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Distributed Bayesian diagnosis for modular assembly systems—A case study
Journal of Manufacturing Systems 32 (2013) 480–488
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Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys
Technical paper
Distributed Bayesian diagnosis for modular assembly systems—A case study Mohamed Samir Sayed ∗ , Niels Lohse Manufacturing Division, The University of Nottingham, Nottingham NG7 2RD, UK
a r t i c l e
i n f o
Article history: Received 16 September 2012 Received in revised form 11 February 2013 Accepted 4 March 2013 Available online 1 May 2013 Keywords: Assembly Modular design Bayesian networks Error diagnosis Multi-agent systems
a b s t r a c t The growing interest in modular and distributed approaches for the design and control of intelligent manufacturing systems gives rise to new challenges. One of the major challenges that have not yet been well addressed is monitoring and diagnosis in distributed manufacturing systems. In this paper we propose the use of a multi-agent Bayesian framework known as Multiply Sectioned Bayesian Networks (MSBNs) as the basis for multi-agent distributed diagnosis in modular assembly systems. We use a closeto-industry case study to demonstrate how MSBNs can be used to build component-based Bayesian sub-models, how to verify the resultant models, and how to compile the multi-agent models into runtime structures to allow consistent multi-agent belief update and inference. © 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction New market conditions imply that manufacturing systems today need to be more flexible and responsive to enable quicker response to the changes in the market and the introduction of new products and product designs while being robust in the face of disturbances and unexpected failures [1]. To respond to these new challenges, new paradigms for the design and control of manufacturing systems have been proposed within the last two decades, the main drive being towards decentralized/distributed control combined with tendency to modular component-oriented system design approaches. The most notable of these paradigms being reconfigurable manufacturing systems [2], Holonic manufacturing systems [3] and more recently evolvable production systems [4]. 1.1. The need for modular diagnosis One of the main features that need to be properly addressed in order to realize the vision for robust modular manufacturing systems is the ability to diagnose faults quickly and hence allowing quicker recovery times and less down time and stoppage costs. The ability to monitor the system during the operation means the ability of the control system to adapt to changes and unexpected behaviour and hence resulting in more reliable systems. It has been reported that during a production system downtime, repairing the cause of the error does take a small fraction of the downtime. It is
∗ Corresponding author. Tel.: +441159513875. E-mail addresses: [email protected] (M.S. Sayed), [email protected] (N. Lohse).
locating the source of the problem (i.e. diagnosis) that is responsible for the majority of downtime [5]. The difficulty in identifying causes of errors becomes even more relevant in complex production systems. Another recent drive for diagnosis and prognosis efforts has been the growing interest in building integrated frameworks for condition-based maintenance management in industrial organizations where diagnosis and prognosis models are used for the optimal planning and scheduling of maintenance activities [6]. Most of the available work on diagnosis is designed for centralized systems. Hence there is a need for new decentralized methods to address monitoring and diagnosis in modular, component-based physical systems. The drive towards component-based systems design, in fact brings new opportunities for more efficient affordable monitoring and diagnosis systems because specific component suppliers should then be able to design the monitoring and diagnosis models for their component as an integral part of the component design effort. Consequently, the diagnostic design effort, which represents the main obstacle in designing large scale diagnostic systems, will be distributed among specialized component suppliers allowing the people who know the most about each component to design its diagnostic sub-system. In order for this vision to be realized there is a crucial need for an underlying framework or that allows independently developed diagnostic sub-systems to be integrated into a wider diagnosis system once the concerned physical system is built from its modular components. Since the use of multi-agent systems is becoming more prominent in the control of modular manufacturing systems (for example, evolvable production systems and Holonic manufacturing systems), it becomes very attractive option to embody the monitoring and diagnosis functionalities into the paradigm
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M.S. Sayed, N. Lohse / Journal of Manufacturing Systems 32 (2013) 480–488
of multi-agent systems for manufacturing control. However, the decentralized nature of these modular systems introduce new challenges from a diagnostic point of view, mainly due to the dynamic nature of these systems where modules are expected to be rapidly added and removed from the system. This makes the use of classical centralized approaches to diagnosis impractical due to the difficulty of foreseeing all possible system modules and their potential configurations and interactions beforehand and capturing that in one global model. Other new challenges relate to communicating observations across the system and the need to systematically orchestrate that while responding to issues of fault propagation across various modules [7]. Various approaches do exist for centralized fault diagnosis in industrial systems depending on the types of faults to be diagnosed. One prominent approach that has been studied in various domains including fault diagnosis recently is Bayesian networks with promising results. However, all of the work on industrial diagnosis using Bayesian networks has been applied in a centralized manner using the classical notion of single Bayesian network. A growing research interest has been directed to develop new approaches that would extend the use of Bayesian networks knowledge representation and inference techniques with their proven merits into multi-agent systems. A few notable works have been reported in literature suggesting new approaches to achieve this goal [8,9]. It is our belief that there exists a unique opportunity to extend these new research endeavours into the field of monitoring and diagnosis of modular manufacturing systems in order to materialize the vision of component-based monitoring and diagnosis systems for modular manufacturing systems. This paper reports on our recent work in using multi-agent Bayesian reasoning for the problem of multi-station assembly systems diagnosis. The rest of this paper is organized as follows: Section 2 gives a background review on the state of the art in manufacturing diagnosis. In Section 3 the proposed distributed diagnosis framework is described and some relevant background on Bayesian networks and MSBNs is given. Section 4 describes our case study that is used to demonstrate the proposed approach, and finally Section 5 finishes with some concluding remarks.
2. Diagnosis in manufacturing Many attempts have been devised to provide fault diagnosis capabilities for manufacturing systems. Some of these approaches have been applied on specific devices or production units while others have been applied on the scale of the entire production system. The diagnostic approaches used in each work vary depending on the researchers’ background and the problem context they are tackling. Hence different approaches originating from different domains have been proposed and applied. This includes approaches such as model based reasoning, case based reasoning, artificial neural networks, probabilistic reasoning, fuzzy logic, induction trees as well as data-driven methods in addition to many hybrid approaches that combine different approaches. The majority of the work that has been carried out in manufacturing diagnosis has been aimed at specific individual components within a production facility due to the relative simplicity and focus of the problem. However, considerable other work has also been aimed at addressing the problem of fault diagnosis in the production system as a whole through providing system-level diagnostic capabilities. As different components with different attributes and characteristics need to be diagnosed in this case, the diagnostic process becomes far more complex than in the case of single component. New issues arise in this case when considering the diagnosis of a complex system as a whole, some of these issues relate to factors such as fault propagation from one component into another, fault
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interactions and faults accumulations across various stages in the system [7]. Discrete event systems (DES) have been used in [10] for fault diagnosis on the manufacturing system level through the use of time templates as an improvement to the conventional discrete event systems models. In [11] a DES approach is used for combining diagnosis and process optimization in a multi-stage manufacturing process. Despite their theoretical soundness, however, DES-based approaches do suffer from major limitations when applied to complex systems due to state explosion and the need for accurate detailed modelling which is not always feasible for manufacturing systems [7]. On the other hand, data driven approaches with little modelling requirements have also been investigated. The initial modelling effort required here is comparatively less than that of DES-based approaches where the nominal behaviour of the system normally needs to be captured. These include artificial neural networks [12], fuzzy logic [13] and Bayesian networks [14] among others. The models here do not necessarily capture precise nominal system behaviour as in DES-based approaches, rather a general understanding of how the system works, and the types of expected faults and associated symptoms can be used to obtain a basic diagnostic model. Artificial neural networks (ANN) have been used by Monostori [15] for the monitoring of machining processes, where back propagation networks were used for state estimation of machine tools. In [16] an integrated method is proposed for using ANNs for diagnosis and monitoring of manufacturing systems with focus on product defects where ANNs are integrated with a rough set approach to allow the extraction of causal relationships between product defects and the associated process parameters. Although ANNs have proven to yield some promising results, however these approaches were not widely adopted due to the need for large training sets and the fact that it is not possible to understand how the diagnostic decision is reached from the model [7]. Another research avenue that was pursued is the use of statistical and probabilistic models. Various statistical approaches have been used to tackle diagnostic problems focusing on dimensional variation source and root cause identification in assembly and multi-stage manufacturing systems. Among these are pattern matching techniques such as principal component analysis (PCA) which was used in [17] for the identification of automotive assembly variation sources. This PCA method was then further developed into a diagnostic methodology assuming the availability of large measurement data and structured noise in [18]. Another major approach for manufacturing systems diagnosis that has gained considerable interest is the stream of variation (SoV) theory [19] which integrates multivariate statistics with control theory and design knowledge to enable prediction and diagnosis for dimensional variations in multi-stage manufacturing systems. SoV has been successfully applied to various types of multi-stage manufacturing processes including automotive body assembly [20] and multi-stage machining processes [19]. However, the theory is mainly proposed to be applied in centralized settings as it is not clear how the diagnostic reasoning process can be distributed across several equipment modules. In these statistical data-driven approaches the assembly process is usually considered to be a linear process, however in reality this ceases to exist as various assembly processes are in fact nonlinear such as welding thermal deformation, compliant deformation and contact interaction [21]. These nonlinearities render estimation-based approaches for diagnosis inaccurate. In addition to that other factors such as measurement inaccuracies, noise, incomplete data sets and relatively small data sets especially during the first phases of production make such manufacturing processes highly characterized by uncertainty [22]. This motivated the need for employing modelling and reasoning approaches that are capable of handling and reasoning under uncertainty.
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Other statistical approaches that were initially developed in the domain of probabilistic artificial intelligence such as Bayesian networks and Markov models came to use in order to respond to these uncertainty challenges. Bayesian networks are specifically good for representing probabilistic causal relations among random variables and hence allow dealing explicitly with domain uncertainty. Therefore; they have recently been used extensively to model multi-fault multi-symptom dependency relations as a mean for diagnostic modelling and reasoning in various domains with very promising results, for example in telecom networks [23] and electric power systems in aerospace applications [24] among many others. Bayesian networks have also been used for manufacturing monitoring and diagnosis. In [25] Bayesian networks are used for multi-stage machining process variation diagnosis and in [26] they are used for the diagnosis and monitoring of a multi-stage manufacturing process. In [22] they are used for assembly fixture fault diagnosis where the possibilities for learning Bayesian models from operational data were demonstrated. Bayesian methods are also used in [27] for learning causal relationships between product characteristics and process variables from extensive datasets in manufacturing process quality control, the resultant causal models are then used for process control. Although a lot of work has been reported in literature on the use of Bayesian models for diagnosis, all of these approaches are based on the classical notion of Bayesian networks where the whole model is constructed as a single central entity that captures all causal relationships in the system and hence making it particularly impractical to model large complex systems. In this paper we propose a novel component-based distributed approach for Bayesian diagnosis in modular systems using the notion of multi-agent Bayesian networks in order to allow the distribution of modelling efforts and the emergence of diagnostic capabilities when the integration of the modular manufacturing system takes place, this framework is described in some detail in the subsequent section.
We are proposing the use of Multiply Sectioned Bayesian Networks (MSBNs) as the modelling and reasoning framework to achieve that. MSBNs allow modelling local diagnostic submodels using Bayesian Networks in a multi-agent environment, where each submodel captures a limited part of the concerned domain or system and is encapsulated into an intelligent agent. These local Bayesian submodels are later integrated into a global representation structure through multi-agent communication that allows global system level reasoning and hence emergent system-level diagnostic capabilities. An overview of the proposed framework is shown in Fig. 1. In the next section, the theory behind the modelling framework will be briefly presented; a brief background about Bayesian networks is first given followed by some background material about Multiply Sectioned Bayesian Networks (MSBN).
3.1. Bayesian networks A Bayesian network is a directed acyclic graph where random variables are represented by nodes and the directed arcs connecting pairs of nodes represent the probabilistic causal dependency relationships between the random variables [28]. The node where the arc originates from is called the parent node and the one where the arc ends is called the child node. Each node in the network has a conditional probability table (CPT) that quantifies the dependency relationships between the node and all of its parent nodes. A Bayesian network could be defined as a tuple G, P, X where G is a directed acyclic graph (DAG) whose nodes represent a set of random variables X = {X1 , X2 ,. . ., Xn } and whose edges represent dependency relationships among the variables. The third component P = Pr (X1 | X ), . . . , Pr (Xn | X ) is a set of conditional
given as: 3. Distributed diagnosis framework The diagnostic framework proposed in this work is based on the assumption that modular manufacturing systems can be viewed as a collection of intelligent modules or subsystems. Our approach is to associate each of these modules with a local diagnostic model that is only concerned with that specific module. These component-based diagnostic submodels are to be developed by module suppliers independently of the wider system they will be deployed into. During the system integration phase, these local diagnostic submodels should then be integrated into a wider system-level global diagnostic model. This component-based framework puts emphasis on the modelling process which may suggest increased cost for the component supplier in terms of modelling effort. However, the gained benefit justifies this cost. The cost of modelling will be high at the component design phase, but high reductions in maintenance and system downtime costs will consequently be obtained as a result of applying these methods. Also using this component-based approach implies that the people who know the most about the specific component will be responsible of developing its diagnostic capabilities which means appropriate use and capture of the available knowledge compared to the approaches currently used where separate people are responsible of designing diagnostic capabilities for the whole system once it is operational. Moreover, the added modelling cost will only be added at the component supplier; therefore, the overall modelling cost per produced component will be very low compared to tailoring a specific diagnostic system for a complex system at the customer’s site.
n
1
probability tables (CPT) that quantify the dependency relationships between every node in G and its parents nodes where for every node Xi ∈ X one CPT exists that defines a conditional probability distribution Pr (Xi | X ). The joint probability distribution over X can be i
Pr (X) = Pr (X1 , . . . , Xn ) =
n
Pr (Xi |
i=1
Xi
)
The diagnostic process in Bayesian networks involves inferring the likelihood of the occurrence of an unobservable fault hypothesis based on the measured (observed) evidence (Symptoms). In other words inferring the probability of Xi being in a certain state, given the observed evidence E, which is expressed as Pr (Xi = x|E) where E = (y1 , . . ., ym ), yj being the observed state of the variable Yj and (Y1 , . . ., Ym ) ⊂ (X1 , . . ., Xn ). A very important and powerful characteristic of Bayesian networks is their ability of belief updating via bidirectional propagation of new evidences throughout the network. This allows for the conditional probability of each node to be updated as new evidences or observations become available. One can distinguish between two components of Bayesian diagnostic framework, the Bayesian model and the inference method. The Bayesian model represents the knowledge about the causal relationships that relate various errors to symptoms. These relationships can be elicited from human experts and available engineering knowledge about the system. The inference method is the algorithm used to infer error causes from observed symptoms. A big body of literature exists on building the two elements. However, very little work addresses Bayesian modelling and inference in multi-agent environments. A prominent approach for multi-agent Bayesian modelling and reasoning is Multiply Sectioned Bayesian Networks (MSBNs) [8] which will be presented in more detail.
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Fig. 1. Framework for distributed, component-based diagnosis.
3.2. Multiply Sectioned Bayesian Networks (MSBNs) Multiply Sectioned Bayesian Networks (MSBNs) is a knowledge representation formalism that extends conventional Bayesian networks to enable cooperative multi-agent probabilistic reasoning. It can be used to model a domain using a set of Bayesian subnets, each subnet representing a subset of the domain. The framework defines a number of constraints that need to be satisfied in order to ensure coherent distributed inference, which are presented in detail in [8], these constraints are [29]: i. All subnets must be organized in a hyper tree structure, which is defined as: Definition 1. Let G1 = (Ni , Ei )(i = 0, . . ., n − 1) define a set of n graphs, and let the graph G = Ui Gi be their union. If for every i and j, the set of nodes defined by Iij = Ni ∩ Nj spans identical subgraphs in both Gi and Gj , then G is sectioned and Iij is the separator between Gi and Gj . Definition 2. For a set of subgraphs Gi that section a connected graph G, if the set of Gi is organized as a connected tree H in which every node is a Gi and every link is a separator with the condition that for every i and j, the separator Iij is contained in each subgraph on the path between Gi and Gj on H. In this case we call H a hypertree over G, each node Gi a hypernode and each separator I a hyperlink. Gi s here represent the Bayesian subnets that correspond to individual agent internal knowledge representation, and the aim of this constrain is to ensure that no circular information passing takes place during multi-agent belief update, which extends the structural constraint of classical Bayesian networks.
Verification of this constraint requires cooperation of all agents in the graph through message passing over the hyper-tree according to the algorithm detailed in [30]. ii. A directed acyclic graph (DAG) must be used to represent each agent’s knowledge (subnets).This constraint is the same constraint for classical Bayesian networks which can be verified independently for each agent/subnet. iii. The set of variables shared by pairs of agents should form a d-sepset. This is to ensure that the shared interface between neighbouring agents allows sufficient information to be passed as necessary during belief updating (concise message passing). Definition. Let Gi = (Vi , Ei ) (i = 0, 1) be two DAGs such that G = G0 ∪ G1 is a DAG. A node x ∈ I = V0 ∩ V1 with its parents (x) in G is a d-sep node between G0 and G1 if either (x) ⊆ V0 or (x) ⊆ V1 . If every x ∈ I is a d-sepnode, then I is a d-sepset. Given a group of individual subnets that represent a common domain, in order to establish a MSBN that allows coherent distributed inference, a number of steps need to be followed, which can be generally described as: i. Through coordinated message passing among neighbouring agent, checking the graph consistency of neighbouring subnets. ii. Through coordinated message passing among agents, moralization of the subnets. iii. Triangulation of the moralized graph through message passing among the agents. iv. The construction of the linked junction forest from the triangulated graph. The resultant linked junction forest is the MSBN representation used for belief update and reasoning.
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M.S. Sayed, N. Lohse / Journal of Manufacturing Systems 32 (2013) 480–488 Table 1 Root nodes’ prior probabilities.
Fig. 2. A modular production station from HAS200.
4. MSBN-based monitoring and diagnosis case study MSBNs appear to be a very promising framework for monitoring and diagnosis in a multi-agent environment such as evolvable assembly systems for example. The monitored system can be modelled using a number of subnets each corresponding to an equipment component. The subnet will represent the local diagnostic knowledge of the autonomous agent monitoring the component. We will demonstrate the concept using a close-to-industry modular assembly system. 4.1. Diagnosing HAS-200 HAS200 is the system under consideration of which one station is shown in Fig. 2. It is a modular multi-station educational assembly system that constitutes three production stations, quality check stations, in addition to packaging and warehousing stations. It employs a distributed control strategy as every station is controlled through a dedicated local controller. The production stations fill a box with different types of materials to produce a variety of products depending on the weight ratios among material types in the final produced box. After the three process steps have finished the height of the final produced box is checked at the quality check station, and depending on pre-set height thresholds, the processed box is either accepted or rejected. When a box is rejected, it would be important to know the most probable cause for that. To allow such queries to be made, a diagnostic Bayesian network is built for every station describing error–symptom causal relationships along with prior probabilities. The different error symptoms that indicate the presence of an error are related to possible underlying causes using the notions of Bayesian networks. Symptoms and errors are all modelled using two state random variables that alternate between two states, present and not present. The prior probabilities of error are obtained from expert knowledge mainly based on the reliability information of the different system components, some details about the conditional probabilities in the model is given in Section 4.2. During run-time, observations are collected from across the system and are then used to update the prior probabilities of error in order to obtain the posterior probabilities of errors. Fig. 3 shows the overall Bayesian diagnostic model representing the three stations together. It relates the possible errors, namely, feeding errors, handling errors, measurement errors and material errors (box geometry in this case) to the possible observable error symptoms in the three stations. This global network is sectioned into three individual subnets, each of which will be assigned to an individual autonomous monitoring agent dedicated for one station only. This means that every agent will be observing a number of
Node
Pr(OK)
Pr(NOK)
Box Scale 1 Handling1 Feeder1 Scale2 Handling2 Feeder2 Scale3 Handling3 Feeder3
0.8 0.85 0.75 0.75 0.85 0.75 0.75 0.85 0.75 0.75
0.2 0.15 0.25 0.25 0.15 0.25 0.25 0.15 0.25 0.25
variables local to its station and will not be aware of any other variables within the scope of other agents. The sectioning into separate networks should be in a way that guarantees maximum possible decoupling among individual agents by minimizing the number of shared variables where possible. The shared variables will be the means or the interface through which neighbouring agents communicate with each other, while the local variables will be hidden and only used for internal reasoning within individual agents. The three first errors are local to the each individual station and hence they are represented with local variables within the network. On the other hand the box geometry error is considered to be a global error since it affects all of the three stations unlike the rest of the errors which are confined within the station; therefore, it is represented using a shared variable. Other shared variables are the local height measurement variables which affect the height measurements in the following station; therefore, a height variable is also shared between two consecutive stations.
4.2. Defining the model parameters (probabilities) Many approaches exist for obtaining the conditional probabilities that govern the dependency relationships among the variables; some are learning-driven while others are expert driven. Here in this example all modelling efforts are expert driven and hence the definition of probabilities is derived from domain knowledge and specialized knowledge about the system. This includes knowledge about the reliability of various components and the repeatability characteristics of the process steps. For the root causes (nodes with no parents) the prior probability is easy to obtain from engineering knowledge about the reliability of the equipment/process or from knowledge about frequency of fault and maintenance records. These are shown in Table 1. For the other nodes, one needs to specify conditional probability distributions of observations given the faults. It is not an easy task for experts to elicit this type of knowledge, and it is normally much easier to learn these parameters from a set of learning cases. The start will be by defining these probabilities from an expert point of view depending on the experience with the system faults, then during operation with when more data about the system becomes available these parameters can be refined using various Bayesian learning techniques. However, in this case we are only relying on expert knowledge. Below are the main conditional probability tables for the main nodes. These are T, Spillage, Feeding, Measure, Height1, and Height2 (which is identical to Height3). Noting that due to the fact that the overall network was constructed from smaller network fragments that reoccurred across the network, this will be utilized once more here when defining the probability distributions, as some causal relations do share the same underlying structure and hence share similar probability distributions (Tables 2–6).
M.S. Sayed, N. Lohse / Journal of Manufacturing Systems 32 (2013) 480–488
Feed1
T1
485
Station2
Measure11
Feed2
T2
Handle2
Spillage2
Measure21
Scale1
Scale2 Measure12
Handle1
Spillage1
Measure22 Box
Station1 Hight1
Hight2
Feed3
T3
Measure31 Scale3 Measure32
Handle3
Spillage3
Station3
Hight3
Fig. 3. 3-Station Bayesian diagnostic model for the HAS200 system.
Table 2 CPT for T and Spillage.
Table 5 CPT for Height1.
Feeding
Pr(T = x)
OK NOK Handling
X = OK
X = NOK
0.9 0.05
0.1 0.95
Pr(Spillage = x)
OK NOK
X = OK
X = NOK
0.9 0.05
0.1 0.95
OK OK NOK NOK
Feeder
OK OK NOK NOK
Box
OK OK OK OK NOK NOK NOK NOK
OK OK NOK NOK OK OK NOK NOK
OK NOK OK NOK OK NOK OK NOK
OK NOK OK NOK
Feeding3
Pr(Feeding = x) X = OK
X = NOK
1 0 0.5 0
0 1 0.5 1
Table 4 CPT for Measure2. Scale2
Handling1
Pr(Height1 = x) X = OK
X = NOK
1 0.3 0.3 0.1 0.3 0.01 0.01 0
0 0.7 0.7 0.9 0.7 0.99 0.99 1
Table 6 CPT for Height3.
Table 3 CPT for Feeding. Measure
Feeding
Box
OK NOK OK NOK
Pr(Measure2 = x) X = OK
X = NOK
0.75 0.75 0 0
0.25 0.25 1 1
4.3. Model verification Once the component-based subnets for individual agents have been constructed, they should then be verified for MSBNconsistency, i.e. checking that MSBN constraints are satisfied to guarantee efficient distributed inference.
OK OK OK OK OK OK OK OK NOK NOK NOK NOK NOK NOK NOK NOK
Handling3
OK OK OK OK NOK NOK NOK NOK OK OK OK OK NOK NOK NOK NOK
Box
OK OK NOK NOK OK OK NOK NOK OK OK NOK NOK OK OK NOK NOK
Height2
OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK
Pr(Height3 = x) X = OK
X = NOK
1 0.01 0.8 0.01 0.2 0.01 0.2 0 0.2 0.01 0.1 0 0.01 0 0.01 0
0 0.99 0.2 0.99 0.8 0.99 0.8 1 0.8 0.99 0.9 1 0.99 1 0.99 1
The constraints presented in Section 3 are firstly verified locally within each agent and then verified for the whole system through message passing among agents. This cooperative verification makes use only of the public variables shared among neighbouring subnets. This is a very important feature, as it allows the global verification to take place without the need for detailed knowledge
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Fig. 4. Agent Station1 model compilation, (a) Bayesian subnet, (b) moral sub-graph, (c) chordal sub-graph and (d) junction tree.
about the internal structure of individual subnets. This feature makes the verification of individually developed subnets easy to perform and more importantly it accommodates for knowledge protection for component suppliers who might be unwilling to share proprietary knowledge about the internal functionalities of their components. Certainly this entails the need for special care to be taken during the construction of individual subnets in terms of selecting shared variables that each agent makes accessible to the neighbouring agents. Constraint (iii) in Section 3.2 implies that variables of each individual subnet are conditionally independent of those of other subnets given the d-sepset. This entails that when designing modular subnets for equipment modules, this assumption should always be considered to ensure that any root cause within one module is conditionally independent of the variables in other modules given the d-sepset. The model verification process here and all the subsequent steps for model compilation and inference are carried out using the software toolkit WEBWEAVR IV [31] which provides tools for multi-agent probabilistic modelling and inference.
4.4. Model compilation Once the individual subnets have been built and cooperatively verified for MSBN consistency, they should then be compiled into a runtime secondary representation to allow efficient and coherent unified reasoning and inference. This compilation involves three steps: • First, each subnet is independently moralized by connecting parents of each node together and dropping link directions. Then through message passing, neighbouring moral subnets are checked for consistency on the shared nodes. • Next step is triangulation on the moral subnets, where each subnet is locally converted into a chordal graph so that the set of consistent chordal sub-graphs defines the super-graph of the union of the set of sub-graphs. A chordal graph is defined by having at least one perfect elimination sequence.
• The set of chordal graphs is then converted into a corresponding set of junction trees. Moreover, a junction tree is established for each d-sepset between two sub-graphs, these junction trees are known as linkage trees. The conversion of sub-graphs into junction trees is to allow effective inference using message passing algorithms [32] and the linkage trees are to ensure concise message passing among agents through beliefs on d-sepsets.
The resultant representation for the whole system is called linked junction forest which is then used for online MSBN inference. The online reasoning is performed on the linked junction forest as each agent uses a junction tree for its internal representation and the associated linkage trees for communicating with the neighbouring agents on the hypertree structure. Fig. 4 shows the model compilation steps on the agent representing station1. To explain the need for multi-agent communication during the belief update process we will consider a case from this illustrative example. We can see that as every agent only has access to the states of the local variables in the station, it cannot always make appropriate belief updates on the local variables without communicating with neighbouring agents. For example in Station 3, assume the local variables are observed to confirm the absence of any errors within the station, i.e. both feeding and handling variables are observed and known to be error-free or in OK state. Assuming that Measurement variable is not directly observable in Station 3, Station 3 agent will not be able to update the state of Measurement variable. To do so it needs to communicate with the previous station in the line to update its belief on the previous height measurement and accordingly update its belief about the state of its measurement process. So assuming the final quality check rejected the box due to height being unacceptable, then Station 3 agent will update its belief on the state of its measuring device depending on the belief of Station 2 about the height in Station 2. Neighbouring agents propagate their belief on the shared variables along the hypertree by responding to belief update requests. After the communication takes place, all agents’ beliefs will be consistent with all observations accumulated across the system.
Table 7 Observations and the resulting most probable cause using the global BN. Observations
Most probable cause
Height3
Spillage1
Spillage2
Spillage3
T1
T2
T3
NOK NOK NOK
OK OK Unknown
OK OK OK
OK OK OK
OK Unknown Unknown
OK OK OK
OK OK OK
Box Feeder1 Handling1
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Table 8 Observations and the resulting most probable cause using the distributed BN. Observations
Most probable cause
Height3
Spillage1
Spillage2
Spillage3
T1
T2
T3
NOK NOK NOK
OK OK Unknown
OK OK OK
OK OK OK
OK Unknown Unknown
OK OK OK
OK OK OK
For performance evaluation purposes both the global Bayesian network and the distributed network were used for diagnostic reasoning with injected faults and three different sets of observations. In both cases the observed fault was final product height out of range (Height3 = NOK). Then different combinations of observations were used through setting and un-setting the states of the possible observable variables as shown in Table 7 for the global BN and in Table 8 for the distributed BN. Then through belief updating, the probabilities of each of the equipment variables being faulty (NOK) were estimated to identify the most probable cause that explains each set of observations. The resulting causes are shown in the right-most column in Table 7 for centralized belief update (global BN) and in Table 8 for cooperative belief update (distributed BN). From both tables one can see that the same fault cause was identified using both approaches in each of the three cases, which suggests that the distributed reasoning framework achieves similar fault detection accuracy as the global network. In terms of computation requirements, the results from both approaches were obtained on a 3 GHz dual core PC with 3 GB of memory and running Ubuntu® operating system.
5. Conclusions In this paper the need for new modular component-based diagnosis frameworks for modular manufacturing systems was explained along with the associated challenges. To respond to these challenges, the use of multi-agent Bayesian approaches as a distributed diagnostic framework was suggested. We successfully demonstrated how MSBNs can be used to model a diagnostic system for a lab-based modular assembly system. MSBNs allow distributed autonomous and collaborative inference. Moreover, the processes of model verification, model compilation and inference are carried out while protecting agents’ privacy. We have used the Java-based software toolkit WEBWEAVR IV to implement the component-based diagnostic system and to demonstrate the process of distributed modelling, multi-agent model verification, multi-agent model compilation and belief update for consistent system level inference. It is the first time that MSBN approach was used for manufacturing system diagnosis purposes. The initial results suggest that the method is capable of providing a framework for distributed component-based modelling and inference with comparable performance to classical Bayesian networks in terms of detection accuracy. Although in this example the suggested approach for obtaining the model parameters was entirely expert driven, however, possibilities for learning these parameters from data should also be considered. The fact that the global model is made of smaller network fragments that are expected to be designed and owned by component suppliers makes it even more interesting to explore Bayesian learning possibilities as extensive operational datasets will be available from the operation of these equipment modules within various settings. Follow up work will be focused on the performance evaluation of the proposed method in terms of accuracy of detection and computation efficiency to allow more understanding of the advantages and limitations of the method. It is also important to further investigate systematic approaches for sub-model generation with specific focus on
Box Feeder1 Handling1
advising procedures and design rules to ensure model modularity. Acknowledgement The reported work is partially funded by the European Commission as part of the CP-FP 246083-2 IDEAS project. The support is gratefully acknowledged. References [1] ElMaraghy H. Flexible and reconfigurable manufacturing systems paradigms. International Journal of Flexible Manufacturing Systems 2005;17(4):261–76. [2] Koren Y, Heisel U, Jovane F, Moriwaki T, Pritschow G, Ulsoy G, et al. Reconfigurable manufacturing systems. CIRP Annals – Manufacturing Technology 1999;48(2):527–40. [3] Valckenaers P, Van Brussel H, Bongaerts L, Wyns J. Holonic manufacturing systems. Integrated Computer-Aided Engineering 1997;4(3):191–201. [4] Onori M. Evolvable assembly systems—a new paradigm? Proceedings of the 33rd international symposium on robotics (ISR). 2002. [5] Mendelbaum G, Mizuno R. Directions in maintenance. Maintenance Technology Magazine 1992:45–8. [6] Wu S, Gebraeel N, Lawley MA, Yih Y. A neural network integrated decision support system for condition-based optimal predictive maintenance policy. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 2007;37(2):226–36. [7] Ribeiro L, Barata J. Re-thinking diagnosis for future automation systems: an analysis of current diagnostic practices and their applicability in emerging IT based production paradigms. Computers in Industry 2011;62(7):639–59. [8] Xiang Y. Probabilistic reasoning in multiagent systems: a graphical models approach. New York, USA: Cambridge Univ. Press; 2002. [9] Pavlin G, De Oude P, Maris M, Nunnink J, Hood T. A multi-agent systems approach to distributed Bayesian information fusion. Information Fusion 2010;11(3):267–82. [10] Holloway LE, Chand S. Time templates for discrete event fault monitoring in manufacturing systems. In: American control conference. 1994. p. 701–6. [11] Balduzzi F, Di Febbraro A. Combining fault detection and process optimization in manufacturing systems using first-order hybrid Petri nets. In: IEEE international conference on robotics and automation, 2001. Proceedings 2001 – ICRA, vol. 1. 2001. p. 40–5. [12] Bae YH, Lee SH, Kim HC, Lee BR, Jang J, Lee J. A real-time intelligent multiple fault diagnostic system. International Journal of Advanced Manufacturing Technology 2006;29(5):590–7. [13] Tzafestas S. Concerning automated assembly: knowledge-based issues and a fuzzy system for assembly under uncertainty. Computer Integrated Manufacturing Systems 1997;10(3):183–92. [14] McNaught K, Chan A. Bayesian networks in manufacturing. Journal of Manufacturing Technology Management 2011;22(6):734–47. [15] Monostori L, Prohaszka J. A step towards intelligent manufacturing: modelling and monitoring of manufacturing processes through artificial neural networks. CIRP Annals – Manufacturing Technology 1993;42(1):485–8. [16] Hou TH, Liu WL, Lin L. Intelligent remote monitoring and diagnosis of manufacturing processes using an integrated approach of neural networks and rough sets. Journal of Intelligent Manufacturing 2003;14(2):239–53. [17] Hu SJ, Wu S. Identifying sources of variation in automobile body assembly using principal component analysis. Transactions of NAMRI/SME 1992;20:311–6. [18] Shi J, Ceglarek D. Fixture failure diagnosis for autobody assembly using pattern recognition. Journal of Engineering for Industry 1996;118:55. [19] Shi J. Stream of variation modeling and analysis for multistage manufacturing processes, vol. 10. Boca Raton, FL: CRC; 2006. [20] Hu SJ, Koren Y. Stream-of-variation theory for automotive body assembly. CIRP Annals – Manufacturing Technology 1997;46(1):1–6. [21] Xie K, Wells L, Camelio JA, Youn BD. Variation propagation analysis on compliant assemblies considering contact interaction. Journal of Manufacturing Science and Engineering 2007;129:934. [22] Liu Y, Jin S. BN approach for dimensional variation diagnosis in assembly process. In: 2009 International workshop on intelligent systems and applications. 2009. p. 1–5. [23] Khanafer RM, Solana B, Triola J, Barco R, Moltsen L, Altman Z, et al. Automated diagnosis for UMTS networks using bayesian network approach. IEEE Transactions on Vehicular Technology 2008;57(4):2451–61.
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[24] Mengshoel OJ, Chavira M, Cascio K, Darwiche A, Poll S, Uckun S. Probabilistic model-based diagnosis: an electrical power system case study. IEEE Transactions on Systems, Man, and Cybernetics – Part A: Systems and Humans 2010;40(5):874–85. [25] Dey S, Stori J. A Bayesian network approach to root cause diagnosis of process variations. International Journal of Machine Tools and Manufacture 2005;45(1):75–91. [26] Wolbrecht E, D‘Ambrosio B, Paasch R, Kirby D. Monitoring and diagnosis of a multistage manufacturing process using Bayesian networks. Ai Edam 2000;14(01). [27] Li J, Shi J. Knowledge discovery from observational data for process control using causal Bayesian networks. IIE Transactions 2007;39(6):681–90. [28] Pearl J. Probabilistic reasoning in intelligent systems: networks of plausible inference. San Francisco: Morgan Kaufmann; 1988. [29] Xiang Y, Geng H. Distributed monitoring and diagnosis with multiply sectioned Bayesian networks. In: AAAI spring symposium on AI in equipment service maintenance and support. 1999. [30] Xiang Y. Verification of DAG structures in cooperative belief network-based multiagent systems. Networks 1998;31(3):183–91. [31] Xiang Y. WebWeavr-IV Research Toolkit. www.cis.uoguelph.ca/∼yxiang/ww3/
[32] Jensen FV, Nielsen TD. Bayesian networks and decision graphs. New York: Springer Verlag; 2007. Mohamed Samir Sayed is a Nottingham’s Dean of Engineering Doctoral Research Scholar; he is currently doing his PhD at the University of Nottingham focusing on manufacturing systems diagnosis. He holds MSc in Electronic Communications Engineering from The University of Nottingham, UK and BSc (Hon) in Electrical Engineering from The University of Khartoum, Sudan. Dr. Niels Lohse is a lecturer of advanced manufacturing technology at the University of Nottingham. He graduated with a Diplom-Engineer degree in Mechanical Engineering from the University of Applied Science Hamburg, Germany in 2000. Dr Lohse obtained his MSc in Technology Management from the University of Portsmouth in 2001 and received his PhD in Manufacturing Engineering and Operations Management from the University of Nottingham in 2006. His research is focused on intelligent automation including manufacturing system modelling, distributed control, diagnostics and design decision-support with a primary focus on modular and evolvable production systems and applications of artificial intelligence techniques in manufacturing.
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Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys
Technical paper
Distributed Bayesian diagnosis for modular assembly systems—A case study Mohamed Samir Sayed ∗ , Niels Lohse Manufacturing Division, The University of Nottingham, Nottingham NG7 2RD, UK
a r t i c l e
i n f o
Article history: Received 16 September 2012 Received in revised form 11 February 2013 Accepted 4 March 2013 Available online 1 May 2013 Keywords: Assembly Modular design Bayesian networks Error diagnosis Multi-agent systems
a b s t r a c t The growing interest in modular and distributed approaches for the design and control of intelligent manufacturing systems gives rise to new challenges. One of the major challenges that have not yet been well addressed is monitoring and diagnosis in distributed manufacturing systems. In this paper we propose the use of a multi-agent Bayesian framework known as Multiply Sectioned Bayesian Networks (MSBNs) as the basis for multi-agent distributed diagnosis in modular assembly systems. We use a closeto-industry case study to demonstrate how MSBNs can be used to build component-based Bayesian sub-models, how to verify the resultant models, and how to compile the multi-agent models into runtime structures to allow consistent multi-agent belief update and inference. © 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction New market conditions imply that manufacturing systems today need to be more flexible and responsive to enable quicker response to the changes in the market and the introduction of new products and product designs while being robust in the face of disturbances and unexpected failures [1]. To respond to these new challenges, new paradigms for the design and control of manufacturing systems have been proposed within the last two decades, the main drive being towards decentralized/distributed control combined with tendency to modular component-oriented system design approaches. The most notable of these paradigms being reconfigurable manufacturing systems [2], Holonic manufacturing systems [3] and more recently evolvable production systems [4]. 1.1. The need for modular diagnosis One of the main features that need to be properly addressed in order to realize the vision for robust modular manufacturing systems is the ability to diagnose faults quickly and hence allowing quicker recovery times and less down time and stoppage costs. The ability to monitor the system during the operation means the ability of the control system to adapt to changes and unexpected behaviour and hence resulting in more reliable systems. It has been reported that during a production system downtime, repairing the cause of the error does take a small fraction of the downtime. It is
∗ Corresponding author. Tel.: +441159513875. E-mail addresses: [email protected] (M.S. Sayed), [email protected] (N. Lohse).
locating the source of the problem (i.e. diagnosis) that is responsible for the majority of downtime [5]. The difficulty in identifying causes of errors becomes even more relevant in complex production systems. Another recent drive for diagnosis and prognosis efforts has been the growing interest in building integrated frameworks for condition-based maintenance management in industrial organizations where diagnosis and prognosis models are used for the optimal planning and scheduling of maintenance activities [6]. Most of the available work on diagnosis is designed for centralized systems. Hence there is a need for new decentralized methods to address monitoring and diagnosis in modular, component-based physical systems. The drive towards component-based systems design, in fact brings new opportunities for more efficient affordable monitoring and diagnosis systems because specific component suppliers should then be able to design the monitoring and diagnosis models for their component as an integral part of the component design effort. Consequently, the diagnostic design effort, which represents the main obstacle in designing large scale diagnostic systems, will be distributed among specialized component suppliers allowing the people who know the most about each component to design its diagnostic sub-system. In order for this vision to be realized there is a crucial need for an underlying framework or that allows independently developed diagnostic sub-systems to be integrated into a wider diagnosis system once the concerned physical system is built from its modular components. Since the use of multi-agent systems is becoming more prominent in the control of modular manufacturing systems (for example, evolvable production systems and Holonic manufacturing systems), it becomes very attractive option to embody the monitoring and diagnosis functionalities into the paradigm
0278-6125/$ – see front matter © 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmsy.2013.03.001
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of multi-agent systems for manufacturing control. However, the decentralized nature of these modular systems introduce new challenges from a diagnostic point of view, mainly due to the dynamic nature of these systems where modules are expected to be rapidly added and removed from the system. This makes the use of classical centralized approaches to diagnosis impractical due to the difficulty of foreseeing all possible system modules and their potential configurations and interactions beforehand and capturing that in one global model. Other new challenges relate to communicating observations across the system and the need to systematically orchestrate that while responding to issues of fault propagation across various modules [7]. Various approaches do exist for centralized fault diagnosis in industrial systems depending on the types of faults to be diagnosed. One prominent approach that has been studied in various domains including fault diagnosis recently is Bayesian networks with promising results. However, all of the work on industrial diagnosis using Bayesian networks has been applied in a centralized manner using the classical notion of single Bayesian network. A growing research interest has been directed to develop new approaches that would extend the use of Bayesian networks knowledge representation and inference techniques with their proven merits into multi-agent systems. A few notable works have been reported in literature suggesting new approaches to achieve this goal [8,9]. It is our belief that there exists a unique opportunity to extend these new research endeavours into the field of monitoring and diagnosis of modular manufacturing systems in order to materialize the vision of component-based monitoring and diagnosis systems for modular manufacturing systems. This paper reports on our recent work in using multi-agent Bayesian reasoning for the problem of multi-station assembly systems diagnosis. The rest of this paper is organized as follows: Section 2 gives a background review on the state of the art in manufacturing diagnosis. In Section 3 the proposed distributed diagnosis framework is described and some relevant background on Bayesian networks and MSBNs is given. Section 4 describes our case study that is used to demonstrate the proposed approach, and finally Section 5 finishes with some concluding remarks.
2. Diagnosis in manufacturing Many attempts have been devised to provide fault diagnosis capabilities for manufacturing systems. Some of these approaches have been applied on specific devices or production units while others have been applied on the scale of the entire production system. The diagnostic approaches used in each work vary depending on the researchers’ background and the problem context they are tackling. Hence different approaches originating from different domains have been proposed and applied. This includes approaches such as model based reasoning, case based reasoning, artificial neural networks, probabilistic reasoning, fuzzy logic, induction trees as well as data-driven methods in addition to many hybrid approaches that combine different approaches. The majority of the work that has been carried out in manufacturing diagnosis has been aimed at specific individual components within a production facility due to the relative simplicity and focus of the problem. However, considerable other work has also been aimed at addressing the problem of fault diagnosis in the production system as a whole through providing system-level diagnostic capabilities. As different components with different attributes and characteristics need to be diagnosed in this case, the diagnostic process becomes far more complex than in the case of single component. New issues arise in this case when considering the diagnosis of a complex system as a whole, some of these issues relate to factors such as fault propagation from one component into another, fault
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interactions and faults accumulations across various stages in the system [7]. Discrete event systems (DES) have been used in [10] for fault diagnosis on the manufacturing system level through the use of time templates as an improvement to the conventional discrete event systems models. In [11] a DES approach is used for combining diagnosis and process optimization in a multi-stage manufacturing process. Despite their theoretical soundness, however, DES-based approaches do suffer from major limitations when applied to complex systems due to state explosion and the need for accurate detailed modelling which is not always feasible for manufacturing systems [7]. On the other hand, data driven approaches with little modelling requirements have also been investigated. The initial modelling effort required here is comparatively less than that of DES-based approaches where the nominal behaviour of the system normally needs to be captured. These include artificial neural networks [12], fuzzy logic [13] and Bayesian networks [14] among others. The models here do not necessarily capture precise nominal system behaviour as in DES-based approaches, rather a general understanding of how the system works, and the types of expected faults and associated symptoms can be used to obtain a basic diagnostic model. Artificial neural networks (ANN) have been used by Monostori [15] for the monitoring of machining processes, where back propagation networks were used for state estimation of machine tools. In [16] an integrated method is proposed for using ANNs for diagnosis and monitoring of manufacturing systems with focus on product defects where ANNs are integrated with a rough set approach to allow the extraction of causal relationships between product defects and the associated process parameters. Although ANNs have proven to yield some promising results, however these approaches were not widely adopted due to the need for large training sets and the fact that it is not possible to understand how the diagnostic decision is reached from the model [7]. Another research avenue that was pursued is the use of statistical and probabilistic models. Various statistical approaches have been used to tackle diagnostic problems focusing on dimensional variation source and root cause identification in assembly and multi-stage manufacturing systems. Among these are pattern matching techniques such as principal component analysis (PCA) which was used in [17] for the identification of automotive assembly variation sources. This PCA method was then further developed into a diagnostic methodology assuming the availability of large measurement data and structured noise in [18]. Another major approach for manufacturing systems diagnosis that has gained considerable interest is the stream of variation (SoV) theory [19] which integrates multivariate statistics with control theory and design knowledge to enable prediction and diagnosis for dimensional variations in multi-stage manufacturing systems. SoV has been successfully applied to various types of multi-stage manufacturing processes including automotive body assembly [20] and multi-stage machining processes [19]. However, the theory is mainly proposed to be applied in centralized settings as it is not clear how the diagnostic reasoning process can be distributed across several equipment modules. In these statistical data-driven approaches the assembly process is usually considered to be a linear process, however in reality this ceases to exist as various assembly processes are in fact nonlinear such as welding thermal deformation, compliant deformation and contact interaction [21]. These nonlinearities render estimation-based approaches for diagnosis inaccurate. In addition to that other factors such as measurement inaccuracies, noise, incomplete data sets and relatively small data sets especially during the first phases of production make such manufacturing processes highly characterized by uncertainty [22]. This motivated the need for employing modelling and reasoning approaches that are capable of handling and reasoning under uncertainty.
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Other statistical approaches that were initially developed in the domain of probabilistic artificial intelligence such as Bayesian networks and Markov models came to use in order to respond to these uncertainty challenges. Bayesian networks are specifically good for representing probabilistic causal relations among random variables and hence allow dealing explicitly with domain uncertainty. Therefore; they have recently been used extensively to model multi-fault multi-symptom dependency relations as a mean for diagnostic modelling and reasoning in various domains with very promising results, for example in telecom networks [23] and electric power systems in aerospace applications [24] among many others. Bayesian networks have also been used for manufacturing monitoring and diagnosis. In [25] Bayesian networks are used for multi-stage machining process variation diagnosis and in [26] they are used for the diagnosis and monitoring of a multi-stage manufacturing process. In [22] they are used for assembly fixture fault diagnosis where the possibilities for learning Bayesian models from operational data were demonstrated. Bayesian methods are also used in [27] for learning causal relationships between product characteristics and process variables from extensive datasets in manufacturing process quality control, the resultant causal models are then used for process control. Although a lot of work has been reported in literature on the use of Bayesian models for diagnosis, all of these approaches are based on the classical notion of Bayesian networks where the whole model is constructed as a single central entity that captures all causal relationships in the system and hence making it particularly impractical to model large complex systems. In this paper we propose a novel component-based distributed approach for Bayesian diagnosis in modular systems using the notion of multi-agent Bayesian networks in order to allow the distribution of modelling efforts and the emergence of diagnostic capabilities when the integration of the modular manufacturing system takes place, this framework is described in some detail in the subsequent section.
We are proposing the use of Multiply Sectioned Bayesian Networks (MSBNs) as the modelling and reasoning framework to achieve that. MSBNs allow modelling local diagnostic submodels using Bayesian Networks in a multi-agent environment, where each submodel captures a limited part of the concerned domain or system and is encapsulated into an intelligent agent. These local Bayesian submodels are later integrated into a global representation structure through multi-agent communication that allows global system level reasoning and hence emergent system-level diagnostic capabilities. An overview of the proposed framework is shown in Fig. 1. In the next section, the theory behind the modelling framework will be briefly presented; a brief background about Bayesian networks is first given followed by some background material about Multiply Sectioned Bayesian Networks (MSBN).
3.1. Bayesian networks A Bayesian network is a directed acyclic graph where random variables are represented by nodes and the directed arcs connecting pairs of nodes represent the probabilistic causal dependency relationships between the random variables [28]. The node where the arc originates from is called the parent node and the one where the arc ends is called the child node. Each node in the network has a conditional probability table (CPT) that quantifies the dependency relationships between the node and all of its parent nodes. A Bayesian network could be defined as a tuple G, P, X where G is a directed acyclic graph (DAG) whose nodes represent a set of random variables X = {X1 , X2 ,. . ., Xn } and whose edges represent dependency relationships among the variables. The third component P = Pr (X1 | X ), . . . , Pr (Xn | X ) is a set of conditional
given as: 3. Distributed diagnosis framework The diagnostic framework proposed in this work is based on the assumption that modular manufacturing systems can be viewed as a collection of intelligent modules or subsystems. Our approach is to associate each of these modules with a local diagnostic model that is only concerned with that specific module. These component-based diagnostic submodels are to be developed by module suppliers independently of the wider system they will be deployed into. During the system integration phase, these local diagnostic submodels should then be integrated into a wider system-level global diagnostic model. This component-based framework puts emphasis on the modelling process which may suggest increased cost for the component supplier in terms of modelling effort. However, the gained benefit justifies this cost. The cost of modelling will be high at the component design phase, but high reductions in maintenance and system downtime costs will consequently be obtained as a result of applying these methods. Also using this component-based approach implies that the people who know the most about the specific component will be responsible of developing its diagnostic capabilities which means appropriate use and capture of the available knowledge compared to the approaches currently used where separate people are responsible of designing diagnostic capabilities for the whole system once it is operational. Moreover, the added modelling cost will only be added at the component supplier; therefore, the overall modelling cost per produced component will be very low compared to tailoring a specific diagnostic system for a complex system at the customer’s site.
n
1
probability tables (CPT) that quantify the dependency relationships between every node in G and its parents nodes where for every node Xi ∈ X one CPT exists that defines a conditional probability distribution Pr (Xi | X ). The joint probability distribution over X can be i
Pr (X) = Pr (X1 , . . . , Xn ) =
n
Pr (Xi |
i=1
Xi
)
The diagnostic process in Bayesian networks involves inferring the likelihood of the occurrence of an unobservable fault hypothesis based on the measured (observed) evidence (Symptoms). In other words inferring the probability of Xi being in a certain state, given the observed evidence E, which is expressed as Pr (Xi = x|E) where E = (y1 , . . ., ym ), yj being the observed state of the variable Yj and (Y1 , . . ., Ym ) ⊂ (X1 , . . ., Xn ). A very important and powerful characteristic of Bayesian networks is their ability of belief updating via bidirectional propagation of new evidences throughout the network. This allows for the conditional probability of each node to be updated as new evidences or observations become available. One can distinguish between two components of Bayesian diagnostic framework, the Bayesian model and the inference method. The Bayesian model represents the knowledge about the causal relationships that relate various errors to symptoms. These relationships can be elicited from human experts and available engineering knowledge about the system. The inference method is the algorithm used to infer error causes from observed symptoms. A big body of literature exists on building the two elements. However, very little work addresses Bayesian modelling and inference in multi-agent environments. A prominent approach for multi-agent Bayesian modelling and reasoning is Multiply Sectioned Bayesian Networks (MSBNs) [8] which will be presented in more detail.
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Fig. 1. Framework for distributed, component-based diagnosis.
3.2. Multiply Sectioned Bayesian Networks (MSBNs) Multiply Sectioned Bayesian Networks (MSBNs) is a knowledge representation formalism that extends conventional Bayesian networks to enable cooperative multi-agent probabilistic reasoning. It can be used to model a domain using a set of Bayesian subnets, each subnet representing a subset of the domain. The framework defines a number of constraints that need to be satisfied in order to ensure coherent distributed inference, which are presented in detail in [8], these constraints are [29]: i. All subnets must be organized in a hyper tree structure, which is defined as: Definition 1. Let G1 = (Ni , Ei )(i = 0, . . ., n − 1) define a set of n graphs, and let the graph G = Ui Gi be their union. If for every i and j, the set of nodes defined by Iij = Ni ∩ Nj spans identical subgraphs in both Gi and Gj , then G is sectioned and Iij is the separator between Gi and Gj . Definition 2. For a set of subgraphs Gi that section a connected graph G, if the set of Gi is organized as a connected tree H in which every node is a Gi and every link is a separator with the condition that for every i and j, the separator Iij is contained in each subgraph on the path between Gi and Gj on H. In this case we call H a hypertree over G, each node Gi a hypernode and each separator I a hyperlink. Gi s here represent the Bayesian subnets that correspond to individual agent internal knowledge representation, and the aim of this constrain is to ensure that no circular information passing takes place during multi-agent belief update, which extends the structural constraint of classical Bayesian networks.
Verification of this constraint requires cooperation of all agents in the graph through message passing over the hyper-tree according to the algorithm detailed in [30]. ii. A directed acyclic graph (DAG) must be used to represent each agent’s knowledge (subnets).This constraint is the same constraint for classical Bayesian networks which can be verified independently for each agent/subnet. iii. The set of variables shared by pairs of agents should form a d-sepset. This is to ensure that the shared interface between neighbouring agents allows sufficient information to be passed as necessary during belief updating (concise message passing). Definition. Let Gi = (Vi , Ei ) (i = 0, 1) be two DAGs such that G = G0 ∪ G1 is a DAG. A node x ∈ I = V0 ∩ V1 with its parents (x) in G is a d-sep node between G0 and G1 if either (x) ⊆ V0 or (x) ⊆ V1 . If every x ∈ I is a d-sepnode, then I is a d-sepset. Given a group of individual subnets that represent a common domain, in order to establish a MSBN that allows coherent distributed inference, a number of steps need to be followed, which can be generally described as: i. Through coordinated message passing among neighbouring agent, checking the graph consistency of neighbouring subnets. ii. Through coordinated message passing among agents, moralization of the subnets. iii. Triangulation of the moralized graph through message passing among the agents. iv. The construction of the linked junction forest from the triangulated graph. The resultant linked junction forest is the MSBN representation used for belief update and reasoning.
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M.S. Sayed, N. Lohse / Journal of Manufacturing Systems 32 (2013) 480–488 Table 1 Root nodes’ prior probabilities.
Fig. 2. A modular production station from HAS200.
4. MSBN-based monitoring and diagnosis case study MSBNs appear to be a very promising framework for monitoring and diagnosis in a multi-agent environment such as evolvable assembly systems for example. The monitored system can be modelled using a number of subnets each corresponding to an equipment component. The subnet will represent the local diagnostic knowledge of the autonomous agent monitoring the component. We will demonstrate the concept using a close-to-industry modular assembly system. 4.1. Diagnosing HAS-200 HAS200 is the system under consideration of which one station is shown in Fig. 2. It is a modular multi-station educational assembly system that constitutes three production stations, quality check stations, in addition to packaging and warehousing stations. It employs a distributed control strategy as every station is controlled through a dedicated local controller. The production stations fill a box with different types of materials to produce a variety of products depending on the weight ratios among material types in the final produced box. After the three process steps have finished the height of the final produced box is checked at the quality check station, and depending on pre-set height thresholds, the processed box is either accepted or rejected. When a box is rejected, it would be important to know the most probable cause for that. To allow such queries to be made, a diagnostic Bayesian network is built for every station describing error–symptom causal relationships along with prior probabilities. The different error symptoms that indicate the presence of an error are related to possible underlying causes using the notions of Bayesian networks. Symptoms and errors are all modelled using two state random variables that alternate between two states, present and not present. The prior probabilities of error are obtained from expert knowledge mainly based on the reliability information of the different system components, some details about the conditional probabilities in the model is given in Section 4.2. During run-time, observations are collected from across the system and are then used to update the prior probabilities of error in order to obtain the posterior probabilities of errors. Fig. 3 shows the overall Bayesian diagnostic model representing the three stations together. It relates the possible errors, namely, feeding errors, handling errors, measurement errors and material errors (box geometry in this case) to the possible observable error symptoms in the three stations. This global network is sectioned into three individual subnets, each of which will be assigned to an individual autonomous monitoring agent dedicated for one station only. This means that every agent will be observing a number of
Node
Pr(OK)
Pr(NOK)
Box Scale 1 Handling1 Feeder1 Scale2 Handling2 Feeder2 Scale3 Handling3 Feeder3
0.8 0.85 0.75 0.75 0.85 0.75 0.75 0.85 0.75 0.75
0.2 0.15 0.25 0.25 0.15 0.25 0.25 0.15 0.25 0.25
variables local to its station and will not be aware of any other variables within the scope of other agents. The sectioning into separate networks should be in a way that guarantees maximum possible decoupling among individual agents by minimizing the number of shared variables where possible. The shared variables will be the means or the interface through which neighbouring agents communicate with each other, while the local variables will be hidden and only used for internal reasoning within individual agents. The three first errors are local to the each individual station and hence they are represented with local variables within the network. On the other hand the box geometry error is considered to be a global error since it affects all of the three stations unlike the rest of the errors which are confined within the station; therefore, it is represented using a shared variable. Other shared variables are the local height measurement variables which affect the height measurements in the following station; therefore, a height variable is also shared between two consecutive stations.
4.2. Defining the model parameters (probabilities) Many approaches exist for obtaining the conditional probabilities that govern the dependency relationships among the variables; some are learning-driven while others are expert driven. Here in this example all modelling efforts are expert driven and hence the definition of probabilities is derived from domain knowledge and specialized knowledge about the system. This includes knowledge about the reliability of various components and the repeatability characteristics of the process steps. For the root causes (nodes with no parents) the prior probability is easy to obtain from engineering knowledge about the reliability of the equipment/process or from knowledge about frequency of fault and maintenance records. These are shown in Table 1. For the other nodes, one needs to specify conditional probability distributions of observations given the faults. It is not an easy task for experts to elicit this type of knowledge, and it is normally much easier to learn these parameters from a set of learning cases. The start will be by defining these probabilities from an expert point of view depending on the experience with the system faults, then during operation with when more data about the system becomes available these parameters can be refined using various Bayesian learning techniques. However, in this case we are only relying on expert knowledge. Below are the main conditional probability tables for the main nodes. These are T, Spillage, Feeding, Measure, Height1, and Height2 (which is identical to Height3). Noting that due to the fact that the overall network was constructed from smaller network fragments that reoccurred across the network, this will be utilized once more here when defining the probability distributions, as some causal relations do share the same underlying structure and hence share similar probability distributions (Tables 2–6).
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Feed1
T1
485
Station2
Measure11
Feed2
T2
Handle2
Spillage2
Measure21
Scale1
Scale2 Measure12
Handle1
Spillage1
Measure22 Box
Station1 Hight1
Hight2
Feed3
T3
Measure31 Scale3 Measure32
Handle3
Spillage3
Station3
Hight3
Fig. 3. 3-Station Bayesian diagnostic model for the HAS200 system.
Table 2 CPT for T and Spillage.
Table 5 CPT for Height1.
Feeding
Pr(T = x)
OK NOK Handling
X = OK
X = NOK
0.9 0.05
0.1 0.95
Pr(Spillage = x)
OK NOK
X = OK
X = NOK
0.9 0.05
0.1 0.95
OK OK NOK NOK
Feeder
OK OK NOK NOK
Box
OK OK OK OK NOK NOK NOK NOK
OK OK NOK NOK OK OK NOK NOK
OK NOK OK NOK OK NOK OK NOK
OK NOK OK NOK
Feeding3
Pr(Feeding = x) X = OK
X = NOK
1 0 0.5 0
0 1 0.5 1
Table 4 CPT for Measure2. Scale2
Handling1
Pr(Height1 = x) X = OK
X = NOK
1 0.3 0.3 0.1 0.3 0.01 0.01 0
0 0.7 0.7 0.9 0.7 0.99 0.99 1
Table 6 CPT for Height3.
Table 3 CPT for Feeding. Measure
Feeding
Box
OK NOK OK NOK
Pr(Measure2 = x) X = OK
X = NOK
0.75 0.75 0 0
0.25 0.25 1 1
4.3. Model verification Once the component-based subnets for individual agents have been constructed, they should then be verified for MSBNconsistency, i.e. checking that MSBN constraints are satisfied to guarantee efficient distributed inference.
OK OK OK OK OK OK OK OK NOK NOK NOK NOK NOK NOK NOK NOK
Handling3
OK OK OK OK NOK NOK NOK NOK OK OK OK OK NOK NOK NOK NOK
Box
OK OK NOK NOK OK OK NOK NOK OK OK NOK NOK OK OK NOK NOK
Height2
OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK OK NOK
Pr(Height3 = x) X = OK
X = NOK
1 0.01 0.8 0.01 0.2 0.01 0.2 0 0.2 0.01 0.1 0 0.01 0 0.01 0
0 0.99 0.2 0.99 0.8 0.99 0.8 1 0.8 0.99 0.9 1 0.99 1 0.99 1
The constraints presented in Section 3 are firstly verified locally within each agent and then verified for the whole system through message passing among agents. This cooperative verification makes use only of the public variables shared among neighbouring subnets. This is a very important feature, as it allows the global verification to take place without the need for detailed knowledge
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Fig. 4. Agent Station1 model compilation, (a) Bayesian subnet, (b) moral sub-graph, (c) chordal sub-graph and (d) junction tree.
about the internal structure of individual subnets. This feature makes the verification of individually developed subnets easy to perform and more importantly it accommodates for knowledge protection for component suppliers who might be unwilling to share proprietary knowledge about the internal functionalities of their components. Certainly this entails the need for special care to be taken during the construction of individual subnets in terms of selecting shared variables that each agent makes accessible to the neighbouring agents. Constraint (iii) in Section 3.2 implies that variables of each individual subnet are conditionally independent of those of other subnets given the d-sepset. This entails that when designing modular subnets for equipment modules, this assumption should always be considered to ensure that any root cause within one module is conditionally independent of the variables in other modules given the d-sepset. The model verification process here and all the subsequent steps for model compilation and inference are carried out using the software toolkit WEBWEAVR IV [31] which provides tools for multi-agent probabilistic modelling and inference.
4.4. Model compilation Once the individual subnets have been built and cooperatively verified for MSBN consistency, they should then be compiled into a runtime secondary representation to allow efficient and coherent unified reasoning and inference. This compilation involves three steps: • First, each subnet is independently moralized by connecting parents of each node together and dropping link directions. Then through message passing, neighbouring moral subnets are checked for consistency on the shared nodes. • Next step is triangulation on the moral subnets, where each subnet is locally converted into a chordal graph so that the set of consistent chordal sub-graphs defines the super-graph of the union of the set of sub-graphs. A chordal graph is defined by having at least one perfect elimination sequence.
• The set of chordal graphs is then converted into a corresponding set of junction trees. Moreover, a junction tree is established for each d-sepset between two sub-graphs, these junction trees are known as linkage trees. The conversion of sub-graphs into junction trees is to allow effective inference using message passing algorithms [32] and the linkage trees are to ensure concise message passing among agents through beliefs on d-sepsets.
The resultant representation for the whole system is called linked junction forest which is then used for online MSBN inference. The online reasoning is performed on the linked junction forest as each agent uses a junction tree for its internal representation and the associated linkage trees for communicating with the neighbouring agents on the hypertree structure. Fig. 4 shows the model compilation steps on the agent representing station1. To explain the need for multi-agent communication during the belief update process we will consider a case from this illustrative example. We can see that as every agent only has access to the states of the local variables in the station, it cannot always make appropriate belief updates on the local variables without communicating with neighbouring agents. For example in Station 3, assume the local variables are observed to confirm the absence of any errors within the station, i.e. both feeding and handling variables are observed and known to be error-free or in OK state. Assuming that Measurement variable is not directly observable in Station 3, Station 3 agent will not be able to update the state of Measurement variable. To do so it needs to communicate with the previous station in the line to update its belief on the previous height measurement and accordingly update its belief about the state of its measurement process. So assuming the final quality check rejected the box due to height being unacceptable, then Station 3 agent will update its belief on the state of its measuring device depending on the belief of Station 2 about the height in Station 2. Neighbouring agents propagate their belief on the shared variables along the hypertree by responding to belief update requests. After the communication takes place, all agents’ beliefs will be consistent with all observations accumulated across the system.
Table 7 Observations and the resulting most probable cause using the global BN. Observations
Most probable cause
Height3
Spillage1
Spillage2
Spillage3
T1
T2
T3
NOK NOK NOK
OK OK Unknown
OK OK OK
OK OK OK
OK Unknown Unknown
OK OK OK
OK OK OK
Box Feeder1 Handling1
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Table 8 Observations and the resulting most probable cause using the distributed BN. Observations
Most probable cause
Height3
Spillage1
Spillage2
Spillage3
T1
T2
T3
NOK NOK NOK
OK OK Unknown
OK OK OK
OK OK OK
OK Unknown Unknown
OK OK OK
OK OK OK
For performance evaluation purposes both the global Bayesian network and the distributed network were used for diagnostic reasoning with injected faults and three different sets of observations. In both cases the observed fault was final product height out of range (Height3 = NOK). Then different combinations of observations were used through setting and un-setting the states of the possible observable variables as shown in Table 7 for the global BN and in Table 8 for the distributed BN. Then through belief updating, the probabilities of each of the equipment variables being faulty (NOK) were estimated to identify the most probable cause that explains each set of observations. The resulting causes are shown in the right-most column in Table 7 for centralized belief update (global BN) and in Table 8 for cooperative belief update (distributed BN). From both tables one can see that the same fault cause was identified using both approaches in each of the three cases, which suggests that the distributed reasoning framework achieves similar fault detection accuracy as the global network. In terms of computation requirements, the results from both approaches were obtained on a 3 GHz dual core PC with 3 GB of memory and running Ubuntu® operating system.
5. Conclusions In this paper the need for new modular component-based diagnosis frameworks for modular manufacturing systems was explained along with the associated challenges. To respond to these challenges, the use of multi-agent Bayesian approaches as a distributed diagnostic framework was suggested. We successfully demonstrated how MSBNs can be used to model a diagnostic system for a lab-based modular assembly system. MSBNs allow distributed autonomous and collaborative inference. Moreover, the processes of model verification, model compilation and inference are carried out while protecting agents’ privacy. We have used the Java-based software toolkit WEBWEAVR IV to implement the component-based diagnostic system and to demonstrate the process of distributed modelling, multi-agent model verification, multi-agent model compilation and belief update for consistent system level inference. It is the first time that MSBN approach was used for manufacturing system diagnosis purposes. The initial results suggest that the method is capable of providing a framework for distributed component-based modelling and inference with comparable performance to classical Bayesian networks in terms of detection accuracy. Although in this example the suggested approach for obtaining the model parameters was entirely expert driven, however, possibilities for learning these parameters from data should also be considered. The fact that the global model is made of smaller network fragments that are expected to be designed and owned by component suppliers makes it even more interesting to explore Bayesian learning possibilities as extensive operational datasets will be available from the operation of these equipment modules within various settings. Follow up work will be focused on the performance evaluation of the proposed method in terms of accuracy of detection and computation efficiency to allow more understanding of the advantages and limitations of the method. It is also important to further investigate systematic approaches for sub-model generation with specific focus on
Box Feeder1 Handling1
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[32] Jensen FV, Nielsen TD. Bayesian networks and decision graphs. New York: Springer Verlag; 2007. Mohamed Samir Sayed is a Nottingham’s Dean of Engineering Doctoral Research Scholar; he is currently doing his PhD at the University of Nottingham focusing on manufacturing systems diagnosis. He holds MSc in Electronic Communications Engineering from The University of Nottingham, UK and BSc (Hon) in Electrical Engineering from The University of Khartoum, Sudan. Dr. Niels Lohse is a lecturer of advanced manufacturing technology at the University of Nottingham. He graduated with a Diplom-Engineer degree in Mechanical Engineering from the University of Applied Science Hamburg, Germany in 2000. Dr Lohse obtained his MSc in Technology Management from the University of Portsmouth in 2001 and received his PhD in Manufacturing Engineering and Operations Management from the University of Nottingham in 2006. His research is focused on intelligent automation including manufacturing system modelling, distributed control, diagnostics and design decision-support with a primary focus on modular and evolvable production systems and applications of artificial intelligence techniques in manufacturing.