Time-dependent Reliability Analysis Method Research Articles

Sequential time-dependent reliability analysis for the lower extremity exoskeleton under uncertainty

This paper proposes a sequential time-dependent reliability analysis method by considering time sequence and correlation of failure processes for the lower extremity exoskeleton under uncertainty, which will provide an approach to improving the comfort and safety for the wearer. A kernel density function based uncertainty quantification method is provided for precisely quantitatively estimating the time-dependent reliability of joints and the position of the end-effector firstly. After decoupling time sequence and failures correlation due to error propagation, the original reliability problem is then transferred to a series time-dependent reliability model. The time-dependent system reliability analysis is finally realized by calculating conditional probability. A case study is implemented to testify the effectiveness of the proposed method.

Snap-Through Buckling Reliability Analysis Under Spatiotemporal Variability and Epistemic Uncertainty

Surrogate models often provide an effective tradeoff between accuracy and efficiency during reliability analysis with expensive physics models. In snap-through buckling reliability analysis, a surrogate model could be built for the critical buckling load, as a function of loading, material properties, geometry, and boundary conditions. However, in the presence of spatiotemporal variability, the response surface of the critical buckling load is often highly nonlinear and irregular, thus rendering commonly used response surface-type surrogate modeling strategies ineffective. This paper proposes a new buckling reliability analysis method based on support vector machines for structures subjected to spatiotemporal variability and in the presence of epistemic uncertainty regarding model inputs and parameters. Bayesian calibration is first used to quantify the epistemic uncertainty in the modeling of spatiotemporal variability under limited data. Upon the modeling of spatiotemporal variability and epistemic uncertainty, a time-dependent reliability analysis method is developed for the snap-through buckling failure by constructing a nonlinear support vector machine classifier. Considering that the computer simulation is computationally expensive and the support vector machine classifier may not be well trained due to limited computational resources, a method is also developed to quantify the uncertainty in the reliability estimate due to classification uncertainty. A curved beam with an uncertain boundary condition, spatially varying cross-section geometry, and spatiotemporally varying loading is used to demonstrate the effectiveness of the proposed method.

A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis

Current surrogate modeling methods for time-dependent reliability analysis implement a double-loop procedure, with the computation of extreme value response in the outer loop and optimization in the inner loop. The computational effort of the double-loop procedure is quite high even though improvements have been made to improve the efficiency of the inner loop. This paper proposes a single-loop Kriging (SILK) surrogate modeling method for time-dependent reliability analysis. The optimization loop used in current methods is completely removed in the proposed method. A single surrogate model is built for the purpose of time-dependent reliability assessment. Training points of random variables and over time are generated at the same level instead of at two separate levels. The surrogate model is refined adaptively based on a learning function modified from time-independent reliability analysis and a newly developed convergence criterion. Strategies for building the surrogate model are investigated for problems with and without stochastic processes. Results of three numerical examples show that the proposed single-loop procedure significantly increases the efficiency of time-dependent reliability analysis without sacrificing the accuracy.

Simplified Method for Time-Dependent Reliability Analysis of Aging Bridges Subjected to Nonstationary Loads

The performance of existing bridges may deteriorate in time due to aggressive environmental or operating conditions in service, which may eventually cause changes in structural resistance and reliability beyond the baseline assumed for new ones. In addition, the increasing trend of live loads applied to the bridges, which has been reported in many researches, also contributes to the reduction of structural reliability. In order to perform time-dependent reliability assessment for aging bridges subjected to nonstationary loading process with improved efficiency, a simplified method is proposed in this paper, where lower dimensional integral is involved in the calculation of reliability. With the proposed method, time-dependent reliability of a real aging RC bridge is conducted, and the effect of nonstationarity in load intensity on structural reliability is investigated. It is found that structural reliability is sensitive to the increase of load intensity, and is less sensitive to the varying mechanism of load intensity.

Time-Dependent Reliability Analysis for Function Generator Mechanisms

A function generator mechanism links its motion output and motion input with a desired functional relationship. The probability of realizing such functional relationship is the kinematic reliability. The time-dependent kinematic reliability is desired because it provides the reliability over the time interval where the functional relationship is defined. But the methodologies of time-dependent reliability are currently lacking for function generator mechanisms. We propose a mean value first-passage method for time-dependent reliability analysis. With the assumption of normality for random dimension variables with small variances, the motion error becomes a nonstationary Gaussian process. We at first derive analytical equations for upcrossing and downcrossing rates and then develop a numerical procedure that integrates the two rates to obtain the kinematic reliability. A four-bar function generator is used as an example. The proposed method is accurate and efficient for normally distributed dimension variables with small variances.

Time-Dependent Reliability Estimation for Dynamic Problems Using a Niching Genetic Algorithm

A time-dependent reliability analysis method is presented for dynamic systems under uncertainty using a niching genetic algorithm (GA). The system response is modeled as a parametric random process. A double-loop optimization algorithm is used. The inner loop calculates the maximum response in time, using a hybrid (global-local) optimization algorithm. A global GA quickly locates the vicinity of the global maximum, and a gradient-based optimizer subsequently refines its location. A time-dependent problem is, therefore, transformed into a time-independent one. The outer loop calculates multiple most probable points (MPPs), which are commonly encountered in vibration problems. The dominant MPPs with the highest contribution to the probability of failure are identified. A niching GA is used because of its ability to simultaneously identify multiple solutions. All potential MPPs are initially identified approximately, and their location is efficiently refined using a gradient-based optimizer with local metamodels. For computational efficiency, the local metamodels are built using mostly available sample points from the niching GA. Among all MPPs, the significant and independent ones are identified using a correlation analysis. Approximate limit states are built at the identified MPPs, and the system failure probability is estimated using bimodal bounds. The vibration response of a cantilever plate under a random oscillating pressure load and a point load is used to illustrate the present method and demonstrate its robustness and efficiency. A finite-element model is used to calculate the plate response.