Shengkui Zeng

Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos

Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.

Real time reliability analysis based on the performance degradation data and Bayesian method

Failure data is difficult to obtain for the product with high reliability. Through analyzing the performance degradation data, analysis result of reliability will be more reasonable than through traditional approach. A real time reliability evaluation method is developed utilizing the field data, which integrates the advantages of reliability evaluation method based on performance degradation data and Bayesian method. Firstly, the degradation model is created based on the history performance degradation data, and the parameters of the model are estimated as the prior information of Bayesian method; then the model is updated and the reliability is evaluated simultaneously; finally, a piston pump is selected as the study case to verify the validity of this method. Through utilizing the history data of the other same type products and field data of the individual product, the proposed method can fully describe the particularity, and the reliability evaluation result will become much more accurate with the accumulating of the field data.

Accelerated storage degradation test and life extension assessment method for hermetically sealed electromagnetic relay

For products which are required for long-term storage, its difficult to assess their reliability or life extension due to lack of historical usage data or test data. This paper presents a life extension assessment method based on the accelerated storage degradation test (ASDT) and the degradation model with random performance parameters. The typical failure modes and mechanisms of hermetically sealed electromagnetic relay under the storage condition are analyzed. The degradation process of contact resistance (contact failure) is described using the Arrhenius model. In the accelerated storage degradation test, the contact resistance is selected as the major performance parameter to be measured. The composite activation energy parameter in the Arrhenius model was obtained by the degradation model with random performance parameters. Then, the life extension and the reliability are assessed combining with the historical storage environment data. The assessment result shows that the electromagnetic relay used in the airborne electronic part can satisfy the operating requirement of life extension for 10-year.

Time-Dependent Global Sensitivity Analysis for Long-Term Degeneracy Model Using Polynomial Chaos

Global sensitivity is used to quantify the influence of uncertain model inputs on the output variability of static models in general. However, very few approaches can be applied for the sensitivity analysis of long-term degeneracy models, as far as time-dependent reliability is concerned. The reason is that the static sensitivity may not reflect the completed sensitivity during the entire life circle. This paper presents time-dependent global sensitivity analysis for long-term degeneracy models based on polynomial chaos expansion (PCE). Sobol’ indices are employed as the time-dependent global sensitivity since they provide accurate information on the selected uncertain inputs. In order to compute Sobol’ indices more efficiently, this paper proposes a moving least squares (MLS) method to obtain the time-dependent PCE coefficients with acceptable simulation effort. Then Sobol’ indices can be calculated analytically as a postprocessing of the time-dependent PCE coefficients with almost no additional cost. A test case is used to show how to conduct the proposed method, then this approach is applied to an engineering case, and the time-dependent global sensitivity is obtained for the long-term degeneracy mechanism model.

The fault modeling methodology of actuator system based on Modelica

The multi-domain model established based on Modelica can effectively describe the dynamics and randomicity of failure behavior in complex systems. Firstly, the characteristics of multi-domain model are described, and the modeling methodology of failure behavior in complex systems based on multi-domain language is introduced; then the multi-domain model of actuator is established based on the components behavioral model library; finally, the actuator system is simulated and results are analyzed. The results show that not only the dynamic failure behaviors of complex systems, transfer process of different behaviors and performance fluctuations caused by failure behavior, but also the stochastic time when fault happens and uncertainty of parameters can be described by the proposed modeling methodology. It is validated that the methodology is useful for engineering application.

A mechanism reliability analysis method based on polynomial chaos expansion

Mechanism reliability analysis method is proposed based on polynomial chaos expansion, which is adopted to approximate to the limit function in this paper. The computational efficiency of reliability analysis is improved while achieving the same accuracy level. Firstly, uncertainty input variables are transformed into standard Gaussian distribution variables and the limit function is expressed as polynomial chaos expansion using Hermite polynomial bases. Thus the complexity of polynomial chaos expansion is greatly simplified with orthogonal characteristics between Hermite polynomial and standard Gaussian distribution probability density function. Then, the Probability Collocation method is adopted to determine the coefficient of polynomial chaos expansion and achieve complete polynomial chaos expansion. On this basis, the random simulation method is used to compute the mechanism reliability. Finally, reliability analysis is carried out with this method to a four-link mechanism. After the contrast with Monte Carlo method, the results indicate that polynomial chaos expansion improves the computational efficiency while achieving the same accuracy level.

Nonintrusive-Polynomial-Chaos-Based Kinematic Reliability Analysis for Mechanisms with Mixed Uncertainty

Due to the scarcity of statistical data, epistemic uncertainties are inevitable in the mechanism. As a promising uncertainty quantification technique, polynomial chaos has advantages over other methods in terms of accuracy and efficiency. In this paper, an improved nonintrusive polynomial chaos method is proposed for the kinematic reliability analysis of the mechanism with fuzzy and random variables as well as fuzzy failure/safety states. Klir log-scale transformation is applied to unify the fuzzy and random variables. Meanwhile, the polynomial-chaos-based probability formula of the fuzzy event is developed to characterize the fuzzy failure/safety states. The proposed method is applied to the reliability analysis of a retractable mechanical system.The results show good accuracy and efficiency of the proposed method when compared with the response surface method (RSM), Kriging method, and Monte Carlo simulation (MCS).

Research on the reliability analysis method of an actuator under stochastic load

Traditional time-dependent reliability analysis methods aim to predict the product failure time based on binary component and system status, which have not considered the influence of some stochastic characters for the reliability such as internal parameters variation and environment factors fluctuation. Current integrated design method considers performance and reliability requirements simultaneously, and has synthesized all the uncertain factors during the reliability analysis process, while this method is based on Monte-Carlo and large number of simulation times, which delivers low efficiency extremely. As we have known, systems unreliability is always resulted from all kinds of random factors, so this paper presents a special reliability analysis method for a flight control actuator system under stochastic processes. First, we introduce the concept of the stochastic processes briefly, then we give an expression model for the stochastic wind, based on the mathematical model and load model, and suppose all the uncertainties come from the stochastic wind, we analyze the effect of the stochastic load for the actuator rotation angle. Furthermore, we select some performance characters as the criteria and calculate the actuator system reliability under the stochastic load. Finally, we create the mathematical model and stochastic wind model in Matlab, and compare the reliability value getting through simulation and analysis method, result shows that this method is feasible.

Reliability modeling for dependent competing failure processes with mutually dependent degradation process and shock process

Many systems experience dependent competing failure processes resulting from simultaneous exposure to degradation processes and random shocks. Moreover, the degradation process and shock process may be mutually dependent. On the one hand, shocks can cause sudden degradation increments, which accelerate degradation process. On the other hand, the occurrence intensity of shock process will increase with the accumulation of degradation. Due to the mutual dependence between degradation and random shocks, the arrival shocks can cause abrupt degradation and then facilitate the occurrence of random shocks recursively. Therefore, the intensity is dependent on the number of arrival shocks, and the shock process cannot be described by the Poisson process used in previous studies. In this paper, a Facilitation model, which is a special type of Markov point process, is introduced to model the shock process. Furthermore, based on the Facilitation model, a novel analytical reliability model with the mutual dependence is developed. A case of a jet pipe servo valve is presented to demonstrate the developed model. The result showed that the reliability declines significantly when considering the mutual dependence.

Research on an integrated methodology of the dynamic performance and reliability evaluation

Dynamic performance and reliability of systems are influenced by many dynamic factors and most of them are dynamic processes with stochastic characteristics. The static techniques of reliability analysis are difficult to assess the dynamic reliability accurately. In addition, despite the fact that classical probabilistic dynamics in the field of dynamic reliability can be used to solve the problems of dynamic reliability, it must depend on the function of physical parameters strictly which is relative to random loads, initial variables or time. So this paper proposes an integrated methodology of the dynamic performance reliability evaluation which can take into account all kinds of random factors and does not need function express. Firstly, dynamic factors can be classified as structure state factor and physics parameter factor. And Markov model of systems is constructed based on structure state factor, the catastrophic failure of components or structure redundancy. Then, physics parameter factors are imported as a random factor to the probabilistic dynamics model. Discrete physics parameters can be obtained through simulation of dynamic systems. Finally, these discrete parameters and state probability computed using Markov models are substituted into probability dynamics model. Then the failure rate and reliability with time forward are achieved. The applicability and effectiveness of this method are demonstrated by the quadruple redundancy Electro-Hydrostatic Actuator (EHA) system.