Time-Dependent Reliability Sensitivity Analysis for Performance Degradation Mechanism

Development of clustered polynomial chaos expansion model for stochastic hydrological prediction

Improving parameter estimation with an efficient sequential probabilistic collocation-based optimal design method

Corrosion is one of the most critical failure mechanisms for engineering structures and systems, as corrosion damages grow with the increase of service time, thus diminish system reliability gradually. Despite tremendous efforts, effectively carrying out reliability analysis considering the complicated coupling effects for corrosion remains to be a grand challenge. There is a substantial need to develop sophisticated corrosion reliability models and effective reliability analysis approaches considering corrosion damage growth under coupled effects such as mechanical stresses. This paper presents a physics-of-failure model for pitting corrosion with the coupled effect of corrosion environment and mechanical stresses. With the developed model, corrosion damage growth can be projected and corrosion reliability can be analyzed. To carry out corrosion reliability analysis, the developed pitting corrosion model can be formulated as time-dependent limit state functions considering pit to crack transition, crack growth, and fracture failure mechanics. A newly developed maximum confidence enhancement (MCE)-based sequential sampling approach is then employed to improve the efficiency of corrosion reliability analysis with the time-dependent limit state functions. A case study is presented to illustrate the efficacy of the developed physics-of-failure model for corrosion considering the coupled mechanical stress effects, and the new corrosion reliability analysis methodology.

Time-dependent reliability (failure probability) aims at measuring the probability of the normal (abnormal) operation for structure/mechanism within the given time interval. To analyze the maximum probable life time under a required time-dependent failure probability (TDFP) constraint, an inverse process corresponding to the time-dependent reliability is proposed by taking the randomness of the input variables into consideration. The proposed inverse process employs the monotonicity between the TDFP and the upper boundary of the given time interval which reflects the life time, and an adaptive single-loop sampling meta-model for the time-dependent limit state function is presented to estimate the TDFP at the given time interval flexibly. Since the TDFP is generally monotonic to the upper boundary of the given time interval, thus by adjusting the probable upper and lower boundaries of the time interval in which the corresponding TDFPs include the required TDFP constraint, the proposed approach can always search the maximum probable life time at the required TDFP by the dichotomy. By introducing the time variable as an input which is the same level as the input random variables and constructing the adaptive single-loop sampling meta-model for the time-dependent limit state function in a longer time interval with the TDFP bigger than the required TDFP, the TDFP in any subintervals of the time interval involved in the constructed meta-model can be estimated as a byproduct of the constructed meta-model without any additional actual limit state evaluations. Then the efficiency for analyzing the maximum probable life time is improved by the dichotomy and the unified meta-model of the time-dependent limit state function. Two examples are employed to illustrate the accuracy and the efficiency of the proposed approach.

Uncertainty in ocean environmental parameters is often the dominant source of uncertainty in an underwater acoustic field calculation. In addition, the relationship between environmental parameters and the resulting field prediction may be highly nonlinear, leading to the explicit determination of the resulting field uncertainty uneasy. The direct Monte Carlo (MC) sampling method which is conventionally used to compute the field uncertainty is computationally prohibitive. To overcome the drawbacks of the existing methods, this paper proposed a Probabilistic Collocation Method (PCM) based method to propagate the uncertainty efficiently. The basic concept of the method is to represent the random acoustic field by Polynomial Chaos Expansions (PCE) and to calculate the coefficients in the PCE using PCM. Statistical properties can then be obtained from the PCE easily. Computer simulations show that PCM can propagate the uncertainty efficiently when the distribution of the result acoustic is unimodal.

In this study, we present an efficient approach, called the probabilistic collocation method (PCM), for uncertainty analysis of flow in unsaturated zones, in which the constitutive relationship between the pressure head and the unsaturated conductivity is assumed to follow the van Genuchten‐Mualem model. Spatial variability of soil parameters leads to uncertainty in predicting flow behaviors. The aim is to quantify the uncertainty associated with flow quantities such as the pressure head and the effective saturation. In the proposed approach, input random fields, i.e., the soil parameters, are represented via the Karhunen‐Loeve expansion, and the flow quantities are expressed by polynomial chaos expansions (PCEs). The coefficients in the PCEs are determined by solving the equations for a set of carefully selected collocation points in the probability space. To illustrate this approach, we use two‐dimensional examples with different input variances and correlation scales and under steady state and transient conditions. We also demonstrate how to deal with multiple‐input random parameters. To validate the PCM, we compare the resulting mean and variance of the flow quantities with those from Monte Carlo (MC) simulations. The comparison reveals that the PCM can accurately estimate the flow statistics with a much smaller computational effort than the MC.

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Here, we examine the suitability of truncated Polynomial Chaos Expansions (PCE) and truncated Gram-Charlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents.These two methods rely on truncated Galerkin projections of either the system variables in a fixed polynomial basis spanning the 'uncertain' subspace (PCE) or a suitable eigenfunction expansion of the joint probability distribution associated with the uncertain evolution of the system (GrChE).Based on a simple, statistically exactly solvable non-linear and non-Gaussian test model, we show in detail that methods exploiting truncated spectral expansions, be it PCE or GrChE, have significant limitations for uncertainty quantification in systems with intermittent instabilities or parametric uncertainties in the damping.Intermittency and fat-tailed probability densities are hallmark features of the inertial and dissipation ranges of turbulence and we show that in such important dynamical regimes PCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique utilized earlier by the authors in a different context for UQ within a framework of Empirical Information Theory.Moreover, we show that the non-realizability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times.These limitations of the two types of truncated spectral expansions arise from the following: (i) Non-uniform convergence in time of PCE and GrChE resulting in a rapidly increasing number of terms necessary for a good approximation of the random process as time evolves, (ii) Fundamental problems with capturing the constant flux of randomness due to white Gaussian noise forcing via finite truncations of the spectral representation of the associated Wiener process, (iii) Slow decay of PCE and GrChE coefficients in the presence of intermittency, hampering implementation of sparse truncation methods which have been widely used in nearly elliptic problems or in low Reynolds number flows.Rigorous justification of these limitations is richly illustrated by straightforward tests exploiting a simple nonlinear and non-Gaussian but statistically exactly solvable test model which is proposed here as a challenging benchmark for algorithms for UQ in systems with intermittency.

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

During the service of the missile suspension structure, the unexpected fatigue failure is emerged because of the dimension dispersibility resulting from machining deviation and design tolerance. In order to get the main factor of failure, based on the moment method of structural reliability assessment and PCL (Patran Command Language) redevelopment technology of finite element parameter analysis, an effective method is proposed to perform the missile suspension structure fatigue life reliability and parameter sensitivity analysis. Using proposed method, the result of reliability and parameter sensitivity analysis can be got readily with only 81 samples of finite element analysis. Compared with Monte-Carlo, proposed method in this paper is more effective with deducing the number of samples, especially fit for some structural reliability and parameter sensitivity analysis under implicit limit state equation.

Reliability sensitivity analysis for water hammer-induced stress failure of fluid-conveying pipe

This study presents an innovative method to estimate the reliability sensitivity based on the low-discrepancy sampling which is a new technique for structural reliability analysis. Two advantages are contributed to the method: one is that, by developing a general importance sampling procedure for reliability sensitivity analysis, the partial derivative of the failure probability with respect to the distribution parameter can be directly obtained with typically insignificant additional computations on the basis of structural reliability analysis; and the other is that, by combining various low-discrepancy sequences with the above importance sampling procedure, the proposed method is far more efficient than that based on the classical Monte Carlo method in estimating reliability sensitivity, especially for problems of small failure probability or problems that require a large number of costly finite element analyses. Examples involving both numerical and structural problems illustrate the application and effectiveness of the method developed, which indicate that the proposed method can provide accurate and computationally efficient estimates of reliability sensitivity.

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross-polarization of an inset-fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high-volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem-specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte-Carlo analysis.