Model uncertainty in structural reliability

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.

Structural Reliability Analysis (SRA) is a useful tool in structural engineering. Uncertainty in input parameters and model uncertainties in the analysis predictions are explicitly modelled by random variables. With this methodology, the uncertainties involved are handled in a consistent and transparent way. Compared to a deterministic analysis, SRA provides improved insight in how the various uncertainties involved influence the results. The main results from SRA is the calculated probability of structural failure, but other useful results such as uncertainty importance factors and design points being the most likely combination of all variables at failure represent helpful information. The present paper illustrates some the features using SRA for two different types of application. The first application is the use of SRA as a tool for code calibration and the second shows the application of SRA to a problem where common practice is likely to be rather conservative and therefore leading to unacceptable results, but where the degree of conservatism is not known. Two examples are chosen to illustrate code calibration; i.e. hull girder ultimate limit state (ULS) for tankers and ULS for mooring design in the ULS for floating offshore vessels. Code calibration involves both SRA and design analysis following the code. It is shown how the design analysis can be modified in order to better reflect a chosen target reliability level across a selected set of test cases representative for what the code should cover. Fatigue of subsea wellhead systems is selected as an example of a special case when application of existing rules may lead to unsatisfactory results which are likely to be rather conservative. It is shown how results can be presented in terms of the accumulated probability of fatigue failure as a function of time. This may be a more suitable basis for decision making than a calculated fatigue life from a standard analysis. It is also illustrated how importance factors from the SRA can be used as guidance on how to prioritize effort in order to improve prediction of the fatigue damage. The present paper is not intended to be detailed in all input and analysis methodology, but draw the attention towards the possibilities and benefits of applying SRA in structural engineering, where the examples are used to illustrate this potential.

: 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.

Due to the existing of various kinds of uncertainties, predicting structural performance is always a great challenge in practical applications. The reliability of structure under the probabilistic uncertainty has been well studied in the past decade. However, the randomness is not the only attribute of reality. This paper attempts to investigate approach for the structural reliability analysis via the fuzzy safety state which is defined by state variable and fuzzy random allowable interval. The fuzziness of safety criterion, the fuzziness and randomness of generalized stress and generalized strength are considered in the limit state models, and the membership function of the fuzzy structural reliability are derived by the defined fuzzy safety state.

This paper focuses on a reliability analysis of an offshore wind turbine support structure which is part of an assessment and monitoring framework for wind turbines in operation. The reliability analysis builds upon structural, loading, limit state and uncertainty models comprising design, production and erection data. This model basis facilitates the reliability analysis of the ultimate, the fatigue and the serviceability limit states utilizing stochastic finite elements. The complexity of the individual models dictates an efficient solution scheme for the reliability analysis. Such an algorithm is developed in the present paper consisting of an adaptive response surface algorithm and an importance sampling Monte-Carlo algorithm. The response surface algorithm is based on predetermined experimental designs and facilitates the adjustment of design parameters for an optimized prediction variance in the design point region. Approaches for the consideration of multiple design points and the augmentation of the design for reduction of the prediction variance are introduced. In this paper, a reliability analysis for a tripod support structure of a Multibrid M5000 wind turbine is performed. A comparison with the target reliabilities specified in DIN EN 1990 (2002) shows that the requirements are fully met. However, the consideration of system reliability leads to the conclusion that at the end of the service life there is a significant probability of fatigue damages. The quantification of the reliability for the individual structural components for all limit states facilitates an identification of sensitive components. The results of this study can support the targeted application of monitoring systems, the optimization of the support structures and additionally highlight the need for criteria to the systems reliability.

PurposeBecause of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).Design/methodology/approachIn DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.FindingsThe computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.Originality/valueThis paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

The probability density evolution of structural dynamic prediction models under several times random loads are proposed in this paper. Firstly, the probability density of several times stochastic loads can be obtained from the probability density of single time stochastic load. The prediction models of structural reliability from time responses under several times stochastic loads with and without strength degeneration over time are derived using the stress-strength interference theory and probability density evolution method. The differential equation in the models can be solved using the forward finite difference method. The probability density functions of the structural strength redundancy at any time can be obtained. In the end, structural dynamic reliability can be calculated using integral method. The efficiency of the proposed method is demonstrated numerically through a speed reducer. The results have shown that the proposed method is practicable, feasible and gives reasonable accurate prediction.

Some transmission structures exhibit important geometric and material nonlinearities that should be considered in their analysis and design. Unless simplifying assumptions are made, reliability analysis of these structures is complex and can be very computer-time intensive. This paper describes an approximate method to conduct reliability analysis of nonlinear transmission structures. It is shown that for most transmission structures, the design point is close to the 50-year return period loads. Using this result, approximate g-functions for nonlinear problems are obtained with minimum computational effort. It is also shown that when the material strengths are highly correlated, g-functions that include interaction of axial load and bending moments may be reduced to g-functions with no interaction. These simplifying results are implemented in a microcomputer program, RELIAB, which can handle complex transmission structures such as large latticed structures, tension-only structures, or structures that exhibit nonlinearities. RELIAB's accuracy is ascertained by comparing results with another computer program, TRANSREL, which accounts for the residual strength of latticed towers following progressive failure of one or more components.

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

The limit state function (LSF) is implicit to many structure reliability analysis problems, which may make some classical reliability method complicated to be applied. One of the surrogate methods-support vector classification (SVC) was applied in the structural reliability analysis herein which has not been applied to structure reliability analysis until recent years. Then the advanced first order second moment method (AFOSM) can be applied. The expressions of structure system reliability sensitivity to basic variable were deduced. The flow of how to call the SVC program was presented. An example was shown to compare the SVC based method with some other classical reliability analysis methods. The results are accurately accepted and the advantages of SVC are analyzed.

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

Effect of maintenance on structural reliability

Power overhead line regulations and codes generally apply prescriptive methods to the design of structures using working loads multiplied by factors of safety. In contrast, the probabilistic method is founded on designing to a limit state in which strength is matched to stress, with the risk of failure defined by the overlap of the distributions of the limit state model. This work indicates how a stress limit state using probability concepts can be applied to the design of round pole distribution line structures. It indicates that unlike the transmission line, variations which occur in the layout of distribution lines necessitate the use of some contingency factors. Design studies of new and existing lines show that there are substantial savings to be made.

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.