Structural reliability analysis based on probability and probability box hybrid model

A new hybrid reliability analysis technique based on the convex modeling theory is developed for structures with multi-source uncertainties, which may contain randomness, fuzziness, and non-probabilistic boundedness. By solving the convex modeling reliability problem and further analyzing the correlation within uncertainties, the structural hybrid reliability is obtained. Considering various cases of uncertainties of the structure, four hybrid models including the convex with random, convex with fuzzy random, convex with interval, and convex with other three are built, respectively. The present hybrid models are compared with the conventional probabilistic and the non-probabilistic models by two typical numerical examples. The results demonstrate the accuracy and effectiveness of the proposed hybrid reliability analysis method.

RFOR-DQHFEM: Hybrid relaxed first-Order reliability and differential quadrature hierarchical finite element method for multi-physics reliability analysis of conical shells

Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.

In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method.

Interval reliability analysis under the specification of statistical information on the input variables

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

The possibility of applying the measure of information uncertainty (entropy) in structural reliability analysis of electricity distribution networks is assessed. The essential factors influencing the process of reliability analysis and related to the presence of information uncertainty are highlighted. The peculiarities of reliability analysis in network designing and operation, when it is required to estimate the state of elements and choose the efficient structure of a network are considered. The opportunities and limitations in the application of existing methods of structural reliability analysis are evaluated; it proves the importance of information uncertainty measurement. The conceptual apparatus of entropy includes the mathematical procedure of its calculation. Fail-safe operation probability and probability of network element failure are taken as reliability index. The mathematical expressions proposed for calculating entropy are applicable when there are two independently functioning network elements, each of which will be able to be in one of two states with a fraction of probability: operable and non-operable. The obtained results allowed identifying the more reliable elements/objects. The application of the proposed mathematical procedure allows to compare network elements with each other through the value of entropy and to choose the most reliable ones. Thus, the proposed solution is a preliminary step in the uncertainty removal task.

Structural performance of the Nigerian grown Abura timber bridge beam subjected to compression and shearing forces

High-speed rolling bearing lubrication reliability analysis based on probability box model

A structural reliability analysis was performed on concrete masonry under axial compression using the First Order Reliability Method (FORM) to assess the reliability levels under the current (2004) and preceding (1994) editions of the Canadian masonry design standard S304.1. The Hasofer–Lind reliability index was evaluated at different live-to-dead load and snow-to-dead load ratios using the Rackwitz–Fiessler procedure. The reliability analysis revealed that neither the masonry material resistance factor of 0.6 adopted in the current Canadian masonry design standard (S304.1-04) nor the previous value of 0.55 in its predecessor (S304.1-94) achieve acceptable reliability levels for masonry in compression under combined dead and live or snow loads. Reliability levels close to the target reliability index recommended by the Canadian standard S408-11 and the levels evaluated for concrete in compression designed to the Canadian standard A23.3-04 were achieved when a masonry material resistance factor of 0.5 was used.

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

A dimension-wise analysis driven active learning paired-Kriging (DWA-ALK) method for the hybrid reliability analysis

This paper combines time varying failure rates and Markov chain analysis to obtain a hybrid reliability and availability analysis. However, combining these techniques can, depending on the size of the system, result in solutions of the Markov chain differential matrix equations that are intractable. This paper identifies solutions that are tractable, These form the analytical baseline for the reliability and availability analysis of systems with time varying failure rates. Tractable solutions were found for the 1-component 2-state and the 2-component 4-state configurations. Time varying failure rates were characterized by a general polynomial expression. Constant, linear, and Weibull failure rate functions are special cases of this polynomial. The general polynomial failure rate provides flexibility in modeling the time varying failure rates that occur in practice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

: The Aircraft Structural Reliability and Risk Handbook provides: a) A reference on basic statistics, probability, and reliability techniques required for conducting structural risk and reliability analyses, and b) Illustrative examples of how to apply these techniques to problems involving the nucleation and growth of fatigue cracks in metallic airframe structure. This particular volume describes the fundamentals of probabilistic analysis and structural reliability analysis for the next flight.

A stress-strength interference model in its interval form, with uncertain quantities of structures described by interval numbers, is used for reliability analysis. Such structural reliability analysis problem is called structural interval reliability analysis. A discrete possibility degree method for structural interval reliability is proposed. By comparing equally-spaced-points of structural interval stress value and structural interval strength value, a partition for comparison relations (big, equal or small) between interval stress and interval strength is built. Based on this partition, new concepts for interval reliability analysis are defined, such as structural safety possibility degree and structural failure possibility degree, etc. By one simple example, the feasibility and effectiveness of discrete possibility degree method for structural interval reliability are demonstrated.