Bayesian Melding Method Research Articles

A sequential multi-prior integration and updating method for complex multi-level system based on Bayesian melding method

In engineering, there exist multiple priors about system and subsystems uncertainties, which should be integrated properly to analyze the system reliability. In the past research, an iterative updating procedure based on Bayesian Melding Method (I-BMM) was developed to merge and update multiple priors for the double-level system. However, the in-depth study in this paper shows that the original iterative procedure has no effect on the prior updating. Thus it is proposed that only a single BMM iteration process is needed following the original prior integration and updating formulation. BMM involves the sampling procedure for the probability density function (PDF) updating, wherein it is generally difficult to define the sampling number properly for obtaining accurate priors. To address this problem, a sequential prior integration and updating framework based on the original single BMM iteration process (S-BMM) is developed in this paper. In each cycle of prior updating, the sample number is sequentially added, and the difference between prior distributions obtained in the two consecutive cycles is measured with the symmetric Kullback-Leibler Divergence (SKLD). The sequential procedure is continued until the convergence to the accurate updated prior. The S-BMM framework for double-level systems is further extended for multi-level systems. Situations with some missing subsystem or component priors are also discussed. Finally, two numerical examples and one satellite engineering case are used to demonstrate and verify the proposed algorithms.

An information aggregation method for hierarchical system reliability analysis with insufficient reliability information based on Bayesian Melding Method

In practical engineering, the reliability analysis of the hierarchical system structure is a hot topic, which has made great progress in recent years. From former experiments, there exists multi-source reliability information for the complex system. In the literature, the Bayesian Melding Method is a useful tool to merge the subsystem and system information based on the deterministic structure. However, when the system reliability information is insufficient, how to integrate the limited information for the system reliability analysis remains a problem to be solved. In this paper, an information aggregation method is developed for the hierarchical system to make full use of the limited reliability information based on the traditional Bayesian Melding Method. Three main steps are involved in the proposed method, i.e. distribution assumption, structure reconstruction, and reliability inference, based on which the existed reliability information can be fully merged and partial missing reliability information can be acquired through the system structure. Finally, the benefit illustration and effectiveness verification of the proposed method are given in the numerical example.

An Adaptive Bayesian Melding Method for Reliability Evaluation Via Limited Failure Data: An Application to the Servo Turret

In the early stage of product development, reliability evaluation is an indispensable step before launching a product onto the market. It is not realistic to evaluate the reliability of a new product by a host of reliability tests due to the limiting factors of time and test costs. Evaluating the reliability of products in a short time is a challenging problem. In this paper, an approach is proposed that combines a group of experts’ judgments and limited failure data. Novel features of this approach are that it can reflect various kinds of information without considering the individual weight and reduces aggregation error in the uncertainty quantification of multiple inconsistent pieces of information. First, an expert system is established by the Bayesian best–worst method and fuzzy logic inference, which collects and aggregates a group of expert opinions to estimate the reliability improvement factor. Then, an adaptive Bayesian melding method is investigated to generate a posterior by inaccurate prior knowledge and limited test data; this method is made more computationally efficient by implementing an improved sampling importance resampling algorithm. Finally, an application for the reliability evaluation of a subsystem of a CNC lathe is discussed to illustrate the framework, which is shown to validate the reasonability and robustness of our proposal.

An iterative information integration method for multi-level system reliability analysis based on Bayesian Melding Method

For uncertainty modeling and reliability analysis of a complex system, there generally exists multi-source information, which should be fully considered and used synthetically. Research shows that the Bayesian Melding Method (BMM) is a useful tool to merge the multi-source information. However, how to apply BMM for the complex system with a multi-level hierarchical structure remains a challenging issue. To address this problem, this paper proposes an iterative information integration method for multi-level system structures so as to fully integrate the information between different levels. A complete single iteration consists of the updating process from the system bottom to top level and then from the system top to bottom level. To facilitate the updating process, the complex multi-level system is first decomposed into several basic double-level units, within which the information integration can be conveniently conducted with the proposed discrete or continuous BMM methods. To check the iteration convergence, the symmetric Kullback-Leibler Divergence (SKLD) is adopted to measure the difference between the updated system distributions obtained in the two consecutive iteration processes.Finally, three case studies with discrete and continuous information integration problems are used to demonstrate and validate the proposed method.

On the performance evaluation of a hierarchical-structure prototype product using inconsistent prior information and limited test data

Performance evaluation or parameter estimation for a hierarchical structure prototype product is an imperative yet difficult task. The challenge comes from both inaccurate prior knowledge and insufficient data acquisition at its early usage period. In this paper, we propose an innovative Bayesian inference framework for the uncertainty quantification of the performance of a newly developed product with hierarchical structure characteristics. We focus particularly on the presence of inconsistent prior distributions on one quantity. An adaptive Bayesian melding method is investigated to aggregate multi-source information in a flexible way. We realize this method via a modified sampling importance re-sampling algorithm. This algorithm is designed to substitute for the MCMC methods and is computationally efficient. We use a practical engineering case to validate our proposal.

A Bayesian approach for integrating multilevel priors and data for aerospace system reliability assessment

This paper investigates Bayesian methods for aerospace system reliability analysis using various sources of test data and expert knowledge at both subsystem and system levels. Four scenarios based on available information for the priors and test data of a system and/or subsystems are studied using specific Bayesian inference techniques. This paper proposes the Bayesian melding method for integrating subsystem-level priors with system-level priors for both system- and subsystem-level reliability analysis. System and subsystem reliability outcomes are compared under different scenarios. Computational challenges for posterior inferences using the sophisticated Bayesian melding method are addressed using Markov Chain Monte Carlo (MCMC) and adaptive Sampling Importance Re-sampling (SIR) methods. A case study with simulation results illustrates the applications of the proposed methods and provides insights for aerospace system reliability analysis using available multilevel information.

System reliability assessment with multilevel information using the Bayesian melding method

This paper investigates the Bayesian melding method (BMM) for system reliability analysis by effectively integrating various available sources of expert knowledge and data at both subsystem and system levels. The integration of multiple priors is investigated under both linear and geometric pooling methods. The aggregated system prior distributions using various pooling methods including the BMM are evaluated and compared. Based on these integrated and updated prior distributions and three scenarios of data availability from a system and/or subsystems, methods for posterior system reliability inference are proposed. Computational challenges for posterior inferences using the sophisticated BMM are addressed using the adaptive sampling importance re-sampling (SIR) method. A numerical example with simulation results illustrates the applications of the proposed methods and provides insights for system reliability analysis using multilevel information.

Bayesian Melding of Deterministic Models and Kriging for Analysis of Spatially Dependent Data

The link between geographic information systems and decision making approach own the invention and development of spatial data melding method. These methods combine different data sets, to achieve better results. In this paper, the Bayesian melding method for combining the measurements and outputs of deterministic models and kriging are considered. Then the ozone data in Tehran city are analyzed by using these methods. Next their results are evaluated and compared in terms of mean square error criterion. Finally, discussion and results are given.

A stochastic infection rate model for estimating and projecting national HIV prevalence rates

BackgroundEvery 2 years, the Joint United Nations Programme on HIV/AIDS (UNAIDS) produces probabilistic estimates and projections of HIV prevalence rates for countries with generalised HIV/AIDS epidemics. To do this they...

Bayesian Melding Estimation of a Stochastic SEIR Model

One of the main problems in estimating stochastic SEIR models is that the data are not completely observed. In this case, the estimation is usually done by least squares or by MCMC. The Bayesian melding method is proposed to estimate SEIR models and to evaluate the likelihood in the presence of incomplete data. The method is illustrated by estimating a model for HIV/TB interaction in the population of a prison.