Ning-Cong Xiao

An Approach to Reliability Assessment Under Degradation and Shock Process

Product performance usually degrades with time. When shocks exist, the degradation could be more rapid. This research investigates the reliability analysis when typical degradation and shocks are involved. Three failure modes are considered: catastrophic (binary state) failure, degradation (continuous processes), and failure due to shocks (impulse processes). The overall reliability equation with three failure modes is derived. The effects of shocks on performance are classified into two types: a sudden increase in the failure rate after a shock, and a direct random change in the degradation after the occurrence of a shock. Two shock scenarios are considered. In the first scenario, shocks occur with a fixed time period; while in the second scenario, shocks occur with varying time periods. An engineering example is given to demonstrate the proposed methods.

A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis

Abstract Surrogate models are often used to alleviate the computational burden for structural systems with expensively time-consuming simulations. In this paper, a new adaptive surrogate model based efficient reliability method is proposed to address the issues that many existing adaptive sequential sampling reliability methods are limited to the Kriging models and Krging model-based Monte Carlo simulation (MCS) reliability methods produce random results even without considering the uncertainty from initial samples. Three learning functions are developed for selecting the most suitable training sample points at each iteration, and the learning functions ψσ and ψm are generally suggested because they were found to perform a bit better in most of the cases. Furthermore, most of the newly selected training sample points are ensured to reside far away from existing sample points and reside as close to the limit-state functions as possible. Two stopping criterions are given to terminate the proposed adaptive sequential sampling algorithm. The main advantages of the proposed method are that it not only provides an efficient manner for structural reliability analysis with multiple failure modes to produce a determined result under without considering the uncertainty from initial samples, but also can be used, in principle, in any existing surrogate models. The accuracy and efficiency as well as applicability of the proposed method are demonstrated using three numerical examples.

Fuzzy Sets Method of Reliability Prediction and Its Application to a Turbocharger of Diesel Engines

Diesel engine is a complex electromechanical system which must operate reliably in harsh working environments. Reliability analysis and prediction play an important role during the design and development of diesel engines. However, in the traditional reliability methods, the analytical result obtained from the conventional failure mode, effects, and criticality analysis (FMECA) is not sufficient, which not only increases the workload of designers in charge of reliability, but also prolongs the product delivery time. This paper performs an in-depth reliability analysis with an emphasis on predicting the lifetime of diesel engines turbocharger, in which the failure mode and the information of criticality provided by FMECA are fully utilized to carry out the reliability predictions. Meanwhile, to ensure the reliability prediction quality, this paper takes into account the expert knowledge and provides a possibility-based prediction model, in which the fuzzy analytic hierarchy process and the fuzzy comprehensive evaluation are combined to assess the criticality of the FMECA.

An efficient method for evaluating the effect of input parameters on the integrity of safety systems

Safety systems are significant to reduce or prevent risk from potentially dangerous activities in industry. Probability of failure to perform its functions on demand (PFD) for safety system usually exhibits variation due to the epistemic uncertainty associated with various input parameters. This paper uses the complementary cumulative distribution function of the PFD to define the exceedance probability (EP) that the PFD of the system is larger than the designed value. Sensitivity analysis of safety system is further investigated, which focuses on the effect of the variance of an individual input parameter on the EP resulting from epistemic uncertainty associated with the input parameters. An available numerical technique called finite difference method is first employed to evaluate the effect, which requires extensive computational cost and needs to select a step size. To address these difficulties, this paper proposes an efficient simulation method to estimate the effect. The proposed method needs only an evaluation to estimate the effects corresponding to all input parameters. Two examples are used to demonstrate that the proposed method can obtain more accurate results with less computation time compared to reported methods.

Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach

In this paper the combinations of maximum entropy method and Bayesian inference for reliability assessment of deteriorating system is proposed. Due to various uncertainties, less data and incomplete information, system parameters usually cannot be determined precisely. These uncertainty parameters can be modeled by fuzzy sets theory and the Bayesian inference which have been proved to be useful for deteriorating systems under small sample sizes. The maximum entropy approach can be used to calculate the maximum entropy density function of uncertainty parameters more accurately for it does not need any additional information and assumptions. Finally, two optimization models are presented which can be used to determine the lower and upper bounds of systems probability of failure under vague environment conditions. Two numerical examples are investigated to demonstrate the proposed method.

Surrogate-model-based reliability method for structural systems with dependent truncated random variables

Calculating probability of failure and reliability sensitivity for a structural system with dependent truncated random variables and multiple failure modes efficiently is a challenge mainly due to the complicated features and intersections for the multiple failure modes, as well as the correlated performance functions. In this article, a new surrogate-model-based reliability method is proposed for structural systems with dependent truncated random variables and multiple failure modes. Copula functions are used to model the correlation for truncated random variables. A small size of uniformly distribution samples in the supported intervals is generated to cover the entire uncertainty space fully and properly. An accurate surrogate model is constructed based on the proposed training points and support vector machines to approximate the relationships between the inputs and system responses accurately for almost the entire uncertainty space. The approaches to calculate probability of failure and reliability sensitivity for structural systems with truncated random variables and multiple failure modes based on the constructed surrogate model are derived. The accuracy and efficiency of the proposed method are demonstrated using two numerical examples.

An Application of Fuzzy Fault Tree Analysis to Uncontained Events of an Areo-Engine Rotor

Abstract Fault tree analysis is an important tool for system reliability analysis. Fuzzy fault tree analysis of uncontained events for aero-engine rotor is performed in this article. In addition, a new methodology based on fuzzy set theory is also used in fault tree analysis to quantify the failure probabilities of basic events. The theory of fuzzy fault tree is introduced firstly. Then the fault tree for uncontained events of an aero-engine rotor is established, in which the descending method is used to determine the minimal cut sets. Furthermore, the interval representation and calculation strategy is presented by using the symmetrical L-R type fuzzy number to describe the failure probability, and the resulting fault tree is analyzed quantitatively in the case study.

Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties:

Due to epistemic uncertainty, precisely determining parameters of all distribution is impossible in engineering practice. In this article, a novel reliability analysis method based on the saddlepoint approximation is proposed for structural systems with parameter uncertainties. The proposed method includes four main steps: (1) sampling for random and probability-box variables, (2) approximating the cumulant generating functions for systems under the best and worst cases, (3) calculating saddlepoints for the best and worst cases, and (4) calculating the lower and upper bounds of the probability of failure. The proposed method is effective because it does not require a large sample size or solving complicated integrals. Furthermore, the proposed method provides results that have the same accuracy as the existing interval Monte Carlo simulation method, but with significantly reduced computational effort. The effectiveness of the proposed method is demonstrated with three examples that are compared against with the interval Monte Carlo simulation method.

Non-probabilistic reliability sensitivity analysis of the model of structural systems with interval variables whose state of dependence is determined by constraints

Non-probabilistic reliability sensitivity analysis for structural systems plays an important role in determining key design variables that affect structural reliability strongly. Traditional non-probabilistic model assumes that all interval variables are mutually independent. However, this assumption may not be true in practical engineering. In this article, the dependency of interval variables is introduced into the non-probabilistic model by using both inequality and equality constraints. The non-probabilistic index model and optimization method for structural systems with interval variables, whose state of dependence is determined by constraints, are proposed on the basis of the existing non-probabilistic index theory. The linear optimization model is alternative when nonlinear optimization model cannot find any solution. Non-probabilistic reliability sensitivity analysis model and optimization method for structural systems, with the interval variables whose state of dependence is determined by constraints, are established based upon the finite difference theory. The proposed method is demonstrated via several examples.

Unified uncertainty analysis by the extension universal generating functions

In this paper, a unified uncertainty analysis method based on the extension universal generating function is proposed for engineering problems described by the mixture of random, interval and p-box variables. In the method, the univariate approximation approach is extended for mixed variables, and then the performance function is divided into three parts. Traditional universal generating function can only model the case that all variables exist in system are random variables. However, in order to calculate the bounds of system probability of failure under mixed variables, the mixed universal generating function is developed to extend the traditional universal generating function. The optimization models based on the mixed universal generating function are presented to calculate system probability of failure under mixed variables. An engineering example is used to validate the proposed method.