Structural Reliability Analysis by Stochastic Dependence Models and Matriceal Techniques

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.

For structural reliability analysis with time-consuming performance functions, an innovative design of experiment (DoE) strategy of the Kriging model is proposed, which is named as the stepwise accuracy-improvement strategy. The epistemic randomness of the performance value at any point provided by the Kriging model is used to derive an accuracy measure of the Kriging model. The basic idea of the proposed strategy is to enhance the accuracy of the Kriging model with the best next point that has the largest improvement with regard to the accuracy measure. An optimization problem is developed to define the best next point. The objective function is the expectation that quantifies how much an untried point could enhance the accuracy of the Kriging model. Markov chain Monte Carlo sampling and Gauss–Hermite quadrature are employed to make several approximations to solve the optimization problem and get the best next point. A structural reliability analysis method is also constructed based on the proposed strategy and the accuracy measure employed. Several examples are studied. The results validate the advantages of the proposed DoE strategy.

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.

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.

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.

Direct differentiation method for response sensitivity analysis of a bounding surface plasticity soil model

Any mechanical or civil engineering structure possesses some natural randomness in its properties which fluctuates over space. These can be modelled as random fields for the purpose of robust optimization or reliability analysis. The high number of random variables required to model a random field often inhibits accurate probabilistic analyses based on Monte Carlo methods. The present paper proposes a method to reduce the random space based on both stochastic criteria and structural performance. This way the most relevant variables are identified in order to be used in a subsequent reliability analysis. For computation of reliablity, an adaptive response surface method is introduced, which utilizes improved Moving Least Squares approximations. It is able to model highly nonlinear limit state functions and can be locally refined. The stability of a cylindrical shell with random geometry is studied. A conventional and the proposed new way to reduce the random space are compared. The structure is then analysed by the adaptive response surface method, results are compared to direct directional simualtion. The probabilistic and structural analyses are performed with the optiSLang, SoS and SLang software packages.

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

In this paper, a new method is developed that can be applied efficiently in reliability analysis and design verification of structures under random vibration. This method is based on singular value decomposition of modal coordinates cross covariance matrix. Computational algorithm and relative flow chart for this method is developed and compatible reliability criterion with this algorithm has been extracted. In order to results verification, we use Miles relation and Monte Carlo simulation -that are two well known methods in reliability analysis- and all of these methods are applied to a simple finite element model. Results show that new algorithm is more efficient for reliability analysis of structures under random vibration.

Operators wish to understand the condition of their pipelines to manage ongoing integrity. Information on the condition of the pipeline along its entire length can be obtained using in-line inspection (ILI). However, some pipelines cannot be internally inspected due, for example, to tee connections, tight bends, low flow or to a lack of launcher and receiver facilities. The condition of these ‘unpiggable’ lines can sometimes be largely unknown. To aid the understating of the pipeline condition without ILI data, operators will often rely on alternative sources of information, such as localised external inspections, model predictions and company and individual experience. However, there may be significant uncertainty associated with these alternative data sources when using them to assess the condition of the entire pipeline. This uncertainty may be understood by applying a probabilistic approach to the assessment of pipeline integrity using structural reliability analysis (SRA) methods. An SRA approach applies probabilistic input parameters to a failure prediction model for a defined limit state function. Previous IPC papers[1,2,3] have presented guidance on probabilistic assessments to model pipeline failure. Recommended probability distributions are presented which account for uncertainties associated with line pipe properties, defect sizing and the error associated with the predicted failure model. However, there is little published guidance readily available on recommended defect characteristic distributions specific to internal corrosion features. Parameter distributions are recommended for defect sizing based on empirical data, which are mainly used for external corrosion features. In this paper, a case study is used to present a practical application of an SRA methodology for assessment of pipeline integrity with respect to internal corrosion. Discussion is presented on alternative sources of information for the assessment when ILI data is unavailable, including targeted external inspections of unpiggable lines and data sets from comparable piggable lines. Probability distributions are derived from the available inspection data for the internal corrosion feature size and corrosion rate input parameters to the SRA. Probabilistic analysis is used to account for the expected population of unknown features in the uninspected parts of the pipelines. The expected feature size, corrosion rate and feature density calculated are used in the SRA to estimate the total probability of failure due to internal corrosion over time for the entire length of the pipeline. Recommendations are provided on the application of an SRA methodology to assess pipeline failure due to internal corrosion.

Time-dependent structural system reliability analysis model and its efficiency solution

There have been few researches on the reliability of prestressed steel structure, especially the study on the reliability considering the failure of key components. In order to study the impact of the component failure on the structure reliability, the response surface method based on central composite design is adopted and APDL language is applied to write a corresponding program, thereby carrying out reliability calculation and analysis to the model. The system reliability and parameters sensitivity of the beam string structure under different failure of components are provided. The results indicate that the impact of cable failure on the reliability is large, but it is weak by the failure of brace rod. The results may serve as a reference for the health monitoring and safety assessment of the prestressed steel structure.

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.

System and measurement uncertainties play a key role in finding the reliability of complex and safety-critical structural systems such as buildings and bridges. Current mainstream techniques in structural reliability analysis use an iterative first-order reliability method that performs an indirect uncertainty evaluation by finding the most probable failure point. However, such an approach could lead to high computational time due to slower convergence, and in some cases, poor convergence that leads to unreliable results. In order to address the shortcomings, this paper applies a new high-order moment propagation technique (that was initially developed for the measurement uncertainty analysis) to structural reliability analysis problems aiming to obtain results that are simultaneously accurate and computational efficient. The proposed approach was implemented on a three-story elastic frame structure, and the presented results prove that the application of a technique from the field of measurement uncertainly can indeed be applied to complex problems in the structural reliability analysis in order to reduce the trade-off between accuracy and computational efficiency.

Physics guided wavelet convolutional neural network for wind-induced vibration modeling with application to structural dynamic reliability analysis