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Abstract: A belief rule base inference methodology using the evidential reasoning (RIMER) approach has been developed recently. A belief rule base (BRB), which can be treated as a more generalized expert system, extends traditional IF-THEN rules, but requires the assignment of some system parameters including rule weights, attribute weights, and belief degrees. These parameters need to be determined with care for reliable system simulation and prediction. Some off-line optimization models have been proposed, but it is expensive to train and re-train these models in particular for large-scale systems. Moreover, the recursive algorithms are also proposed to fine tune a BRB online, which require less calculation time and satisfy the real-time requirement. However, the earlier mentioned learning algorithms are all based on a predetermined structure of the BRB. For a complex system, prior knowledge may not be perfect, which leads to the construction of an incomplete or even inappropriate initial BRB structure. Also, too many rules in an initial BRB may lead to over fitting, whilst too few rules may result in under fitting. Consequently, such a BRB system may not be capable of achieving overall optimal performance. In this paper, we consider one realistic and important case where both a preliminary BRB structure and system parameters assigned to given rules can be adjusted online. Based on the definition of a new statistical utility for a belief rule as investigated in this paper, a sequential learning algorithm for online constructing more compact BRB systems is proposed. Compared with the other learning algorithms, a belief rule can be automatically added into the BRB or pruned from the BRB, and our algorithm can also satisfy the real-time requirement. In addition, our algorithm inherits the feature of RIMER, i.e., only partial input and output information is required, which could be either incomplete or vague, either numerical or judgmental, or mixed. In order to verify the effectiveness of the proposed algorithm, a practical case study about oil pipeline leak detection is studied and examined to demonstrate how the algorithm can be implemented. [Copyright &y& Elsevier]

A belief rule base inference methodology using the evidential reasoning approach (RIMER) has been developed recently, where a new belief rule base (BRB) is proposed to extend traditional IF-THEN rules and can capture more complicated causal relationships using different types of information with uncertainties, but these models are trained off-line and it is very expensive to train and re-train them. As such, recursive algorithms have been developed to update the BRB systems online and their calculation speed is very high, which is very important, particularly for the systems that have a high level of real-time requirement. The optimization models and recursive algorithms have been used for pipeline leak detection. However, because the proposed algorithms are both locally optimal and there may exist some noise in the real engineering systems, the trained or updated BRB may violate some certain running patterns that the pipeline leak should follow. These patterns can be determined by human experts according to some basic physical principles and the historical information. Therefore, this paper describes under expert intervention, how the recursive algorithm update the BRB system so that the updated BRB cannot only be used for pipeline leak detection but also satisfy the given patterns. Pipeline operations under different conditions are modeled by a BRB using expert knowledge, which is then updated and fine tuned using the proposed recursive algorithm and pipeline operating data, and validated by testing data. All training and testing data are collected from a real pipeline. The study demonstrates that under expert intervention, the BRB expert system is flexible, can be automatically tuned to represent complicated expert systems, and may be applied widely in engineering. It is also demonstrated that compared with other methods such as fuzzy neural networks (FNNs), the RIMER has a special characteristic of allowing direct intervention of human experts in deciding the internal structure and the parameters of a BRB expert system. [Copyright &y& Elsevier]

Abstract: Belief rule base (BRB) systems are an extension of traditional IF-THEN rule based systems and capable of capturing complicated nonlinear causal relationships between antecedent attributes and consequents. In a BRB system, various types of information with uncertainties can be represented using belief structures, and a belief rule is designed with belief degrees embedded in its possible consequents. For a set of inputs to antecedent attributes, inference in BRB is implemented using the evidential reasoning (ER) approach. In this paper, the inference mechanism of the ER algorithm is analyzed first and its patterns of monotonic inference and nonlinear approximation are revealed. For a practical BRB system, it is difficult to determine its parameters accurately by using only experts’ subjective knowledge. Moreover, the appropriate adjustment of the parameters of a BRB system using available historical data can lead to significant improvement on its prediction performance. In this paper, a training data selection scheme and an adaptive training method are developed for updating BRB parameters. Finally, numerical studies on a multi-modal function and a practical pipeline leak detection problem are conducted to illustrate the functionality of BRB systems and validate the performance of the adaptive training technique. [Copyright &y& Elsevier]