Case-based reasoning is suitable for capturing and reusing human experiences for complex problem solving, and has earlier shown its success also in the oil drilling domain[1]. However, a pure CBR system suffers from the inability to justify a solution - beyond referring to the best matching case or cases. Further, CBR represents in itself a knowledge-lean method for case retrieval. A model of general domain knowledge would enable cases to be matched based on semantic rather than purely syntactic criteria. Hence, a general domain model combined with CBR will enable the system to generate targeted explanations for the user as well as for its internal reasoning process. Earlier work in our group have addressed this problem by combining CBR with a semantic network of multi relational domain knowledge [2], which implementation is called TrollCreek. A problem with that method was the lack of a formal basis for the semantic network that was used, which made the inference processes within the network difficult to develop and less powerful than wanted. The need for a more formal treatment of uncertainty leads to some initial investigations into how a Bayesian Network (BN) model could be incorporated [3, 4]. Bayesian Network has shown its feasibility to build probabilistic models without introducing unrealistic assumptions of independencies [4]. The probability distribution provided by BN enables the conditioning over any of the variables and supports any direction of reasoning [5]. Also, the Bayesian Networks framework includes an inference engine, which, given some evidence, is capable of updating its beliefs [6]. Moreover, the nature of Bayesian Networks allows for some explanations to be given regarding the reasoning process [4]. All these make BNs a proper candidate for my PhD work.
The literature study done so far addresses the two main aspects of this project, namely the combination of CBR and a multi-relational domain knowledge model, and the combination of CBR with a BN.
The TrollCreek system is an implementation based on the Creek architecture
for knowledge-intensive case-based problem solving and learning, targeted at
addressing problems in open and weak-theory domains [
Additionally, a study over a number of literatures which are investigated the combination of CBR and BN and their applications has been done. 3
While the existing TrollCreek ontology may be useful for human interpretation, its current inference methods are too weak to address the needs of automated data analysis and decision support targeted by my Ph.D. A new approach is called for, which defines three central objectives of this project: – The design of a domain model representation, with suitable inference methods, which captures the essential content of the existing ontology. • In this level of study, Bayesian Network has been utilized as a knowledge model with a strong inference capability. But in this way, the knowledge that are added to the system by the multi relational knowledge models, will be lost. Therefore, we are looking for a way to incorporate CBR with multi relational knowledge and causal knowledge models. – Integration of a case representation and CBR method, that is able to utilize the general domain ontology in its case modeling and reuse process. – Adaptation of machine learning methods that builds abstract process signatures from data with the help of the ontology and the case based reasoning. The existing ontology and CBR methods have been developed within a development environment that is now obsolete. An open source environment or a combination of environments will be studied, assessed and adapted to our needs. Candidates are MyCBR, Colibri Studio, and Protege.
We will use oil well drilling problems as our application domain and rely on the field expert evaluation as our evaluation method. 4
In the line of my PhD plan as a start point of combining CBR and BN research, the prediction of root causes of failures and the generation of explanations given the observed symptoms or errors are studied.
The main structure of a Bayesian network has been designed in order to express the elements’ relations and calculate the updated beliefs based on the prior probabilities assigned by a field expert. The domain concepts are presented by nodes and their causal relations are shown by arrows. A parent causes a child, and each node represents the current belief of the network given its parents. Our approach in the first place, views the BN as a different type of, and a replacement for the knowledge model in TrollCreek (BN-Creek). Then, integrates TrollCreek case retrieval results with the BN-Creek results to get benefit from the other type of relations that been considered in TrollCreek. Fig. 2 depicts the graphical structure for the proposed approach. The filled and not filled circles are indicators of Bayesian network nodes and cases, respectively. TrollCreek and the present approach are extracting the cases from the raw data, but the main difference between them is their knowledge models. TrollCreek uses a multi relational semantic based knowledge model while the new approach uses a probabilistic causal model as its knowledge model.
The field expert’s knowledge has been exploited to create the aforementioned BN. The causal relations between the oil well drilling process’ concepts were identified by the expert and were used as the prior probabilities of the BN. The main task in this study is to answer the query of: ”What is the whole probability distribution over variable X given evidence e?”. In other words, the most plausible causes of the failure under study, given some observations, is desired. In our approach, the mentioned query will be answered in the following three steps.
Step one:This step utilizes BN to calculate a temporal probability distribution of the new case. By creating a new case, a copy of the domain’s prior Bayesian network is assigned to it. The inference process is started, by applying each of the observed concepts as evidence in the network. Then the network’s beliefs will be updated given those evidence and the result will be shown as the posterior distribution (PD) of the network, corresponding to that specific case.
Step two: In this step, we utilize the CBR’s capability of employing the past experiences, aimed to improve the BN’s accuracy in suggesting the root causes. TrollCreek is used to retrieve the most similar cases to the new one. The bestmatched case is considered and an impact factor is assigned to its recorded PD, based on its similarity degree.
TrollCreek uses MAC-FAC method [
Pi=1 Pjm=1 sim(fi, fj) ∗ relevancef actorfj n
Pjm=1 relevancef actorfj
(1)
In Eq.1 the CIN stands for the under study case and and CRE demonstrates the
retrieved case. n and fi, m and fj are the number of findings and the finding’s
number in the CIN and CRE , respectively. The sim(CIN , CRE ) is equal to 1 if
fi = fj, otherwise it’s value would be 0. The relevance factor is a number that
combines the predictive strength and importance of a feature for a stored case
and comes from the expert [
The FAC phase considers the paths in the semantic network that represent relation sequences between un-identical features. Based on a method for calculating the closeness between two features at each end of such a sequence, the two features are given a local similarity score.
Step three: This step integrates the probability distributions from the first two steps and calculates the new case’s finalized probability distribution. In other words, in this step we have added the CBR’s capability in employing the past experiences, to improve the BN’s accuracy in suggesting the root causes. The result of step three is the system’s outcome.
Eq.2 integrates the effect of the pure BN and CBR from the first two steps and generates the finalized posterior distribution for the new case.
P Pjf =
k Pi=1 P Pji ∗ αi
k Pi=1 αi (2) In Eq.2 the PP stands for the posterior probabilities which are the elements of the Posterior distribution. The 0 < α < 1 is the impact factor that is larger for the cases with higher similarity. The ’k’ is the number of PDs that are integrated together and would be higher than two in a situation that the expert wants to involve the effect of less matched cases. ’j’ and ’i’ a’re the indicators of a specific PP in a PD and the PD’s number, respectively. Consequently, the P Pjf stands for the finalized posterior probability of the PP number ’j’. The index ’f’ stands for finalized PP.
After completion of the third step, the finalized updated network’s beliefs (PD) are achieved. Using the final PD, the strengths of the potential root causes are listed and are given to the expert for assessment.