On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

STABILITY MARGIN OF SYSTEMS WITH MIXED UNCERTAINTIES UNDER THE IQC DESCRIPTIONS

Stability perturbation bounds problem for systems with mixed uncertainties is discussed. It is supposed that the linear part in the forward loop is of parametric uncertainties described by interval perturbation mode, and that the nonlinear part in the feedback loop is characterized by an integral quadratic constraint (IQC). The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional. The infinite stability checking problem of the mixed uncertain system can be converted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave junctions and their properties. The result is illustrated to be efficient through an example.

A new structural reliability analysis method in presence of mixed uncertainty variables

For structures with both random and fuzzy uncertainty,this paper presents a novel method for determining the membership function in fuzzy reliability with the Automatic Updating Extreme Response Surface(AUERS)method.In the proposed method,fuzzy variables are initially converted into a value domain under the given cut level and the extreme point in the domain where the reliability reaches its extreme value is considered.Second,the Particle Swarm Optimization(PSO)algorithm is used to determine the extreme point according to the extreme responses for different sets of random sample inputs.A kriging response surface is subsequently constructed between the random variables and the corresponding extreme points.An automatic updating strategy is then introduced based on the Relative Mean Square Predicted Error(RMSPE)before performing every iteration of reliability analysis.By adding new sample points,the approximate quality of the kriging response surface is improved.Finally,reliability analysis is used to determine the reliability bound under the given cut level.The proposed method assures the accuracy and computation efficiency of the mixed uncertainty reliability analysis results while it prevents the solution from becoming trapped in a local optimum,which occurs in classical optimization methods.Two example analyses are used to demonstrate the validity and advantages of the proposed method.

Progress on the Use of Stable Isotope Techniques in Catchment Hydrograph Separation: A Review

Hydrograph separation is a fundamental catchment descriptor,revealing information about sources of water in runoff generation processes. The water isotopes are ideal tracers in studying hydrological processes since the isotope fractionation produces a natural labeling effect within the hydrologic cycle. The water isotope technique has become one of effective means for investigating complex hydrologic system on a catchment scale. This paper reviews the progress on the use of stable water isotope techniques in catchment hydrograph separation in last decades. Also,the isotope mixing model for hydrograph separation and its uncertainties are explained in detail. In future research,there are three hot issues in the use of isotopic hydrograph separation（ IHS） ： integrating new approaches into IHS,calibration and verification of IHS model and IHS application in large river basins.

Response-surface-based structural reliability analysis with random and interval mixed uncertainties

Traditional reliability analysis requires probability distributions of all the uncertain parameters.However,in many practical applications,the variation bounds can be only determined for the parameters with limited information.A complex hybrid reliability problem then will be caused when the random and interval variables coexist in a same structure.In this paper,by introducing the response surface technique,we develop a new hybrid reliability method to efficiently compute the interval of the failure probability of the structure due to the probability-interval hybrid uncertainty.The present method consists of a sequence of iterations.At each step,a response surface model is constructed for the limit-state function by using a quadratic polynomial and a modified axial experimental design method.An approximate hybrid reliability problem is created based on the response surface model,which is subsequently solved by an efficient decoupling approach.An updating strategy is suggested to improve the quality of the response surface and whereby ensure the reliability analysis precision.A computational procedure is then summarized for the whole iterations.Four numerical examples and also a practical application are provided to demonstrate the effectiveness of the present method.