A space-probabilistic separation approach for Structure Static reliability analysis (original) (raw)
Related papers
Probabilistic Computational Methods in Structural Failure Analysis
Probabilistic methods are used in engineering where a computational model contains random variables. Each random variable in the probabilistic calculations contains uncertainties. Typical sources of uncertainties are properties of the material and production and/or assembly inaccuracies in the geometry or the environment where the structure should be located. The paper is focused on methods for the calculations of failure probabilities in structural failure and reliability analysis with special attention on newly developed probabilistic method: Direct Optimized Probabilistic Calculation (DOProC), which is highly efficient in terms of calculation time and the accuracy of the solution. The novelty of the proposed method lies in an optimized numerical integration that does not require any simulation technique. The algorithm has been implemented in mentioned software applications, and has been used several times in probabilistic tasks and probabilistic reliability assessments.
A method for the reliability analysis of structural systems of medium complexity is proposed. The aim is to reduce the necessary computing effort for an accurate evaluation of the failure probabilities of the structure and its elements. This is achieved through domain decomposition (partitioning) of the probabilistic space and subsequent biased sampling in the areas close to the fail-safe surface. The results from the proposed algorithm are compared with those obtained from Monte Carlo simulation and the performance of the method is examined. In particular, the reliability of "optimal" deterministic designs based on the provisions of Eurocodes is investigated. Moreover, the robustness and computing efficiency of the method is examined for a non-linear limit state function and a 31-bar truss. Two parametric studies are performed with respect to the parameters of the method and the effects of indeterminacy on the reliability index of the structure are outlined.
1995
The article begins by examining the fundamentals of traditional deterministic design philosophy. The initial section outlinu the concepts of failure criteria and limit state functions, two traditional notions that an embedded in dctcrministic design philosophyy. This is followed by a discussion regarding safety factors (a possible limit state function) and the common utilization of starktical concepts in deterministic engineering design approaches. Next. the fundamental aspects of a probabilistic failure alpi is arc explored, and it k shown that dettnninistic design concepts mentioned in the i n i t i a l podon of the axticlc arc embedded in probabilistic design methods. For components fabricated from ceramic materials (and other similarly bxittle materials) the probabilistic design approach yields the widely used Weibull analysis after suitable assumptions arc incorporated. The authors point out that Weibull analysis provides the rare instance where closed form solutions arc available for a probabilistic failure analysis. Since numerical methods a n usually rcquirrd to evaluate component rcliabilities, a section on Monte Carlo methods is included to introduce the concept. The article concludes with a presentation of the technical aspects that support the numerical methodknown as fast probability integration (FPI). T h i s includes a discussion of the Hasofcr-Lind and Rackwitz-Ficssler approximations.
The paper is focused on the newly developed probabilistic method of Direct Optimized Probabilistic Calculation – DOProC, which seems to be very effective for solving a number of probabil-istic tasksand probabilistic reliability assessments. The calculation, which does not use any of simulation techniques, solve the resulting probability purely numerical way using optimized numerical integration. Computational procedure of DOProC method is based on the basic concepts of probability theory. The accuracy of the solution is only influenced by numerical errors and error arising from the discretization of input and output variables. For application of DOProC method can currently use the program system so-called ProbCalc, which is still being developed. Using ProbCalc is possible to implement relatively easy analytical and numerical transformation model of the probabilistic tasks under the solution. The input random quantities (such as load, geometry, material properties, or imperfections) can be in the DOProC method as with the other probabilistic calculations expressed by histograms with nonparametric (empirical) or parametric probability distribution. Statistical correlation of random input statistically dependent variables can be expressed in the DOProC method using the so-called multidimensional histograms, which can be used to determine the numerical correlation index for characterization of the dependence not only for the linear relationship between two variables, but also for nonlinear dependence, or even for more than two random variables.
Errors and uncertainties in probabilistic engineering analysis
NASA CONFERENCE …, 2001
The developing field of probabilistic design has matured to the point where several classes of analysis methods have been proven to be useful for engineering analysis of large high fidelity structures with uncertain parameters. However, several barriers still stand in ...
Structural Reliability Assessment using a Direct Determined Probabilistic Calculation
Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing, 2009
The Direct Determined Fully Probabilistic Method ("DDFPM") is newly developed probabilistic numerical calculation usable especially in the assessment of structural reliability. The random input variables (such as the load, geometry, material properties, or imperfections) can be expressed by means of histograms with parametric and non-parametric distribution created from sets of random quantities that have been measured or observed.
Probabilistic safety analysis of structures under hybrid uncertainty
International Journal for Numerical Methods in Engineering, 2007
The probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives.
A convex model approach for structure non-probabilistic reliability analysis
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2017
In this article, a novel approach, that is, convex model method of set theory, is proposed to investigate the non-probabilistic reliability of bridge crane. Considering the metal structure system of the bridge crane, the finite element method is applied to obtain the stress response of the structure dangerous point. Then, the sample of stress response of the structure danger point and uncertain parameters are obtained. Finally, based on support vector machines, the structure implicit regression function of the system is replaced by explicit expression that calculates the non-probabilistic reliability of the structure. Results show that this approach is useful and efficient to solve the problem of non-probabilistic reliability in the metal structure.
Finite element system modeling and probabilistic methods application for structural safety analysis
A probability-based approach is presented as the integration of probabilistic methods and deterministic modelling based on the finite element method. An existing finite element software package was linked to an existing probabilistic package to analyze the complex mechanics and to perform the transient nonlinear analysis of impact problems. The developed methodology is applied to the analysis of a whipping group distribution header and subsequent impacts with adjacent headers; this is a postulated accident for the Ignalina Nuclear Power Plant RBMK-1500 reactors. The uncertainties of material properties, component geometry data and loads were taken into consideration. The probabilities of failure of the impacted header and of the header support-wall from uncertainties in material properties, geometry parameters and loading were estimated.