Jinhua Mi

Bayesian Degradation Analysis With Inverse Gaussian Process Models Under Time-Varying Degradation Rates

Degradation observations of modern engineering systems, such as manufacturing systems, turbine engines, and high-speed trains, often demonstrate various patterns of time-varying degradation rates. General degradation process models are mainly introduced for constant degradation rates, which cannot be used for time-varying situations. Moreover, the issue of sparse degradation observations and the problem of evolving degradation observations both are practical challenges for the degradation analysis of modern engineering systems. In this paper, parametric inverse Gaussian process models are proposed to model degradation processes with constant, monotonic, and S-shaped degradation rates, where physical meaning of model parameters for time-varying degradation rates is highlighted. Random effects are incorporated into the degradation process models to model the unit-to-unit variability within product population. A general Bayesian framework is extended to deal with the degradation analysis of sparse degradation observations and evolving observations. An illustrative example derived from the reliability analysis of a heavy-duty machine tools spindle system is presented, which is characterized as the degradation analysis of sparse degradation observations and evolving observations under time-varying degradation rates.

Reliability assessment of complex electromechanical systems under epistemic uncertainty

The appearance of macro-engineering and mega-project have led to the increasing complexity of modern electromechanical systems (EMSs). The complexity of the system structure and failure mechanism makes it more difficult for reliability assessment of these systems. Uncertainty, dynamic and nonlinearity characteristics always exist in engineering systems due to the complexity introduced by the changing environments, lack of data and random interference. This paper presents a comprehensive study on the reliability assessment of complex systems. In view of the dynamic characteristics within the system, it makes use of the advantages of the dynamic fault tree (DFT) for characterizing system behaviors. The lifetime of system units can be expressed as bounded closed intervals by incorporating field failures, test data and design expertize. Then the coefficient of variation (COV) method is employed to estimate the parameters of life distributions. An extended probability-box (P-Box) is proposed to convey the present of epistemic uncertainty induced by the incomplete information about the data. By mapping the DFT into an equivalent Bayesian network (BN), relevant reliability parameters and indexes have been calculated. Furthermore, the Monte Carlo (MC) simulation method is utilized to compute the DFT model with consideration of system replacement policy. The results show that this integrated approach is more flexible and effective for assessing the reliability of complex dynamic systems.

Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective

Degradation analysis is critical to reliability assessment and operational management of complex systems. Two types of assumptions are often adopted for degradation analysis: (1) single degradation indicator and (2) constant external factors. However, modern complex systems are generally characterized as multiple functional and suffered from multiple failure modes due to dynamic operating conditions. In this paper, Bayesian degradation analysis of complex systems with multiple degradation indicators under dynamic conditions is investigated. Three practical engineering-driven issues are addressed: (1) to model various combinations of degradation indicators, a generalized multivariate hybrid degradation process model is proposed, which subsumes both monotonic and non-monotonic degradation processes models as special cases, (2) to study effects of external factors, two types of dynamic covariates are incorporated jointly, which include both environmental conditions and operating profiles, and (3) to facilitate degradation based reliability analysis, a serial of Bayesian strategy is constructed, which covers parameter estimation, factor-related degradation prediction, and unit-specific remaining useful life assessment. Finally, degradation analysis of a type of heavy machine tools is presented to demonstrate the application and performance of the proposed method. A comparison of the proposed model with a traditional model is studied as well in the example.

Dynamic fault tree analysis based on continuous-time Bayesian networks under fuzzy numbers:

In the calculation of dynamic fault trees, the existing state space–based methods, such as Markov chain method, are basically global-state models, which make the solution procedure very complex. Bayesian networks have become a popular tool to build probability models and conduct inference for reliability design and analysis in various industry fields. The “state explosion” problem can be alleviated by Bayesian networks. Furthermore, to obtain sufficient failure data sets in real engineering systems is extremely difficult and thus causes the parametric uncertainty in failure data. To address these issues, a novel dynamic fault tree analysis method based on the continuous-time Bayesian networks under fuzzy numbers is proposed in this article. The probability distributions under fuzzy numbers for the output variable of dynamic logic gates are determined. The calculation of fuzzy failure probability of a system is presented. Finally, an example is given to demonstrate the effectiveness of the proposed method.

Belief Universal Generating Function Analysis of Multi-State Systems Under Epistemic Uncertainty and Common Cause Failures

Because of the complexity of engineering systems, and the fact that insufficient data are only available to obtain the precise state probability of components, an extended universal generating function (UGF) based on belief function theory is introduced in this paper to conduct the reliability analysis of multi-state systems (MSSs) with epistemic uncertainty. The behavior of common cause failures (CCFs) is further incorporated, and the occurrence probability of CCFs is evaluated using a weighted impact vector method. A numerical example is used to illustrate how the proposed method works. In addition, a global optimization method is used to obtain the truth interval of the system reliability, and the results are compared with those obtained by using some existing methods. The case study shows that the belief UGF method can effectively avoid the interval expansion problem and the overestimation problem involved in the interval UGF method, and the proposed method can be used to provide a reliable way to evaluate the reliability of MSSs with interval data and CCFs.

Reliability analysis of complex multi-state system with common cause failure based on evidential networks

Abstract With the increasing complexity and size of modern advanced engineering systems, the traditional reliability theory cannot characterize and quantify the complex characteristics of complex systems, such as multi-state properties, epistemic uncertainties, common cause failures (CCFs). This paper focuses on the reliability analysis of complex multi-state system (MSS) with epistemic uncertainty and CCFs. Based on the Bayesian network (BN) method for reliability analysis of MSS, the Dempster-Shafer (DS) evidence theory is used to express the epistemic uncertainty in system through the state space reconstruction of MSS, and an uncertain state used to express the epistemic uncertainty is introduced in the new state space. The integration of evidence theory with BN which called evidential network (EN) is achieved by adapting and updating the conditional probability tables (CPTs) into conditional mass tables (CMTs). When multiple CCF groups (CCFGs) are considered in complex redundant system, a modified β factor parametric model is introduced to model the CCF in system. An EN method is proposed for the reliability analysis and evaluation of complex MSSs in this paper. The reliability analysis of servo feeding control system for CNC heavy-duty horizontal lathes (HDHLs) by this proposed method has shown that CCFs have considerable impact on system reliability. The presented method has high computational efficiency, and the computational accuracy is also verified.

Thermal Cycling Life Prediction of Sn-3.0Ag-0.5Cu Solder Joint Using Type-I Censored Data

Because solder joint interconnections are the weaknesses of microelectronic packaging, their reliability has great influence on the reliability of the entire packaging structure. Based on an accelerated life test the reliability assessment and life prediction of lead-free solder joints using Weibull distribution are investigated. The type-I interval censored lifetime data were collected from a thermal cycling test, which was implemented on microelectronic packaging with lead-free ball grid array (BGA) and fine-pitch ball grid array (FBGA) interconnection structures. The number of cycles to failure of lead-free solder joints is predicted by using a modified Engelmaier fatigue life model and a type-I censored data processing method. Then, the Pan model is employed to calculate the acceleration factor of this test. A comparison of life predictions between the proposed method and the ones calculated directly by Matlab and Minitab is conducted to demonstrate the practicability and effectiveness of the proposed method. At last, failure analysis and microstructure evolution of lead-free solders are carried out to provide useful guidance for the regular maintenance, replacement of substructure, and subsequent processing of electronic products.

Reliability analysis of multi-state systems with common cause failure based on Bayesian Networks

Taking account of the influence of common cause failure (CCF) to system reliability, a method for reliability modeling and assessment of a multi-state system with common cause failure based on Bayesian Network (BN) is proposed by using the advantage of uncertainty reasoning and figurative expression of BN. The model is applied to a two-axis positioning mechanism transmission system to demonstrate its effectiveness and ability to directly calculate the system reliability on the basis of multi-state probabilities of elements. The comparison between the proposed method and the method without considering CCF verifies the efficiency and accuracy of the proposed method.

Reliability Analysis of Complex Multi-state System with Common Cause Failure Based on DS Evidence Theory and Bayesian Network

With the increasing complexity and larger size of modern advanced engineering systems, the traditional reliability theory cannot characterize and quantify the complex characteristics of complex systems, such as multi-state properties, epistemic uncertainties, common cause failures (CCFs), etc. This chapter focuses on the reliability analysis of complex multi-state system (MSS) with epistemic uncertainty and CCFs. Based on the Bayesian network (BN) method for reliability analysis of MSS, the DS evidence theory is used to express the epistemic uncertainty in system through the state space reconstruction of MSS. An uncertain state, which used to express the epistemic uncertainty is introduced in the new state space. The integration of evidence theory with BN is achieved by updating the conditional probability tables. When the multiple CCF groups (CCFGs) are considered in complex redundant systems, a modified factor parametric model is introduced to model the CCF in systems. An evidence theory based BN method is proposed for the reliability analysis and evaluation of complex MSSs in this chapter. The reliability analysis of servo feeding control system for CNC heavy-duty horizontal lathes (HDHLs) by this proposed method has shown that the presented method has high computational efficiency and strong practical value.

Physics of failure-based reliability prediction of turbine blades using multi-source information fusion

Abstract Fatigue and fracture of turbine blades are fatal to aero engines. Reliability prediction of aero engines is indispensable to guarantee their safety. For turbine blades of aero engines, most recent research works only focus on the number of cycles and excavate information from a single source. To remove these limitations, a Physics of failure-based reliability prediction method using multi-source information fusion has been developed in this paper to predict the reliability of turbine blades of aero engines. In the proposed method, the fuzzy theory is employed to represent uncertainties involved in prediction. Case studies of reliability prediction under fuzzy stress with and without fuzzy strength are conducted by using a dynamic stress-strength interference model which takes types of cycles of aero engines into consideration. Results indicate that the proposed method is better in line with engineering practice and more flexible in decision making and it can predict the reliability of aero engine turbine blades to be an interval by utilizing the proposed linear fusion algorithm. In addition, the predicted interval contains results that are predicted by other commonly used information fusion methods Hence, the proposed method conduces to remove confusion made by selection of multiple methods.