Reliability of Transmission Structures Including Nonlinear Effects

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.

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.

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.

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.

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.

An efficient stochastic finite element method is proposed for the reliability analysis of nonlinear frame structures using the first-order second-moment reliability method. The assumed stress-field approach is used in computing nonlinear structural responses and the corresponding response gradients. Both geometric and material nonlinearities of structures are considered. The flexibility of a connection is represented by its moment-relative rotation relationship. Emphasis is placed on the comparison of the reliability indexes of linear structures, nonlinear structures, and nonlinear structures with flexible connections. Both the strength (combined axial compression and bending) and serviceability (deflection) limit states are considered. For stability-related structures, nonlinearity has a considerable influence on the structural reliability, and the reliability will be very different when the flexible connections are taken into consideration. The method is verified using the Monte Carlo simulation technique. The applicability, accuracy, efficiency, and robustness of the method are verified with the help of an example.

A method of determining the micro-cantilever residual stress gradients by studying its deflection and curvature is presented. The stress gradients contribute to both axial load and bending moment, which, in prebuckling regime, cause the structural stiffness change and curving up/down, respectively. As the axial load corresponds to the even polynomial terms of stress gradients and bending moment corresponds to the the odd polynomial terms, the deflection itself is not enough to determine the axial load and bending moment. Curvature together with the deflection can uniquely determine these two parameters. Both linear analysis and nonlinear analysis of micro-cantilever deflection under axial load and bending moment are presented. Because of the stiffening effect due to the nonlinearity of (large) deformation, the difference between linear and nonlinear analyses enlarges as the micro-cantilever deflection increases. The model developed in this paper determines the resultant axial load and bending moment due to the stress gradients. Under proper assumptions, the stress gradients profile is obtained through the resultant axial load and bending moment.

The aim of the paper is to present a methodology for the assessment of the structural reliability of an oil tanker damaged in a hypothetical grounding accident in the Adriatic Sea. The grounding accident affects the ultimate hull girder capacity in the damaged region, the still water bending moment (SWBM) distribution along the vessel as well as the vertical wave bending moments (VWBM). The extent of the damage on the ship’s hull after a grounding accident depends on several parameters such as ship‘s speed, rock size, penetration depth, longitudinal and transversal location of stranding along the hull. These parameters are in the present study assumed as random variables, described by probability density functions. Based on defined statistical properties, random realizations of grounding parameters are simulated by Monte Carlo (MC) simulation. For each such random grounding scenario, the damage size is calculated by the surrogate model based on numerical grounding simulations. Residual ultimate strength and SWBM distribution are determined based on the size and location of the damage. VWBM is calculated for average sea state in the area with increased risk of grounding accident in the Adriatic Sea. Structural reliability analysis is employed to determine the safety index with respect to the ultimate hull girder failure for salvage period of 12 hours. As each grounding scenario results in different hull-girder reliability, histogram of safety indices is obtained representing new measures for the performance assessment of the damaged ship.

An efficient response surface method and its application to structural reliability and reliability-basedoptimization

This paper presents the application of a reliability based design methodology for interference between trawl gear and pipelines, and the associated cost savings in subsea rock installation. As part of Wintershall Norge's Maria development project, a 26 km long 14″ production flowline with DEH (Direct Electrical Heating) and a 46 km (43 km + 3 km infield) long 12″ water injection pipeline has been installed and left exposed on the seabed. The seabed topography in the area is un-even and scarred by iceberg ploughmarks, leading to a significant number of large free spans. Furthermore, fishing activity must be taken into account in the design of these pipelines. According to DNV-RP-F111, if the trawl gear hits in a free span, the pull-over load will be significantly higher than if it hits a section in contact with the seabed. Preliminary analysis indicated that by using the LRFD (Load and Resistance Factor Design) approach as per DNV-RP-F111, a large number of free spans would require rock infill in order to limit the trawl pull-over load. In order to optimize the design and potentially reduce the requirement for free span infill, an optimised methodology based on SRA (Structural Reliability Analysis) was proposed by Wintershall, developed by DNV GL and implemented by Subsea 7 during detail design phase. The optimised methodology involves FE analyses of the sensitivity to various parameters and Monte Carlo simulations, in order to quantitatively assess the probability of failure. Specific FE models analysing the bending moment capacity and response were established. The various input parameters were assessed and included as distributions if deemed required from the sensitivity analysis. Finally, a Monte Carlo simulation was performed to calculate the probability of failure. It was demonstrated that the target safety levels defined by DNV-OS-F101 were reached without free span infill, and hence significant savings in subsea rock installation could be achieved without any deviation from the DNV-OS-F101 code. Cost saving due to reduced subsea rock installation scope is estimated to 7.6 mill Euro. Wintershall facilitated a close dialogue between DNV GL and Subsea 7 throughout the work progress. This resulted in a constructive and open approach, ensuring efficient delivery of the detailed design in line with project schedule. The work carried out has demonstrated two relevant examples where performing a SRA, as opposed to a LRFD, has resulted in a significant reduction of seabed intervention requirements and an associated cost saving, while still being in compliance with DNV-OS-F101 target safety levels. To our knowledge this is the first time the SRA method has been applied for trawl interference design on a live project, and on a CRA (Corrosion Resistant Alloy) lined pipeline with DEH system attached. The success was made possible by close collaboration between the parties involved; Wintershall, DNV GL and Subsea 7.

A mixture distribution with fractional moments for efficient seismic reliability analysis of nonlinear 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.

Structural reliability analysis with fuzzy random variables using error principle

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.

Analysis of catenary action in steel beams using a simplified hand calculation method, Part 1: theory and validation for uniform temperature distribution