Research On Uncertainty Quantification Method Based On Evidence Theory And Its Application In Reliability Engineering

Uncertainty Quantification (UQ) is a new research field in just recent years. As it was proposed to solve engineering problems in reality originally, and had broad applications, it received wide attentions from scientific research units and academic institutions all over the world. As a theory of uncertain information processing, evidence theory has been widely used in data fusion, pattern recognition, decision analysis, and other fields. But the ability of evidence theory on UQ analysis is just paid attention in recent few years. In this work, UQ analysis based on the evidence theory is conducted, and its applications on reliability engineering are also studied. The major contributions are as follows:(1) The unified method of describing heterogeneous information based on evidence theory is studied. The approaches of translating probability distribution, probability boxes, fuzzy distribution, experts’ opinions, small size test data, and other information into evidence bodies are discussed, which are the basis of UQ analysis using evidence theory uniformly. Simultaneously, highly conflicting information fusion problem for interval evidences is discussed. A method of disjointing algorithm is proposed, which reallocates the focal elements and their basic probabilities for intersecting intervals first, then use Dempster’s rule to combine the evidences. Experiments show that the method can get reasonable results in combining interval-valued evidences.(2) A hybrid interval genetic algorithm is proposed to alleviate the computational cost and make evidence theory acceptable in complex system UQ. In this method,taking no account of system state equation is monotonic or not, UQ is accomplished in a unified algorithm framework. Simulation results show that, the computational efficiency of proposed method is far in excess of vertex method and sampling method without decreasing the degree of accuracy. Especially when number of uncertain parameters and focal elements is large, and system is non-monotonic, comparing with sampling method, the computational cost is reduced about5orders of magnitude without sacrificing the accuracy of resulting measurements.(3) Sensitivity analysis approaches of uncertain system are discussed, and a reliability sensitivity analysis method of parameters under experts’ opinions is proposed. The method translates experts’ opions into probability boxes by belief and plausibility functions, and with the hybrid interval genetic algorithm, calculates the interval values of system failure probability before and after uncertainty pinching of uncertain parameters. Then on the basis of the variation of failure probability intervals, sensitivities of input uncertain paremeters is obtained, which can provide a direction to reduce the epistemic uncertainty in system reliability calculation in fulture work.(4) The problem of system reliability calculation in the situation that unit failure probability is imprecise is studied. Methods of failure probability calculation for some common used monotonic coherent and non-coherent systems are explored based on evidence theory. In this method, basic probability assignment are used to represent unit failure probability, and belief and plausibility function are used to calculate the lower and upper bounds of failure probability by evidential reasoning. Some examples are given to show that the proposed methods are more effective, and can get more useful information than some conventional methods.(5) To deal with epistemic uncertainties in reliability analysis, the implementation of evidence theory in Bayesian networks is studied. The method to convert fault trees to Bayesian networks in epistemic uncertainty condition is proposed, and the probability of top event is calculated by belief measure and plausibility measure of evidence theory. Three importances are solved, and a key concept, epistemic importance, is proposed, which definition and algorithm are given. Finally, with a numerical example, it is shown that the proposed method could enhance the ability of Bayesian networks to deal with uncertainty information in reliability analysis, and could obtain additional information.(6) The applications of evidence theory in system reliability approximate calculation are discussed. When aleatory and epistemic uncertainties are in a system simultaneous, a new method to approximately calculate the reliability is proposed. In addition, according to the problem on reliability calculation of stress strength interference model, a new way of only discretizing the stress strength interference area is put forward, with increase the efficiency of reliability calculation further.