On the Application of Structural Reliability Analysis

Structural reliability analysis (SRA) has been used to calculate the probability of mooring line failure in an intact mooring system as a function of the magnitude of the safety factor applied in design. A range of different units have been considered, comprising ship shaped units and semisubmersibles at different water depths from 100 m to 2200 m. Environmental conditions representative for the Norwegian continental shelf and the Gulf of Mexico are used in the analyses, and the characteristics of the results in the different environments are compared and discussed. Analyses for Brazilian environment are currently ongoing, but not included here. Time domain analysis is applied to obtain the short-term, extreme value distribution of line tension, conditional on stationary metocean conditions. A large number of different conditions are considered. A response surface is used to interpolate on the distribution parameters in order to describe the tension response in varying conditions. Joint probabilistic models of the metocean environment corresponding to the different geographical locations have been applied, taking account of wind, wave and current and their respective heading angles. A continuous model is used for the metocean conditions at the Norwegian continental shelf, whereas a hurricane model is used in the Gulf of Mexico. The effects of uncertainties in the response calculation are included. The mooring line component strength is based on strength data from break load tests. Conventional catenary chain-wire chain systems as well as polyester moorings are considered. With the probability of failure as a function of the safety factor, it is shown that present regulations result in a significant scatter in reliability level between the cases. Safety factors have been calibrated considering all cases. Alternative design formats are proposed and tested including a format with 2 safety factors. Calibration results are provided as a function of the target reliability level. The final recommendation on target reliability level is given in an accompanying paper at OMAE 2017, comprising both the ULS and the ALS. It is demonstrated that alternative design formats can provide a more consistent safety level across the cases. A different design philosophy is needed for the Gulf of Mexico in order to achieve acceptable risk. Options for design are discussed. The present work provides a unique and comprehensive set of results, where advanced reliability methods are used in combination with detailed response calculations in the time domain. The results provide a basis for calibration of mooring design for ULS and subsequently for regulators to update their rules. The work has been carried out as part of the NorMoor Joint Industry Project, with participants from oil companies, engineering companies, rig-owners, manufacturers and marine authorities. This paper is the first one in a series of three at OMAE 2017, where the second deals with structural reliability analysis of the ALS and the third one provides summary and recommendations for safe mooring design in ULS and ALS.

The assessment of the risk arising from multiphase flow induced vibrations in subsea production systems is strongly affected by the accuracy of data and modelling for the production conditions, flow induced loading and estimate of the damping of the structure, both structural and flow induced. These uncertainties in the flow conditions and fluid structure interaction analyses are further compounded by uncertainties in the capacity of the structure to withstand vibration and fatigue damage. As most calculation codes rely on deterministic analysis, these uncertainties are often addressed by their characteristic input and through safety factors, which are intended to ensure sufficient safety level. Subjective judgements, with unknown degree of conservatism, may be difficult to avoid. A need to address the associated uncertainties and provide a prediction of the accumulated probability of fatigue failure, using a consistent and sound methodology, has been expressed throughout the industry. Structural Reliability Analysis (SRA) offers a framework to take into account, based on the same modelling basis as the deterministic approach, the uncertainties in all relevant parameters. Moreover, the framework allows for simultaneous consideration of these identified uncertainties when modelled by probability distributions and enables calculation of the probability of fatigue failure. This article describes a general approach to implement reliability principles in the analysis of multiphase flow induced vibrations, discusses the use of the methodology, both in design and in operations. It also concludes on the feasibility of using Bayesian analysis, based on the results of subsea inspection, to update the probability assessment and provide updated input to the risk evaluations for future operations. The methodology may also be used to determine operational limitations for future production.

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.

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.

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.

A logical framework is developed for load and resistance factor design (LRFD) of slopes based on reliability analysis. LRFD of slopes with resistance factors developed in this manner ensures that a target probability of slope failure is not exceeded. Three different target probabilities of failure (0.0001, 0.001 and 0.01) are considered in this report. The ultimate limit state for slope stability (formation of a slip surface and considerable movement along this slip surface) is defined using the Bishop simplified method with a factor of safety equal to unity. Gaussian random field theory is used to generate random realizations of a slope with values of strength and unit weight at any given point of the slope that differ from their mean by a random amount. A slope stability analysis is then performed for each slope realization to find the most critical slip surface and the corresponding driving and resisting moments. The probability of slope failure is calculated by counting the number of slope realizations for which the factor of safety did not exceed 1 and dividing that number by the total number of realizations. The mean of the soil parameters is adjusted and this process repeated until the calculated probability of failure reaches to the target probability of failure. Optimal resistance and load factors are obtained by dividing the resisting and driving moments corresponding to the most probable ultimate limit state by the nominal values of resisting and driving moments. The main goal of this study was to provide specific values of resistance and load factors to implement in limit states and load resistance design of slopes in the context of transportation infrastructure. This report discusses the concepts of load and resistance factors, target probability of failure and the ultimate limit state equation in the context of slope stability analysis. It then presents a detailed algorithm for resistance factor calculation by using reliability analysis. Six cases of real slopes designed and constructed by the Indiana Department of Transportation (INDOT) are examined by using undrained shear strengths in order to illustrate the LRFD procedure and validate the recommended resistance and load factors.

This paper presents a Load and Resistance Factor Design (LRFD) criterion applied to the design of Tension Leg Platform (TLP) tendons in their intact condition. The design criterion considers the Ultimate Limit State (ULS) of any tendon section along its whole length taking into account both dynamic interactions of load effects and the statistics of its associated extreme response. The partial safety factors are calibrated through a long-term reliability-based methodology for the storm environmental conditions, like hurricanes and winter storms, in deep waters of the Campeche Bay, Mexico. In the reliability analysis, the uncertainties in the definition of load effects and analytic limit state models for calculation of tendon strength and randomness of material properties are included. The results show that the partial safety factors reflect both uncertainty content and the importance of the random variables in structural reliability analysis. When tendons are designed according to the developed LRFD criterion, a less scattered variation of reliability indexes is obtained for different tendon sections across a single or various TLP designs.

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 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 new bivariate dimension reduction method for efficient structural reliability analysis

Bounds-based structure reliability analysis of bogie frame under variable load cases

Efficient sampling methods for global reliability sensitivity analysis

The concept presented for the safety assessment of concrete structures integrates nonlinear finite element analysis with stochastic and reliability technology into an advanced engineering tool. The basic aim of the stochastic nonlinear analysis is to calculate the safety index of an existing engineering structure, which characterizes its reliability (and failure probability). The nonlinear solution enables a realistic estimation of the structural response statistics to be obtained (failure load, deflections, cracks, stresses, etc.). The possibility of randomization for such computationally intensive problems is shown. Latin hypercube sampling is used in order to keep the number of required simulations at an acceptable level. Statistical correlation, which is important for a realistic solution, is imposed by using a stochastic optimization technique called simulated annealing. The sensitivity of results to random input parameters can be evaluated using nonparametric rank-order correlation coefficients. The safety index of the analysed structure is calculated from the stochastically obtained structural resistance and expected load distribution using appropriate reliability techniques. The presented approach for the safety assessment of engineering structures supersedes the usual methods based on simplified formulas. It can lead to considerably improved results since the structure is analysed more precisely. Therefore, it supports a higher level of decision-making process in bridge administration and maintenance of transport macrostructure.

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.

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.