مدل سازی سیستم های قابل اعتماد با استفاده از شبکه های بیزی هیبریدی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|28630||2008||8 صفحه PDF||سفارش دهید||3560 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Reliability Engineering & System Safety, Volume 93, Issue 7, July 2008, Pages 933–939
A hybrid Bayesian network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment, the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use in the field of dependability with two example of reliability estimation. Firstly we estimate the reliability of a simple single system and next we implement a hierarchical Bayesian model. In the hierarchical model we compute the reliability of two unknown subsystems from data collected on historically similar subsystems and then input the result into a reliability block model to compute system level reliability. We conclude that dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems.
We have used Bayesian nets (BNs) in a range of real-world applications of system dependability assessment (see for example ,  and ). In such applications, it is inevitable that there will be a mixture of discrete and continuous nodes (the resulting BNs are called hybrid). The traditional approach to handling (non-Gaussian) continuous nodes is static: you have to discretise them using some pre-defined range and intervals. However, this approach is unacceptable for critical type systems where there is a demand for reasonable accuracy. To overcome this problem we have developed a new and powerful approximate algorithm for performing inference in hybrid BNs. We use a process of dynamic discretisation of the domain of all continuous variables in the BN. The approach is influenced by the work of Kozlov and Koller  using entropy error as the basis for approximation. We differ from their approach by integrating an iterative approximation scheme within existing BN software architectures, such as in junction tree (JT) propagation . Thus, rather than support separate data structures and a new propagation algorithm we use the data structures commonly used in JT algorithms. The power and flexibility of the approach is demonstrated by applying it to estimate the reliability of repairable systems represented by a Bayesian hierarchical model. This problem represents a very simplified version of fragments of the wide range of models we have implemented as part of commercial and research projects. These have been in areas as diverse as data fusion, parameter learning, discrete systems simulation, RAM (reliability, availability and maintainability) evaluation and software defect prediction. The modelling has been made possible because our dynamic discretisation algorithm has recently been implemented in the commercial general-purpose BN software tool AgenaRisk .
نتیجه گیری انگلیسی
We have provided an overview of a new approximate inference algorithm designed for a general class of hybrid BNs. This dynamic discretisation algorithm (implemented in the AgenaRisk software) finally frees BN modellers from the burden (and inaccuracies) associated with having to statically discretise continuous nodes. We have first highlighted how this approach enables us to estimate reliability of a simple system, for which the results compare very favourably with analytical methods. We then assess the reliability of a more complex system comprised of two subsystems using a Bayesian hierarchical model, which allows the integration of data and expert opinion, available at different levels. The most common estimation strategy for such hierarchical models, where the resulting joint distribution of the associated model parameters cannot be evaluated analytically, has been to use intensive sampling algorithms, collectively known as Markov Chain Monte Carlo (MCMC) methods, from which approximate solutions can be obtained after drawing probably tens of thousands of dependent samples. We have shown how our combined scheme of dynamic discretisation and robust propagation algorithms on hybrid BNs can be used to obtain accurate results, offering a viable alternative to MCMC approaches, implemented within an easy-to-use and user friendly environment. It is a simple leap from this example to considerably more complex examples, say involving families of systems modelled hierarchically or using censored data, where dynamic discretisation could provide alternative and perhaps better solutions to those provided by other approximate methods such as MCMC. Typical solutions to this involve a variety of complex algorithms not