free differential evolution

The study and research of evolutionary algorithms (EAs) is getting great attention in recent years. Although EAs have earned extensive acceptance through numerous successful applications in many fields, the problem of finding the best combination of evolutionary parameters especially for population size that need the manual settings by the user is still unresolved. In this paper, our system is focusing on differential evolution (DE) and its control parameters. To overcome the problem, two new systems were carried out for the self-adaptive population size to test two different methodologies (absolute encoding and relative encoding) in DE and compared their performances against the original DE. Fifty runs are conducted for every 20 well-known benchmark problems to test on every proposed algorithm in this paper to achieve the function optimization without explicit parameter tuning in DE. The empirical testing results showed that DE with self-adaptive population size using relative encoding performed well in terms of the average performance as well as stability compared to absolute encoding version as well as the original DE.     

A review of: “LOGIC AND PHILOSOPHY IN THE LVOV-WARSAW SCHOOL”, by Jan Woleński,Kluwer, Dordrecht (The Netherlands) and Boston, 1989. xiv + 364 pages.

Qualitative methodology plays an important role within computer simulation; modeling and analysis of complex systems require qualitative methods since humans think naturally in qualitative and linguistic terms. The critical interface for simulationists exploring qualitative simulation should rely on an unambiguous mathematical formalism or method with foundations in systems theory. Currently, many ad hoc formalisms exist for encoding uncertain or qualitative simulation knowledge; however, we have found that fuzzy set theory provides for a formalism where linguistic variables can be encoded as state, parameter, input and output information in the model. Fuzzy numbers, in particular, are useful when population statistics are unavailable—usually due to cost factors. We have constructed fuzzy simulation programs based on our C-based SimPack library and we use fuzzy simulation to hypothesize qualitative system models reflecting real system behavior, and to specify qualitative versions of systems.     

A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima

A numerical method for estimating multiple parameter values of nonlinear systems arising from biology is presented. The uncertain parameters are modeled as random variables. Then the solutions are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. Homotopy continuation method is employed to solve the resulting polynomial system, and more importantly, to compute the multiple optimal parameter values. Several numerical examples, from a single equation to problems with relatively complicated forms of governing equations, are used to demonstrate the robustness and effectiveness of this numerical method.     

Basis of invariants and canonical forms for linear dynamic systems

This paper is a study of the problem of how to parametrize the set of all finite order constant linear systems. The parameters are interpreted as independent invariants for the equivalence relation which defines two systems to be equivalent when they have the same impulse response. Two kinds of canonical representations of the systems are constructed from the invariants, one of the state-space equations type and the other of the transfer function type.     

Fuzzy net present values for capital investments in an uncertain environment

This work presents a series of pragmatic algorithms for calculating the net present values of capital investments in an environment, which are subject to uncertainty from randomness of outcomes and vagueness of estimation. Linguistic terms is adopted to assess the possibilities of future economic scenarios, and fuzzy numbers are then used to represent the linguistic assessments and estimate cash flows and costs of capital. Utilizing the standard fuzzy arithmetic, the text presents the equations of the expected fuzzy net present values for a single project, expected fuzzy equivalent annuity for mutually exclusive projects with equal life spans, and expected fuzzy equivalent annuity to infinity for projects with unequal risks (jointly called expected FNPVs). By further applying the fuzzy arithmetic with requisite constraints, novel equations are proposed for computing the fuzzy variance and standard deviation. The selection of the target is based on the rule of high return (expected FNPVs), low absolute risk (fuzzy standard deviation), and/or low relative risk (coefficient of variation). In addition to efficiently integrating the quantitative information, the developed algorithms are anticipated to measure the subjective qualitative information more effectively than the traditional method.     

基于模糊语言方法的信息检索系统的研究

该文提出了一个基于模糊语言方法的信息检索系统模型。该系统分为查询界面子系统、数据库子系统和检索子系统三大部分。在查询界面子系统,用布尔表达式表示用户的查询请求,并对每个查询关键词赋予了两种不同语义的语言值权重,该权重表达了用户的模糊检索要求;在数据库子系统,用索引词一文档模糊矩阵表示待检索的文档,对每个索引词。根据其在文档中的出现频率大小。引入了数值权重;在检索子系统,运用模糊语言方法,对用户输入的布尔查询表达式与索引词一文档模糊矩阵进行自底向上的模糊匹配,最后返回满足用户要求的检索结果。相对于传统的基于查询关键词精确匹配的检索系统而言,该系统能较好地满足用户查询要求中的灵活性。     

FUZZY TRUST AGGREGATION AND PERSONALIZED TRUST INFERENCE IN VIRTUAL SOCIAL NETWORKS

Virtual marketplaces on the Web provide people with great facilities to buy and sell goods similar to conventional markets. In traditional business, reputation is subjectively built for known persons and companies as the deals are made in the course of time. As it is important to do business with trustful individuals and companies, there is a need to survive the reputation concept in virtual markets. Auction sites generally employ reputation systems based on feedbacks that provide a global view to a cyber dealer. In contrast to global trust, people usually infer their personal trust about someone whose reputation is completely or partially unknown by asking their trusted friends. Personal reputation is what makes a person trusted for some people and untrusted for others. There should be a facility for users in a virtual market to specify how much they trust a friend and also a mechanism that infers the trust of a user to another user who is not directly a friend of her. There are two main issues that should be addressed in trust inference. First, the trust modeling and aggregation problem needs to be challenged. Second, algorithms should be introduced to find and select the best paths among the existing trust paths from a source to a sink. First, as trust to a person can be stated more naturally using linguistic expressions, this work suggests employing linguistic terms for trust specification. To this end, corresponding fuzzy sets are defined for trust linguistic terms and a fuzzy trust aggregation method is also proposed. Comparing the fuzzy aggregation method to the existing aggregation methods shows superiority of fuzzy approach especially at aggregating contradictory information. Second, this paper proposes an incremental trust inference algorithm. The results show improvement in preciseness of inference for the proposed inference algorithm over the existing and recently proposed algorithm named TidalTrust.     

Adaptive coordinated tracking of multi-agent systems with quantized information

In this paper, we study the adaptive coordinated tracking problem for continuous-time first-order integrator systems with quantized information under switching undirected and fixed directed communication graphs, respectively. The combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated. Both the logarithmic quantizers and uniform quantizers are considered. It is shown that when logarithmic quantizers are used, exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used, practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter. Simulation examples are provided to illustrate the results.