Study of the diagnosability of automated production systems based on functional graphs

Functional graphs are a convenient representation that we have introduced to model automated production systems. They are useful for the monitoring and the supervision of manufacturing processes or other industrial processes, such as chemical processes. An approach based on relational theory and graph theory is presented in this paper. This approach allows to characterize formally structural properties of a functional graph and to map it into a set of relations translating all the complete paths existing in the initial graph. Two kinds of functional graphs are analyzed and algorithms exploiting their structures are presented. We introduce the concept of diagnosability as a system property that reflects the possibility to observe the behavior of a system with respect to faults. The diagnosability is defined and analyzed by means of computable states and mathematical relations. Propositions explaining causality relations between functions of a functional graph are given.     

一种动态定性空间关系自动规划方法

为解决定性空间关系的规划问题,在概念邻域图的基础上提出描述动作与定性空间关系交互的邻域划分图.基于邻域划分图,提出了定性空间关系自动规划的形式化表示和推理算法,证明了算法的可靠性,并举例说明了新方法的应用.该方法在处理单方面空间关系规划中具有用通用性,在机器人导航方面具有潜在的应用前景.     

Bayesian learning of graphical vector autoregressions with unequal lag-lengths

Graphical modelling strategies have been recently discovered as a versatile tool for analyzing multivariate stochastic processes. Vector autoregressive processes can be structurally represented by mixed graphs having both directed and undirected edges between the variables representing process components. To allow for more expressive vector autoregressive structures, we consider models with separate time dynamics for each directed edge and non-decomposable graph topologies for the undirected part of the mixed graph.Contrary to static graphical models, the number of possible mixed graphs is extremely large even for small systems, and consequently, standard Bayesian computation based on Markov chain Monte Carlo is not in practice a feasible alternative for model learning. To obtain a numerically efficient approach we utilize a recent Bayesian information theoretic criterion for model learning, which has attractive properties when the potential model complexity is large relative to the size of the observed data set. The performance of our method is illustrated by analyzing both simulated and real data sets. Our simulation experiments demonstrate the gains in predictive accuracy which can obtained by considering structural learning of vector autoregressive processes instead of unstructured models. The analysis of the real data also shows that the understanding of the dynamics of a multivariate process can be improved significantly by considering more flexible model classes.     

基于三维行为关系图的模型一致性检测方法

在业务流程模型的相似性分析过程中,有时会出现环结构。已有的方法一般不考虑环结构,忽略了环结构对模型一致性分析的影响。以Petri网的多重变迁集为基础,提出一种新的一致性度测量方法。首先通过分析5种行为序列关系来刻画Petri网的变迁之间的相互关系,给出了三维行为关系图的概念;然后对Petri网的三维行为关系图间的关系进行研究,提出了基于Petri网的三维行为关系图的一致性检测方法。理论分析和实例测试均表明了该方法的有效性。     

建筑物层次空间聚类方法研究

建筑物空间聚类是实现居民地地图自动综合的有效方法。基于图论和Gestalt原理,发展了一种层次的建筑物聚类方法。该方法可以深层次地挖掘建筑物图形的视觉特性,将面状地物信息充分合理地表达在聚类结果中。依据视觉感知原理,借助Dealaunay三角网构建方法,分析了地图上建筑物的自身形状特性和相互间的邻接关系,并依据建筑物间的可视区域均值距离建立了加权邻近结构图,确定了建筑物的邻近关系（定性约束）。根据Gestalt准则将邻近性、方向性和几何特征等量化为旋转卡壳距离约束和几何相似度约束。通过实例验证了层次聚类方法得到更加符合人类认知的建筑物聚类结果。     

Minimal functional routes in directed graphs with dependent edges

Graphs are mathematical structures used to model a set of objects and the relations between them. One of the basic concepts of graph theory, the path, has wide real‐world applications. In classic graph models, edges ending at a node are assumed to be independent. However, many real graphs/networks can only be correctly described by considering a dependency among nodes or edges. Paths in such graphs may not be functional if the conditional dependency is ignored. In this study, we investigate the routing problem in directed graphs with dependent edges represented by general graph models as alternatives to hypergraphs. We define a minimal functional route (MFR) as a minimal set of nodes and edges that can independently perform information transfer between two given nodes, and formulate the determination of MFRs as a graph search problem. A depth‐first‐search (DFS) top‐down algorithm, an iterative integer linear programming (ILP) bottom‐up algorithm, and a subgraph‐growing bottom‐up algorithm are devised subsequently to solve this problem. Numerical experiments verify the effectiveness of the algorithms. The defined MFR problem and the proposed algorithms are expected to find many practical applications.     

Formal Verification of Dynamic Properties in an Aerospace Application

Formal verification of computer-based engineering systems is only meaningful if the mathematical models used are derived systematically, recording the assumptions made at each modelling stage. In this paper we give an exposition of research efforts in cooperation with aerospace industries in Sweden. We emphasize the need for modelling techniques and languages covering the whole spectrum from informal engineering documents, to hybrid mathematical models. In this modelling process we give as much weight to the physical environment as to the controlling software. In particular, we report on our experience using switched bond graphs for the modelling of hardware components in hybrid systems. We present the basic ideas underlying bond graphs and illustrate the approach by modelling an aircraft landing gear system. This system consists of actuating hydromechanic and electromechanic hardware, as well as controlling components implemented in software and electronics. We present a detailed analysis of the closed loop system with respect to safety and timeliness properties. The proofs are carried out within the proof system of Extended Duration Calculus.     

State-based modelling in hazard identification

The signed directed graph (SDG) is the most commonly used type of model for automated hazard identification in chemical plants. Although SDG models are efficient in simulating the plant, they have some weaknesses, which are discussed here in relation to typical process industry examples. Ways to tackle these problems are suggested, and the view is taken that a state-based formalism is needed, to take account of the discrete components in the system, their connection together, and their behaviour over time. A strong representation for operations and actions is also needed, to make the models appropriate for modelling batch processes. A research prototype for HAZOP studies on batch plants (CHECKOP) is also presented, as an illustration of the suggested approach to modelling.     

Supporting connectivism in knowledge based engineering with graph theory,filtering techniques and model quality assurance

Mass-customization has forced manufacturing companies to put significant efforts to digitize and automate their engineering and production processes. When new products are to be developed and introduced the production is not alone to be automated. The application of knowledge regarding how the product should be designed and produced based on customer requirements also must be automated. One big academic challenge is helping industry to make sure that the background knowledge of the automated engineering processes still can be understood by its stakeholders throughout the product life cycle.The research presented in this paper aims to build an infrastructure to support a connectivistic view on knowledge in knowledge based engineering. Fundamental concepts in connectivism include network formation and contextualization, which are here addressed by using graph theory together with information filtering techniques and quality assurance of CAD-models. The paper shows how engineering knowledge contained in spreadsheets, knowledge-bases and CAD-models can be penetrated and represented as filtered graphs to support a connectivistic working approach. Three software demonstrators developed to extract filtered graphs are presented and discussed in the paper.     

Supervision of an industrial steam generator. Part I: Bond graph modelling

Model based supervision of most process engineering plants is difficult due to the complexities arising out of the energetic couplings in the model. Bond graph modelling is a suitable tool to represent the model structures of such processes along with their control system instrumentation. In this paper, bond graph model of a steam generator installation consisting of complex industrial components such as a boiler, a condenser, etc. is developed and validated through experimental observations. It is further shown that the causal properties of bond graphs not only allow validating the model, but they also provide the computational algorithms to eliminate the unknown variables from coupled thermo-fluid models and thus generate analytical redundancy relations (ARR) in terms of measurements and parameters. Structural analysis of the model is used to obtain the fault signatures and also to identify the hardware redundancies in the sensor placement. Thereafter, quantitative evaluations of ARR are used to yield residuals, which are subsequently implemented in an online integrated supervision system described in the sequel to this paper. The fault tolerant control and reconfiguration strategies implemented in that supervision platform are based on the available hardware redundancies in the process, which have been deduced directly from bond graph model using the methodology presented in this paper.     

Hierarchical representation of complex systems for supporting human decision making

The work presented in this paper is devoted to intelligent on-line supervision tools. In the proposed approach, the human operator remains in the decision loop, at the highest level, and acts on the process. To help operators make decisions, process knowledge is represented with a model whose complexity can be adapted on line to the operation needs at the request of the operator. The model thus helps to focus only on the phenomena that are relevant at a given time. To give the model explanatory capacity, it is represented as a causal directed graph, and allows the representation of temporal phenomena, which is fundamental for dynamic monitoring. A hierarchical representation of the functional properties of the process is proposed. The conception of a hierarchy of causal models with a top-down analysis is discussed. Path algebra is used to construct a higher-level graph on-line at the request of the operator from the most detailed graph, while conserving the semantics of the latter. No intermediate level is defined a priori; only the highest and lowest level graphs are fixed: the others are constructed dynamically. Finally, a study of how graphs can convey information on the dynamics of the process for approximate temporal reasoning that is largely sufficient for supervision purposes is analyzed. An example of a causal graph hierarchy for a nuclear process illustrates the method. As a final point, the use of such causal graphs in advanced industrial supervision tools is considered.     

Graph-based retrieval of building information models for supporting the early design stages

Building information modeling (BIM) principles are transforming today’s communication and working processes in the field of construction, however the early design phases are only rarely supported and information technology is therefore not exploited to its full potential. The early design phases are characterized by an iterative process of searching for plausible solutions. A common approach is to refer to similar examples, which are conventionally found using keyword-based search strategies.To this end we propose a method for indexing spatial configurations along with a sketch-based input method for search strategies that uses so-called semantic fingerprints of buildings. The topology of spatial configurations is extracted from building information models and represented as graphs. For both building information models and the user sketches, the extracted graphs are used as the basis for a subgraph-matching algorithm facilitating an intuitive novel query method for researching similar reference examples. The system is able to present corresponding existing solutions to even rudimentary sketches or fragments of a design idea. In addition to graph matching and sketch-based interaction, more recent BIM-based approaches are also taken into account.     

基于最优传输的层次化图核

已有的图核大多关注图的局部属性,利用局部的拓扑特征构建图的相似性度量,忽略图的层次结构信息.为了解决这个问题,文中提出基于最优传输的层次化图核.首先,将每个图表示成层次化的图结构.在层次化图结构构建过程中,利用K-means聚类算法构造每层图的节点,节点间的概率连接作为图的边.然后,利用带有熵约束的最优传输计算两图的层次结构上每层图之间的最优传输距离.最后,基于最优传输距离计算基于最优传输的层次化图核.在6个真实图数据集上的实验表明,文中方法可提升分类性能.     

面向链接预测的知识图谱表示学习方法综述

作为人工智能的重要基石, 知识图谱能够从互联网海量数据中抽取并表达先验知识, 极大程度解决了智能系统认知决策可解释性差的瓶颈问题, 对智能系统的构建与应用起关键作用. 随着知识图谱技术应用的不断深化, 旨在解决图谱欠完整性问题的知识图谱补全工作迫在眉睫. 链接预测是针对知识图谱中缺失的实体与关系进行预测的任务, 是知识图谱构建与补全中不可或缺的一环. 要充分挖掘知识图谱中的隐藏关系, 利用海量的实体与关系进行计算, 就需要将符号化表示的信息转换为数值形式, 即进行知识图谱表示学习. 基于此, 面向链接预测的知识图谱表示学习成为知识图谱领域的研究热点. 从链接预测与表示学习的基本概念出发, 系统性地介绍面向链接预测的知识图谱表示学习方法最新研究进展. 具体从知识表示形式、算法建模方式两种维度对研究进展进行详细论述. 以知识表示形式的发展历程为线索, 分别介绍二元关系、多元关系和超关系知识表示形式下链接预测任务的数学建模. 基于表示学习建模方式, 将现有方法细化为4类模型: 平移距离模型、张量分解模型、传统神经网络模型和图神经网络模型, 并详细描述每类模型的实现方式与解决不同关系元数链接预测任务的代表模型. 在介绍链接预测的常用的数据集与评判标准基础上, 分别对比分析二元关系、多元关系和超关系3类知识表示形式下, 4类知识表示学习模型的链接预测效果, 并从模型优化、知识表示形式和问题作用域3个方面展望未来发展趋势.     

Efficient subgraph isomorphism detection: a decomposition approach

Graphs are a powerful and universal data structure useful in various subfields of science and engineering. In this paper, we propose a new algorithm for subgraph isomorphism detection from a set of a priori known model graphs to an input graph that is given online. The new approach is based on a compact representation of the model graphs that is computed offline. Subgraphs that appear more than once within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph. In the extreme case where all model graphs are highly similar, the run-time of the new algorithm becomes independent of the number of model graphs. Both a theoretical complexity analysis and practical experiments characterizing the performance of the new approach are given     

Predicting metamorphic relations for testing scientific software: a machine learning approach using graph kernels

Comprehensive, automated software testing requires an oracle to check whether the output produced by a test case matches the expected behaviour of the programme. But the challenges in creating suitable oracles limit the ability to perform automated testing in some programmes, and especially in scientific software. Metamorphic testing is a method for automating the testing process for programmes without test oracles. This technique operates by checking whether the programme behaves according to properties called metamorphic relations. A metamorphic relation describes the change in output when the input is changed in a prescribed way. Unfortunately, finding the metamorphic relations satisfied by a programme or function remains a labour‐intensive task, which is generally performed by a domain expert or a programmer. In this work, we propose a machine learning approach for predicting metamorphic relations that uses a graph‐based representation of a programme to represent control flow and data dependency information. In earlier work, we found that simple features derived from such graphs provide good performance. An analysis of the features used in this earlier work led us to explore the effectiveness of several representations of those graphs using the machine learning framework of graph kernels, which provide various ways of measuring similarity between graphs. Our results show that a graph kernel that evaluates the contribution of all paths in the graph has the best accuracy and that control flow information is more useful than data dependency information. The data used in this study are available for download at http://www.cs.colostate.edu/saxs/MRpred/functions.tar.gz to help researchers in further development of metamorphic relation prediction methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Batch kernel SOM and related Laplacian methods for social network analysis

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch self-organizing map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modelled through a weighted graph that has been directly built from a large corpus of agrarian contracts.     

Gibbs and Markov properties of graphs

Directed acyclic graphs (DAG's) and, more generally, chain graphs have in recent years been widely used for statistical modelling. Their Gibbs and Markov properties are now well understood and are exploited, e.g., in reducing the complexity encountered in estimating the joint distribution of many random variables. The scope of the models has been restricted to acyclic or recursive processes and this restriction was long considered imperative, due to the supposed fundamentally different nature of processes involving reciprocal interactions between variables. Recently however it was shown independently by Spirtes (Spirtes, 1995) and Koster (Koster, 1996) that graphs containing directed cycles may be given a proper Markov interpretation. This paper further generalizes the scope of graphical models. It studies a class of conditional independence (CI) probability models determined by a general graph which may have directed and undirected edges, and may contain directed cycles. This class of graphical models strictly includes the well-known class of graphical chain models studied by Frydenberg et al., and the class of probability models determined by a directed cyclic graph or a reciprocal graph, studied recently by Spirtes and Koster. It is shown that the Markov property determined by a graph is equivalent to the existence of a Gibbs-factorization of the density (assumed positive). To better understand the structural aspects of the Gibbs and Markov properties embodied by graphs the notion of lattice conditional independence (LCI), introduced by Andersson and Perlman (Andersson and Perlman, 1993), is needed. The Gibbs-factorization has an outer ‘skeleton’ which is determined by the ring of all anterior sets of the graph. This revised version was published online in June 2006 with corrections to the Cover Date.     

Time Series Prediction for Graphs in Kernel and Dissimilarity Spaces

Graphs are a flexible and general formalism providing rich models in various important domains, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, that is, changes in the number of nodes or in the graph connectivity. Predicting such changes within graphs can be expected to yield important insight with respect to the underlying dynamics, e.g. with respect to user behaviour. However, predictive techniques in the past have almost exclusively focused on single edges or nodes. In this contribution, we attempt to predict the future state of a graph as a whole. We propose to phrase time series prediction as a regression problem and apply dissimilarity- or kernel-based regression techniques, such as 1-nearest neighbor, kernel regression and Gaussian process regression, which can be applied to graphs via graph kernels. The output of the regression is a point embedded in a pseudo-Euclidean space, which can be analyzed using subsequent dissimilarity- or kernel-based processing methods. We discuss strategies to speed up Gaussian processes regression from cubic to linear time and evaluate our approach on two well-established theoretical models of graph evolution as well as two real data sets from the domain of intelligent tutoring systems. We find that simple regression methods, such as kernel regression, are sufficient to capture the dynamics in the theoretical models, but that Gaussian process regression significantly improves the prediction error for real-world data.