Structural Reliability Analysis by Random Field Modelling with Robustness Methods and Adaptive Response Surfaces

Non-linear numerical models of the injection phase of a carbon sequestration (CS) project are computationally demanding. Thus, the computational cost of the calibration of these models using sampling-based solutions can be formidable. The Bayesian adaptive response surface method (BARSM)—an adaptive response surface method (RSM)—is developed to mitigate the cost of sampling-based, continuous calibration of CS models. It is demonstrated that the adaptive scheme has a negligible effect on accuracy, while providing a significant increase in efficiency. In the BARSM, a meta-model replaces the computationally costly full model during the majority of the calibration cycles. In the remaining cycles, the full model is used and samples of these cycles are utilized for adaptively updating the meta-model. The idea behind the BARSM is to take advantage of the fact that sampling-based calibration algorithms typically tend to sample more frequently from areas with a larger posterior density than from areas with a smaller posterior density. This behavior of the sampling-based calibration algorithms is used to adaptively update the meta-model and to make it more accurate where it is most likely to be evaluated. The BARSM is integrated with Unscented Importance Sampling (UIS) (Sarkarfarshi and Gracie, Stoch Env Res Risk Assess 29: 975–993, 2015), which is an efficient Bayesian calibration algorithm. A synthesized case of supercritical CO2 injection in a heterogeneous saline aquifer is used to assess the performance of the BARSM and to compare it with a classical non-adaptive RSM approach and Bayesian calibration method UIS without using RSM. The BARSM is shown to reduce the computational cost compared to non-adaptive Bayesian calibration by 87 %, with negligible effect on accuracy. It is demonstrated that the error of the meta-model fitted using the BARSM, when samples are drawn from the posterior parameter distribution, is negligible and smaller than the monitoring error.

To enhance the energy absorption performance of support systems in response to the frequent rockburst issues arising from deep coal mining, a new energy-absorbing component with a corrugated core structure is proposed for use in hydraulic support beams. The study explores three core structures: triangular, trapezoidal, and sine. Three structures were designed and analyzed based on a mechanical model, and simulations were conducted using ANSYS software. The study investigates the variations in support reaction force and displacement, energy absorption and displacement, as well as buckling deformation, with a detailed analysis of the simulation results. Using the Adaptive Response Surface Method, structural parameter optimization was carried out with DESIGN EXPERT software for all three core structures. After obtaining the optimal configurations, experimental tests were conducted to verify the feasibility of these new structures as energy-absorbing components for hydraulic supports. The findings suggest that the optimal angle for the triangular corrugated unit is 30° with a thickness of 2.9mm. The trapezoidal corrugated unit exhibits optimal performance at a vertical angle of 34° and a thickness of 4.2mm. With regard to the quasi-sinusoidal corrugated unit, the optimal angle is 32° with a thickness of 3.2mm. Furthermore, in single-layer structures, the sinusoidal corrugated core structure exhibits the best performance in terms of energy absorption and displacement. The introduction of corrugated energy-absorbing components opens new avenues for structural innovation and performance optimization, offering valuable insights for designing anti-impact energy-absorbing structures.

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.

An adaptive response surface method and Gaussian global-best harmony search algorithm for optimization of aircraft stiffened panels

Modelling the Effect of Initial Grain Size on Dynamic Recrystallization Using a Modified Cellular Automata and a Adaptive Response Surface Method

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

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.

Response surface method has won numerous concerns in the reliability analysis of structure due to its simplicity and practicability, especially quadratic response surface taking no account of cross terms is most widely used. However, for the complex ultimate state curved surface corresponding to strongly nonlinear, the approximate accuracy of quadratic response surface is apparently not enough, causing a biggish error in estimation of reliability. Although, theoretically, higher order response surface method can resolve this problem, the sharp increase of undetermined coefficient reduces calculation efficiency, and even, cannot achieve. Therefore, on the basis of univariate analysis of multivariable function, an algorithm which can reasonably determine higher order response surface form is presented in this article, able to effectively reduce the number of undetermined coefficients in response surface, so as to reduce computational difficulties and put forward improving measures for possible problems; In addition, based on the tactics of number-theoretic setpoint, a type of scheme of number-theoretic selecting point applicable to response surface method has been developed. Finally, through the analysis of examples, the suggested algorithm was validated, with the result showing that the algorithm has good accuracy and efficiency.

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.

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.

In this study, an adaptive space mapping method is introduced. A Coarse Model (CM) uses quadratic response surfaces for the objective and constraint functions. A fine simulation model is not only used for the correction of the coarse simulation model and validation of the final solution, but is also applied for construction of the Space Mapping (SM) expressions. The intelligent sampling method is implemented for the generation of initial samples and the Particle Swarm Optimisation (PSO) method is applied to optimise the response surface based on the CM in this work. The main purpose is to combine the SM algorithm and the modification of the distribution of the samples strategy. It promises that the response surface based on the CM should be updated stepwise in the right search direction. To demonstrate the application with the proposed optimisation method, it is successfully applied to the optimisation of geometric parameters of the addendum surface and Blank Holder Forces (BHFs) in a sheet-forming problem in a remarkably short computational time.

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.

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.

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.