Object-oriented Bayesian network for complex system risk assessment

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by SAGE Publications in Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, Vol. 232, Issue 4 on August 2018, available at: https://doi.org/10.1177/1748006X17753026 © 2018 SAGE Publications. Object Oriented Bayesian Network for complex system risk assessment Journal Title XX(X):1–8 c The Author(s) 2016 Reprints and permission: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/ToBeAssigned www.sagepub.com/ Quan Liu1, Ayeley Tchangani2, Franc¸ois P´ er` es3and Vicente Gonzalez-Prida4 Abstract In this paper, we present a novel approach of modelling risk management process for large scale, complex and dynamic systems. To overcome difficulties of modeling a large scale system at once, the main idea in this paper is to split this system into many different structural homogeneous units, but possibly heterogeneous in terms of internal parameters. This approach for a mathematical tool that can apprehend relationships between units being characterized by non homogeneous parameters. To the end we develop a novel tool based on Bayesian network technology referred to extended object oriented Bayesian network as EOOBN for short. The main contribution of this paper consists in establishing algorithms and methods of how to connect units and the adaptation of existing propagation algorithms to this novel model. Keywords complex system, modelling, OOBN, DBN, risk management Introduction In large scale industrial processes, with complex interactions among the components and dynamic evolution, an abnormality or a component failure may result in a cascade phenomenon that can lead to unacceptable risks or the collapse of such networked systems. Therefore risk management engineers must have at their disposal efficient and sound tools, methods or framework to assist managers of such complex systems in their analysis, the prediction of their behaviour, or in their control or management of the effect of possible undesirable events that may affect them. Supplying such a decision support system becomes a challenge for researchers. Modelling risks requires indeed considering the nature of the relationships (influence, causality, etc.), the related uncertainties (about the existence of a relationship, of its intensity or even about the delimitation of the system under consideration), the dynamics (evolution of the model structure and/or parameters over the time) see Bouzarour- Amokrane et al. (2012). The relationships, uncertainties and dynamics characterize the whole system. Considering these characteristics, in modelling process, leads to a complex and large scale system. Within this framework, using classical physical laws to describe it is often unsuitable and the need for new more tractable approaches becomes necessary. In this paper, we attempt to model an industrial process through an extended object oriented Bayesian networks (EOOBN) based on components sharing a same structure. The main idea is first to consider inside these elementary components, uncertainties of interactions among different variables through Bayesian network properties. Then the whole system will be described by associating these components through object oriented mechanisms. This modelling approach will help monitoring and measuring the evolution of the system for a better understanding and controlling of its behaviour. The main purpose of this paper is thus to model a system in order to facilitate risk management and decision making. This paper is structured as follows. Section 2 discusses the main issues of a complex system. Section 3 provides a brief overview of the Bayesian network techniques. Section 4 presents the new extended object oriented Bayesian network and shows in an object. Adapted inference algorithms associated with the developed EOOBN model are introduced in section 5. A case study is used in section 6 to present the modelling steps. Finally, a conclusion, some perspectives and future works are presented in the last section. Notice that is paper is a extension of a communication Liu et al. (2016). Issue description A complex system in general is a large scale system with the following characteristics: it is a multi-components system, these components are interconnected, effects of these interconnections are uncertain, and some of their characteristics are likely to evolve over time (dynamicity); sometimes it has multi-scales and multi-dimensions which is coupling with other scale or dimension. The goal of this paper is to develop an approach for modelling these complex systems in order to evaluate the risk when one or some of their composed components are destabilized by an external event or an internal cause. Such kind of model can be used to assist the assessment process of indicators or the decision making process, in different domains such 1Universit´ e F´ ed´ erale Toulouse Midi-Pyr´ en´ ees, FR 2Universit´ e F´ ed´ erale Toulouse Midi-Pyr´ en´ ees, FR 3Universit´ e F´ ed´ erale Toulouse Midi-Pyr´ en´ ees, FR 4Seville University, ES Corresponding author: Quan Liu, Universit´ e F´ ed´ erale Toulouse Midi-Pyr´ en´ ees - Laboratoire G´ enie de Production, INP-ENIT, 65016 France Email: quan.liu@ enit.fr Prepared using sagej.cls [Version: 2016/06/24 v1.10] 2Journal Title XX(X) as economy, medicine, production and many other fields. In Amaral and Ottino (2004), the author points out issues related to classical modelling methods based on assumptions which eventually can bias the results by ignoring the aspects of interdependency, dynamic and size of the system. Finding another approach to simulate these complex systems when avoiding a great number of hypothesis is worth of research. Bayesian Networks are very efficient for modelling uncertainties. Meanwhile Dynamic Bayesian Network may be used when there is a temporal dimension in the system behaviour see Murphy (2002). In the case of system with a huge number of compoents, a possibility to reduce this complexity is to use the so called Object Oriented Bayesian Networks (OOBN) in order to exploit possibilities offered by this modelling technique. The idea of modelling repeatable systems by object oriented techniques has been already considered in a certain number of studies such as Jaeger (2000),Weber and Jouffe (2006) to mention just a few. In the following paragraph, we introduce basics of static and dynamic Bayesian network characteristics. State of art of Bayesian approach Bayesian Network A Bayesian Network is a directed acyclic graph (DAG) that represents a certain relationships (in general causal relationships) between elements in a certain knowledge domain; each element represents a random variable associated with a probability table characterizing its parameters, the random variable is also called a node in BN. The causal relationship is presented by an arc which is a directed link from one variable which is called parent to the other which is named a child of its parent in the network. Bayes theorem is the central theory in the mechanism of inference in Bayesian Networks. It permits to propagate some local observations through the graph in order to update a priori knowledge about the state of other nodes, see Nielsen and Jensen (2009), Pearl (1988). Figure 1shows an example of a discrete Bayesian Network that has three nodes (A,B and C). A and B are the parents of node C. Node A and B influence their child C, which means A and B are the cause of C in general. For the discrete BN, there are two types of probability tables see Godichaud et al. (2012b): prior probabilities tables for root variables (variables without parents) like A, B and conditional probabilities tables (CPT) for a variables with parents like Csee Godichaud et al. (2012a), Godichaud et al. (2012b). The probability tables are called the parameter for the variable. The parameter is the quantitative part of a BN while the DAG presents the qualitative part. In the example of Fig.1the parameter of A and B are the probability tables and the parameter of C is a conditional probabilities table. Indeed, a BN model is not only a static representation of knowledge but also a tool for the evidence inference which updates the probabilities in the network and enables the refinement of the results according to the observed situation see Ben Hassen et al. (2013). Dynamic Bayesian Network In order to take into account of possible dynamic behaviour of systems, dynamic Bayesian networks (DBN), are Figure 1. Bayesian Network introduced as possible extension of a BN. The DBN is a series of time-slice BN; a typical DBN is a Hidden Markov Models (HMM), see Rabiner and Juang (1986). Learning techniques in a DBN use the same principles as in the classical BN see Murphy (2002). For instance, in the former example of Fig.1, we consider that the node B changes with time. It becomes a dynamic variable; Fig.2shows a DBN model of problem considered in Fig.1with 2 time-slices, where the dynamic node is Bti. The paper between timeslices uses the transition model determined by a transition matrix A as: •the transition model: A=P(Bti|Bti−1) •the initial state: π=P(Bt0) Figure 2. Bayesian Network Object Oriented Bayesian Network Using BN techniques for modelling risk assessment processes becomes increasingly complex when the size of the system increases. For a large scale system with many interacting elements, constructing a BN to represent its functionning behaviour may be very challenging. Meanwhile, when the size of network grows, the model visibility reduces and the update of parameter becomes burdensome. For this reason, an object oriented techniques might be an alternative to reduce the complexity by highlighting a generic pattern representative of the various dimensions of the problem. An object oriented Bayesian network (OOBN), is a direct application of the object paradigm see Bangsø and Wuillemin (2000), Koller and Pfeffer (1997) . The basic element is the class, fragment of a Bayesian network who has three sets of nodes: input, output and internal nodes. The OOBN takes advantage of classic BN but introduces the concept of instance nodes. An instance node is an abstraction of a part of a network which can be used as an elementary component to represent Prepared using sagej.cls Smith and Wittkopf 3 the whole structure. The notion of encapsulation allows the transmission of all properties of the network fragment. An object oriented network can be viewed as a hierarchical description/model of a problem. This makes the modelling easier since the OOBN-fragments at different levels of abstraction are more readable. An OOBN model can be built by asking the experts’ opinions or using the learning techniques. In Langseth and Nielsen (2003) and Wuillemin and Torti (2012), the authors give some insights into OOBN structure learning. The construction of such a model can be facilitated by an ontology representation see Liu et al. (2015). Once the structure of the system is defined, the Conditional Probability Tables (CPTs, also called parameters) have to be parametrized. In Langseth and Bangsø (2001) the author extends the parameter learning algorithm to the objects who have the same structure based on OO assumption. The parameters being identical, this reduces the number of parameters to be specified or learnt. Modelling a complex system by an OOBN allows not only reducing the design work, but also updating calculations. However, most of existing works dealing with this topic consider that parameters do not change from an object to another which is not a realistic assumption in a real world problem modelling context. As our main goal is to use OOBN for the representation of a large, repeatable and inherited system, this shortcoming must be remedied. In the next section, we will describe a proposed extension of OOBN paradigm that we refer to as Extended Object Oriented Bayesian Network or EOOBN for short. An adapted inference mechanism for this EOOBN will be presented in section 5. Construction of an EOOBN In this section, we present an extended object oriented Bayesian network (EOOBN) which introduces much more flexibility, such as the possibility of having different parameters for different objects and taking into account dynamic behaviour of the system, etc. The main steps for constructing an EOOBN will be considered in the subsequent paragraphs showing how the extension is introduced. Basic Definitions To overcome the limitations of classical OOBN associated with the structure building Bangsø and Wuillemin (2000) and Koller and Pfeffer (1997), and the difficulty to take into account dynamic interactions Koller and Pfeffer (1997), we propose here an extended OOBN to ease parameter variation and dynamic consideration process. The original contribution in this paper is to develop an EOOBN which simulates the large scale system with different parameters for objects having the same structure. Moreover our approach is easy to adapt by collaboration mechanism and to propagate observations in a large system. Here below are the main components of an EOOBN. Class, Object, Communication channel, virtual node In this section, we will consider two levels in EOOBN: definition of a class is made at structure level (that is the nodes and their connexions in the object) and the object itself will be instantiated both through the input values and with respect to its parameters at the object level which are likely to evolve with context or time. Class: A class (C) is the structure part (S) in a BN independently of the CPT parameters values. It has three kind of nodes namely: input nodes, output nodes and internal nodes. Only the input and output nodes are visible from outside the class. Object: An object (O{S, P }) in the EOOBN is an instantiation of the corresponding class. There are two parts in an object, the structure (S) which inherits from the class and the parameters (P) which will be defined by experts or learning processes. Instantiate: Instantiate is a procedure of making a class to an object. Namely to obtain an object, we need to set the corresponding parameters to the corresponding class. The parameters come from either a learning process or an expert’s opinion. Communication channel: The input and output build the communication channel for an EOOBN and it is in charge of exchanging information for the class/object. Here are some conditions that must be satisfied: •Input nodes cannot have parents inside the class •Input node is a reference node which is the projection of an output or a normal upstream node •Internal nodes cannot have neither parents nor children outside the class •Output nodes cannot have child inside the class Figure 3presents a class which follows the four conditions above for an EOOBN which has the inputs like A and B, outputs E and F, internal nodes C and F. The class characterizes only the structure of the network. A class can be used only after its instantiation. The EOOBN not only inherits all the advantages of the classical OOBN such as hierarchy or encapsulation but also has much more flexibility in the quantitative part. The possibility of having different parameters values from an object to another varies the possibility of different objects of the same category to have same parameters.????? / Figure 3. A class in EOOBN The necessity to follow the behaviour of real world systems appeal for introducing dynamicity in the model. This can be done by extended classical DBN in object oriented frame as shown in the following paragraph. Although in Bangsø and Wuillemin (2000) a DBN simulation approach is given based on a self-reference node in an object, a confusion might appear when trying to add the dynamic part within a large OOBN. To overcome this issue, we introduce the virtual Prepared using sagej.cls 4Journal Title XX(X) nodes in the EOOBN to simulate the dynamic part. And we obtain an dynamic EOOBN which refers to as a DOOBN. Virtual node: The virtual node is a communication channel for the class/object. It usually stands for the temporal node. •The virtual node is either an input node or an output node in the class/object •It is added for dynamic node in the class/object as a communication channel with other time-slice •The transition model represents the parameters between the virtual input and the dynamic node. Conditional probabilities between a dynamic node and its virtual output are equalled to 1 Figure 4. A dynamic class in EOOBN Figure 5. A dynamic EOOBN Figure 4presents a dynamic class who has one dynamic element Dt. And Figure 5provides a dynamic EOOBN by using the virtual input and output. The virtual input Dt−1 receives the temporal information from the time-slice t−1 and the virtual output Dt+1 for t+ 1 is a projection of the dynamic variable Dt, which transfers the current information to the next time-slice t+ 1. The parameters for the dynamic relationships are: •At,t−1=P(Dt|Dt−1) •At+1,t =P(Dt+1|Dt)=1 Parameter At,t−1is the conditional probability table between time-slice tand t−1and parameter At+1,t = 1 just transfers the information from tto t+ 1. Adding the virtual node in the class/object allows the encapsulation of dynamic information into an object. The communication between the time-slices through the virtual node keeps the independence of each time-slice. Meanwhile the virtual nodes allow the designer to add the dynamic evolution in class/object without changing the mainly structure and parameters for class and object. In this communication, we suppose that time-slice t depends only on time-slice t−1. Construction method The construction of a dynamic EOOBN can be done by carrying out the following steps: 1. Formalize the structure Sof a system (by splitting the system into different classes C) 2. Design the structure of each class (C) with respect to Sand without considering the dynamic part 3. Identify the dynamic node in the class Ntiand add the virtual input and output node around the dynamic node 4. Instantiate the class by introducing the parameters corresponding to the object 5. Connect the objects through their communication channels The instantiation of a class needs parameters which could obtain from an expert’s opinion or an learning process. Due to the spacial characteristics of EOOBN such as the repeatable structure of certain objects, the parameter learning maybe different from the classical learning process. The learning problem for EOOBN will be solved in the future work. The EOOBN that we propose in this part has much flexibility in not only the parameter variations by using class and object but also the introducing the dynamic evolution in a system. The definition of class keeps the independence of the variables in it. This independence provides the independent local computation for an object. So the EOOBN that we propose in this communication is always organized at two levels: global level and object level. In order for existing inference algorithms to work for the proposed EOOBN some adjustments are required that will be presented in the next section. Propagation in EOOBN Here we propose the algorithms for solving the inference problem in an EOOBN. In the real world when an observation is made, it can be used to either predict a future behaviour and/or diagnose the causes resulting in the current system state. The capacity of inference is an advantage of BN. As we have mentioned, the information propagation of a classic OOBN is done by either developing all the objects Bangsø and Wuillemin (2000) to obtain a classical BN or by using the MSBN Koller and Pfeffer (1997); Xiang and Lesser (2000), losing by the way the sense of object oriented modelling. Traditional inference techniques are not suitable for the EOOBN processing due to the number of parameters and variables. Because of the size of EOOBN the inference work should also take into account the calculated size and time. For this reason, we propose here an adapted algorithm for EOOBN calculation using the advantages associated with the virtual nodes. Local calculation At the object level, as input and output nodes separate the objects, inference can be performed locally with no need of extra information provided by its neighbours. The classical BN algorithms can be applied for the object calculation given that all the parameters are known. Indeed internal and output nodes correspond to previous knowledge and input nodes receive the probability from their neighbourhood. Local calculation can result of four situations: Prepared using sagej.cls Smith and Wittkopf 5 1. There is no observation in the global network 2. There is observation(s) in the object 3. There is an update information(s) at the input of an object 4. There is only one type update information(s) at the output of an object “No observation in the network”means that the network spreads by itself with time evolution. If there are several types (input and output) of information update, the semilocal calculation is to be used. Since at this time the soundness of a junction tree is broken, an object needs some more information from its neighbourhoods. At this time, we will use an auxiliary network which regroups the updating informations for different objects. This extra information keeps the soundness of the object. But the semilocal calculation is only needed when inference is performed for a certain object of the global network. The feature of the local calculation is saving the computing time and size. Because computation can be performed in smaller parts of the global network, there is no need to build a big, complex junction tree. Moreover some objects inherit their structures from a same class, and they have the same junction tree. Due to local calculation possibilities, objects may do the computation independently, allowing possible parallel computation. Information flow The computation in an EOOBN has two levels, the object level is the local calculation, and the global level is the information flow. Figure 6. Information flows without observation No observation When there is no observation, the network spreads by itself. The information follows the same direction as the communication channels (see Fig.6). In Fig. 6there is an EOOBN who has Jobjects and Ttime-slices. Here we suppose object Oj tidepends only on the last time t−1 (namely time-slice Oj ti−1) and object j−1(namely object Oj−1 ti). If there are much more dependency between object or time, we could use the virtual nodes to simplify the dependency. Observation If there is an observation in object, the propagation of the information between objects is described in Fig.8. Because the object has the local computation ability, one just needs to control the information flows. The algorithm for the inference is presented in Fig.9. Figure 7. EOOBN with observation Figure 8. Information flow between time-slices and objects In this algorithm, the computation needs to be done first at Om tiwith 1≤m<j and at Oj twith t1≤t<tiwhich correspond to the two red dash parts (A and B in Fig.9). The results of this computation will be stored in a data base for the future calculation and they can be obtained at the same time. This simultaneity reduces the calculation time. After this step, we can also do the inference at the same time in the two blue parts (C and D in Fig.9). Moreover, if the querying object is known, the calculation is oriented directly to this object after the first step. Unlike the traditional method, which develops all the objects, first, builds a junction tree and proceeds to the propagation, the algorithm only needs here a few objects to answer the request by local calculation. Case study In this section, we present how to use the construction methods to build an EOOBN by the cement manufacture process. The objectives are first building the network and then simulating the process. The cement production generally has seven mainly procedures, which are 1. Obtaining the raw material from a quarry by blasting machine 2. Proportioning, blending and grinding by grinding machine 3. Preheating the material in a preheater tower by heating machine 4. Heating in a kiln by heating machine 5. Cooling the clinker by cooling machine 6. Grinding finish by grinding machine 7. Bagging by packaging machine Prepared using sagej.cls 6Journal Title XX(X) Figure 9. Information propagation organigram Figure 10. Cement manufacture process Every procedure contains operation machines and operators. To simplify the simulation, we assume that every step contains one main machine. And we make sure that only the qualified intermediate product could transfer to the next procedure. Every machines has its own operation condition. The fabrication process in each step is a complex physical chemistry dynamic reaction; building the math model for each process is complicated. Meanwhile there are certain simplification and assumption in the math model. The cement manufacturing process should be treated as a complex system; EOOBN is suitable for the simulation. Because we consider the modelling in the uncertain circumstance and split the system by different objects, the EOOBN could avoid certain simplification, condition assumption and the size problem of the system. Step 1: Formalize the structure of a system (by splitting the system into different classes) After analyzing the manufacturing process, we split the system into 7 blocks which corresponds to a procedure in Fig 10. Here we build a general machine model for all the machines by a Bayesian network; the general model is treated as a class in the EOOBN. Step 2:Design the structure of each class with respect to system and without considering the dynamic part A machine involves 7 basic variables which are listed below: •Machine State •Upstream State •Operator skill •Controller •Product •Final Product Fabricating a product depends the operator skill (OS), machine state (MS) and the upstream product (UP). The intermediate product (P) consists the qualified and nonqualified products. The final product (FP) depends on the intermediate product, machine state, operator skill and the controller (C). Without considering the dynamic and communication channel, the basic BN is presented in the left part of Fig.11. The right part of Fig.11 presents the class in the cement process. Because each machine communicates with their intermediate product, the upstream product becomes the input node in the class, and the final product becomes the output in the class. Step 3: Identify the dynamic node in the class and add the virtual input and output node around the dynamic node Prepared using sagej.cls Smith and Wittkopf 7 Figure 11. Basic machine model Because the machine state reduces operating efficiency over time, here it is the dynamic variable (MS) and we put the virtual input and output around it see Fig.12. All the variables Figure 12. Dynamic class in the class are listed in the Tab.1; we consider that all the nodes are discrete variables. Table 1. Input, Internal, Output variables Nodes States Input Nodes Upstream Product(UP) many,normal,few Machine State t-1(MSt−1) good,normal,weak Internal Nodes Operator Skill(OS) skilled,normal, beginning Controller (C) skilled,normal, beginning Product(P) many,normal,few Machine State t(MSt) good,normal,weak Output Nodes Final Product(FP) many,normal,few Machine Sate t+1(MSt+1) good,normal,weak Step 4: Instantiate the class by introducing the parameters corresponding to the object To introduce the heterogeneous for each machine, we affect different parameters to the objects. The parameters come from the learning process or the domain experts. In our case, the machine parameters are decided by authors. Step 5: Connect the objects through their communication channels There are two communication channels which are the intermediate product flow in the process: •Intermediate product flow : final product −→ upstream product, Mj ti−→ Mj+1 tiwith 1⩽j⩽7 •Dynamic machine state : machine state at t −→ machine state at t+1, Mj ti−→ Mj ti+1 with 1⩽j⩽7 Figure 13. EOOBN for the cement process The global network is shown in Fig.13.The simulation result of the last machine is shown in Fig.14 and 15. We could see that the machine working state degrades over time and the productivity reduces with the machine state. The EOOBN simulates the system without building a general physical Mathematica model which avoid making the assumptions. By splitting a big system into different homogeneous pieces, such as the cement manufacture process, reduces the size of modelling. Meanwhile, we consider the heterogeneous by parameterizing the objects of different parameters. Also the dynamic evolution is treated as a second dimension of the system which simplify the construction and the simulation work. Figure 14. Final product - Machine 7 Conclusion A new modelling technique using an extended Bayesian approach referred to as EOOBN and based on the concept of Oriented Object paradigm has been proposed to tackle Prepared using sagej.cls 8Journal Title XX(X) Figure 15. Machine state - Machine 7 modelling challenges raised by large scale and complex real world systems. The principles of defining the structure in the class and distributing the parameters for the instantiation have been shown. EOOBN models appear to be much powerful than the classical OOBN while preserving all its benefits, such as encapsulation, hierarchy and top-down design. When a repetitive structure allows the use of such Object Oriented representation, EOOBN is undoubtedly suitable for modelling complex situations encountered in risk management framework. To take into account the possibility of varying parameters and the system dynamics, EOOBN have been adapted and changed to obtain dynamic OOBN referred to as DOOBN where each time-slice is associated with an object and parameters are allowed to change from slices through the introduction of virtual nodes. An illustrative application in an industrial process has been used along the communication to show the interest of such modelling technique. Furthermore, inference algorithms demonstrate the gain of using EOOBN in terms of local calculation and simultaneous computation. In a future work, learning techniques associated with such modelling will be considered. References Amaral LA and Ottino JM (2004) Complex networks. The European Physical Journal B-Condensed Matter and Complex Systems 38(2): 147–162. Bangsø O and Wuillemin PH (2000) Object oriented bayesian networks a framework for topdown specification of large bayesian networks and repetitive structures . 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