A fuzzy Petri net-based expert system and its application to damageassessment of bridges

In this paper, a fuzzy Petri net approach to modeling fuzzy rule-based reasoning is proposed to bring together the possibilistic entailment and the fuzzy reasoning to handle uncertain and imprecise information. The three key components in our fuzzy rule-based reasoning-fuzzy propositions, truth-qualified fuzzy rules, and truth-qualified fuzzy facts-can be formulated as fuzzy places, uncertain transitions, and uncertain fuzzy tokens, respectively. Four types of uncertain transitions-inference, aggregation, duplication, and aggregation-duplication transitions-are introduced to fulfil the mechanism of fuzzy rule-based reasoning. A framework of integrated expert systems based on our fuzzy Petri net, called fuzzy Petri net-based expert system (FPNES), is implemented in Java. Major features of FPNES include knowledge representation through the use of hierarchical fuzzy Petri nets, a reasoning mechanism based on fuzzy Petri nets, and transformation of modularized fuzzy rule bases into hierarchical fuzzy Petri nets. An application to the damage assessment of the Da-Shi bridge in Taiwan is used as an illustrative example of FPNES.     

Fuzzy rule base systems verification using high-level Petri nets

In this paper, we propose a Petri nets formalism for the verification of rule-based systems. Typical structural errors in a rule-based system are redundancy, inconsistency, incompleteness, and circularity. Since our verification is based on Petri nets and their incidence matrix, we need to transform rules into a Petri nets first, then derive an incidence matrix from the net. In order to let fuzzy rule-based systems detect above the structural errors, we are presenting a Petri-nets-based mechanism. This mechanism consists of three phases: rule normalization, rules transformation, and rule verification. Rules will be first normalized into Horn clauses, then transform the normalized rules into a high-level Petri net, and finally we verify these normalized rules. In addition, we are presenting our approach to simulate the truth conditions which still hold after a transition firing and negation in Petri nets for rule base modeling. In this paper, we refer to fuzzy rules as the rules with certainty factors, the degree of truth is computed in an algebraic form based on state equation which can be implemented in matrix computation in Petri nets. Therefore, the fuzzy reasoning problems can be transformed as the liner equation problems that can be solved in parallel. We have implemented a Petri nets tool to realize the mechanism presented fuzzy rules in this paper.     

An approach towards the verification of expert systems using numerical petri nets

A major difficulty that occurs in the construction of large production rule-based expert systems is maintaining the correctness, consistency, and completeness of the knowledge base. A method of transforming the production rules into a numerical petri nets (NPNs) model is proposed. These NPNs are high level nets that are necessary to effectively model production rules. the net model is then analysed by using a computer-aided tool to perform reachability analysis. an algorithm is given to generate the reachability set of the nets. This allows the verification of the correctness, consistency, and completeness of the knowledge base. Examples showing the use of this approach are given.     

智能网络管理中一种基于Petri网的知识验证技术

知识库是智能网络管理系统中的重要组成部分,知识库的维护要求知识库系统必须具备知识的验证功能。智能网管系统中知识组织的动态性决定了知识的结构性验证必须正确、有效和及时。本文以有色Petri网为基础,针对智能网管系统中知识验证的主要内窝,以一种扩充的有色Petri网作为描述和分析工具,建立了相应的知识表示模型和知识验证模型,提出了一种简洁的、基于有色Petri网的知识验证方法,并给出了相应的判定准则。     

Approximate declarative semantics for rule base anomalies

Despite the fact that there has been a surge of publications in verification and validation of knowledge-based systems and expert systems in the past decade, there are still gaps in the study of verification and validation (V&V) of expert systems, not the least of which is the lack of appropriate semantics for expert system programming languages. Without a semantics, it is hard to formally define and analyze knowledge base anomalies such as inconsistency and redundancy, and it is hard to assess the effectiveness of V&V tools, methods and techniques that have been developed or proposed. In this paper, we develop an approximate declarative semantics for rule-based knowledge bases and provide a formal definition and analysis of knowledge base inconsistency, redundancy, circularity and incompleteness in terms of theories in the first order predicate logic. In the paper, we offer classifications of commonly found cases of inconsistency, redundancy, circularity and incompleteness. Finally, general guidelines on how to remedy knowledge base anomalies are given.     

基于Petri网的一种时序分析方法

Ｐｅｔｒｉ网由于有强大的建模能力和成熟的理论支持,被广泛应用于各种系统的建模．本文通过把Ｐｅｔｒｉ网转换成转移系统,利用转移系统和Ｋｒｉｐｋｅ结构给出时序逻辑语义的解释,从而建立了一种在Ｐｅｔｒｉ网上进行时序分析的方法．这种方法是根据不动点理论,用模型检查验证公式正确性．通过对Ａｄａ程序会合性质进行模型检查,验证了这种方法的有效性．     

An algebraic approach to revising propositional rule-based knowledge bases

One of the important topics in knowledge base revision is to introduce an efficient implementation algorithm. Algebraic approaches have good characteristics and implementation method; they may be a choice to solve the problem. An algebraic approach is presented to revise propositional rule-based knowledge bases in this paper. A way is firstly introduced to transform a propositional rule-based knowledge base into a Petri net. A knowledge base is represented by a Petri net, and facts are represented by the initial marking. Thus, the consistency check of a knowledge base is equivalent to the reachability problem of Petri nets. The reachability of Petri nets can be decided by whether the state equation has a solution; hence the consistency check can also be implemented by algebraic approach. Furthermore, algorithms are introduced to revise a propositional rule-based knowledge base, as well as extended logic programming. Compared with related works, the algorithms presented in the paper are efficient, and the time complexities of these algorithms are polynomial.     

VERIFICATION OF QUALITATIVE PROPERTIES OF RULE-BASED EXPERT SYSTEMS

Frequently, expert systems are developed to operate in dynamic environments where they must reason about time-varying information and generate hypotheses, conclusions, and process inputs that can drastically influence the environment within which they operate. For instance, expert systems used for fault diagnosis and fault accommodation in nuclear power plants reason over sensor data and operator inputs, form fault hypotheses, make recommendations pertaining to safe process operation, and in crisis situations, could generate command inputs to the process to help maintain safe operation. Clearly, there is a pressing need to verify and certify that such expert systems are dependable in their operation and can reliably maintain adequate performance levels. In this article we develop a mathematical approach to verifying qualitative properties of rule-based expert systems that operate in dynamic and uncertain environments. First, we provide mathematical models for the expert system (including the knowledge-base and inference engine) and for the mechanisms for interfacing to the user inputs and the dynamic process. Next, using these mathematical models, we show that while the structure and interconnection of information in the knowledge base influence the expert system's ability to react appropriately in a dynamic environment, the qualitative properties of the full knowledge-base/inference engine loop must be considered to fully characterize an expert system's dynamic behavior. To illustrate the verification approach, we show how to model and analyze the qualitative properties of rule-based expert systems that solve a water-jug filling problem and a simple process control problem. Finally, in our concluding remarks, we highlight some limitations of our approach and provide some future directions for research.     

采用随机Petri网的嵌入式机载软件可靠性检测

针对嵌入式机载软件设计中存在的典型缺陷问题，结合嵌入式机载软件任务调度特性，提出采用随机Petri网对嵌入式机载软件设计进行仿真验证的可靠性检测方法，以提高嵌入式机载软件设计的可靠性。该方法采用随机Petri网对嵌入式机载软件系统行为建模，并给出典型缺陷的检测策略和判定准则，然后通过对Petri网模型进行仿真验证，检测系统是否存在此类设计缺陷；并给出了软件设计的运行流程的仿真验证算法，以支持对相应设计的可靠性检测。通过与其他可靠性检测方法的比较，表明了该方法的有效性。     

基于Petri网的统一知识表示模型

本文讨论知识表示的Ｐｅｔｒｉ网模型。将多种知识分类表示，对于开发具有较宽领域知识的系统具有重要意义。本文从统一的观点出发，在给出了Ｐｅｔｒｉ网的代数规范说明后，将三种主要的知识表示方法分别与Ｐｅｔｒｉ网模型之间建立映射系统，这三种知识表示方法为：逻辑表示法，语义网络和产生式系统。     

Static analysis and process model transformation for an advanced business process to Petri net mapping

Verification of business processes typically relies on Petri net–based process models. While they allow for natural modeling and analysis of aspects such as parallelism and message exchange, such a process model is seldom complete and precise. This is mainly because the available techniques for deriving a Petri net model from the original model neglect process data in favor of feasible verification. In this paper, we present an approach for deriving more precise process models by leveraging a process‐to‐Petri‐net compiler, which takes as input a business process and generates as output a Petri net model for the process. This can be subsequently used for verification. However, in contrast to a conventional compiler, our compiler's objective is not to create the most efficient code but rather to produce a most precise but still effectively verifiable Petri net–based process model.     

基于FMEA和模糊Petri网推理的装备保障过程诊断研究

为满足装备保障过程分析、瓶颈优化的需要,提出基于失效模式影响分析(FMEA)和模糊Petri网推理的装备保障过程诊断方法,通过FMEA建立装备保障过程诊断的因果图,由因果图确定保障过程诊断的推理规则,应用模糊Petri网建立智能的、利于计算机编程实现的保障过程诊断的过程模型。通过研究发现,基于FMEA的规则形成方法便于知识、经验向规则的准确转换提取,模糊Petri网的方法利于将推理过程形式化,实现推理的自动化,提高过程诊断的效率。研究的过程诊断模型和方法已在集群装备保障过程优化决策系统实现中取得较好的效果。     

Knowledge intensive Petri net framework for concurrent intelligent design of automatic assembly systems

The integration of design and planning of flexible assembly system has been recognized as a tool for achieving efficient assembly in a production environment that demands assembly with a high degree of flexibility. This paper proposes a concurrent intelligent approach and framework for the design of robotic flexible assembly systems. The principle of the proposed approach is based on the knowledge Petri net formalisms, incorporating Petri nets with more general problem-solving strategies in AI using knowledge-based system techniques. The complex assembly systems are modeled and analyzed by adopting a formal representation of the system dynamic behaviors through knowledge Petri net modeling from the specifications and the analysis of those models. A template is first defined for a knowledge Petri net model, and then the models for assembly system individuals are established in the form of instances of the template. The design of assembly systems is implemented through a knowledge Petri net-based function–behavior–structure model. The research results show that the proposed knowledge Petri net approach is applicable for design, simulation, analysis and evaluation, and even layout optimization of the flexible assembly system in an integrated intelligent environment. The integration of assembly design and planning process can help reduce the development time of assembly systems.     

一种改进的基于规则的带权模糊推理算法

给出了一种基于带权模糊Petri网的模糊推理算法,这种算法可以适用于一类基于规则的系统,即可以对该类系统的带权模糊Petri网模型进行相应的处理。对系统建立了知识表示的带权模糊Petri网模型,使用该算法可以确定用户给定的库所之间是否存在联系,即相应的命题之间是否存在因果关系,可以计算出命题的模糊真值。对具体的算例进行了分析并与已有的算法进行了比较,得出该算法的优点。     

Verification and validation of Bayesian knowledge-bases

Knowledge-base V&V primarily addresses the question: “Does my knowledge-base contain the right answer and can I arrive at it?” One of the main goals of our work is to properly encapsulate the knowledge representation and allow the expert to work with manageable-sized chunks of the knowledge-base. This work develops a new methodology for the verification and validation of Bayesian knowledge-bases that assists in constructing and testing such knowledge-bases. Assistance takes the form of ensuring that the knowledge is syntactically correct, correcting “imperfect” knowledge, and also identifying when the current knowledge-base is insufficient as well as suggesting ways to resolve this insufficiency. The basis of our approach is the use of probabilistic network models of knowledge. This provides a framework for formally defining and working on the problems of uncertainty in the knowledge-base.

In this paper, we examine the project which is concerned with assisting a human expert to build knowledge-based systems under uncertainty. We focus on how verification and validation are currently achieved in .     

一种用于柔性制造系统仿真的图形Petri网软件工具

本文致力于图形Ｐｅｔｒｉ网软件工具—ＧＰＮＳＴ软件包的设计与实现。首先介绍了ＧＰＮＳＴ的结构和功能，分析了它在Ｐｅｔｒｉ网图形编辑和网结构分析方面的能力；其次正式定义了Ｐｅｔｒｉ网的扩展—赋时着色Ｐｅｔｒｉ网（ＴＣＰＮ），并且使用ＴＣＰＮ建立了柔性制造系统（ＦＭＳ）的简化仿真模型。利用这个模型，能基本实现ＦＭＳ的动态仿真，同时显示整个仿真的过程；最后将调度算法、启发式规则、ＴＣＰＮ模型和仿真结合起来，构成一个基于专家系统的调度器，产生出虽非最优，但是具有比较好结果的可行调度，有效地解决了动态仿真中的ＦＭＳ调度问题。     

基于对象着色Petri网的UML模型研究

UML广泛应用于软件建模,但缺乏有效的模型检测的方法,使用形式化方法对UML模型进行分析,可以发现UML模型的设计问题,提高UML模型的质量。对象着色Petri网是一种拥有接口库所的模块化着色Petri网,既是一种图形化建模工具,又是具有严格的语法语义定义的形式化方法。通过引入事件托肯,改进了将UML模型转换为对象着色Petri网的方法,结合实例将UML状态图和协作图映射为对象着色Petri网模型。并用着色Petri网的方法和工具对模型进行了分析,验证了模型的一系列性质。     

Sufficient conditions for existence of a fixed point in stochasticreward net-based iterative models

Stochastic Petri net models of large systems that are solved by generating the underlying Markov chain pose the problem of largeness of the state-space of the Markov chain. Hierarchical and iterative models of systems have been used extensively to solve this problem. A problem with models which use fixed-point iteration is the theoretical proof of the existence, uniqueness and convergence of the fixed-point equations, which still remains an “art”. In this paper, we establish conditions, in terms of the net structure and the characteristics of the iterated variables, under which existence of a solution is guaranteed when fixed-point iteration is used in stochastic Petri nets. We use these conditions to establish the existence of a fixed point for a model of a priority scheduling system, at which tasks may arrive according to a Poisson process or due to spawning or conditional branching of other tasks in the system     

An object-oriented approach to formally analyze the UML 2.0 activity partitions

Nowadays, UML is the de-facto standard for object-oriented analysis and design. Unfortunately, the deficiency of its dynamic semantics limits the possibility of early specification analysis. UML 2.0 comes to precise and complete this semantics but it remains informal and still lacks tools for automatic validation. The main purpose of this study is to automate the formal validation, according a value-oriented approach, of the behavior of systems expressed in UML. The marriage of Petri nets with temporal logics seems a suitable formalism for translating and then validating UML state-based models. The contributions of the paper are threefold. We first, consider how UML 2.0 activity partitions can be transformed into Object Petri Nets to formalize the object dynamics, in an object-oriented context. Second, we develop an approach based on the object and sequence diagram information to initialize the derived Petri nets in terms of objects and events. Finally, to thoroughly verify if the UML model meets the system required properties, we suggest to use the OCL invariants exploiting their association end constructs. The verification is performed on a predicate/transition net explored by model checking. A case study is given to illustrate this methodology throughout the paper.