Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

PurposeThe purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.Design/methodology/approachIn this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.FindingsThe numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.Originality/valueThe paper provides a useful reference for further theoretical research and engineering application.

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.

An Active Learning Polynomial Chaos Kriging metamodel for reliability assessment of marine structures

Reliability is a critical indicator for evaluating the safety and performance of mechanical structures. Surrogate models are widely employed in reliability analysis to reduce computational costs; however, their accuracy strongly depends on the quality of training samples. This paper proposes an uncertainty and distance-driven sequential sampling deep neural network method (UDDS-DNN) for structural reliability analysis. First, initial training samples were generated from the Monte Carlo population (MCP) using the Minimax sampling strategy. This ensured global coverage of the random variable space. Then, the predictive uncertainty of the DNN was quantified using the Jackknife-based method. The estimated uncertainty, inter-sample distance, and probabilistic characteristics of the input random variables were considered. The adaptive learning function was constructed to guide sequential sample enrichment. The proposed method was validated through two numerical examples and three engineering case studies. Results demonstrated that UDDS-DNN achieves high accuracy and computational efficiency in multivariate, nonlinear, and complex structural reliability problems. The method provided an effective solution for reliability analysis of complex structures using DNN-based sequential sampling.

This paper outlines a logical process based on Bayesian inference to exploit monitoring observations to improve the accuracy in the reliability estimates of civil structures that are retrofitted during their service lives. The proposed approach is particularly effective for complex structures, whose response prediction is affected by structural parameters with significant uncertainty; typical examples are prestressed concrete bridges, heavily influenced by the inherent uncertainties of the material’s creep and shrinkage. The methodology is applied to a real-life complex bridge in Italy, as opposed to academic problems and laboratory tests; the structural model developed for this study includes the original creep law of the Model B3 proposed by Bazant rather than linear approximation or response surfaces. The Bayesian inference is performed using a Markov Chain Monte Carlo (MCMC) method, while the reliability assessment utilises importance sampling (IS) for computational efficiency. The results show the extent to which structural health monitoring (SHM) and Bayesian inference reduce the uncertainty in structural parameters and the prediction of the structural demand. At the same time, they increase structural reliability. Particular attention is given to computational effort, structural modelling and algorithm optimisation.

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

Structural and thermal analysis on high-pressure steam turbine blade to determine the optimum material for its manufacturing

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.

Dynamic neural network method-based improved PSO and BR algorithms for transient probabilistic analysis of flexible mechanism

Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions

For multicomponent structures enduring dynamic workloads coming from multi-physical fields, safety assessment is significant to guarantee the normal operation of entire structure system. In this paper, an enhanced extremum Kriging-based decomposed coordinated framework (E2K-DCF) is proposed to improve the dynamic probabilistic failure analyses of multicomponent structures. In this method, extremum Kriging model (EKM) is developed by introducing Kriging model into extremum response surface method (ERSM) to process the transient response problem and shorten computational burden in dynamic probabilistic failure analyses. Multiple population genetic algorithm (MPGA) is employed to solve maximum likelihood equation (MLE) and find the optimal hyperparameter $\boldsymbol \theta $ in the EKM, which is promising to enhance approximate accuracy; decomposed-coordinated (DC) strategy is used to handle the coordinated relationship of multiple analytical objectives. To validate the proposed E2K-DCF, the probabilistic failure analysis of turbine blisk radial deformation is conducted by comparing with different methods within time domain [0 s, 215 s], considering fluid-thermal-structural interaction. It is revealed that the failure probability of blisk radial deformation is only 0.0022 when the allowable value is $2.5702\times 10^{-3}$ m acquired from real world practice. Compared to the other approaches, this E2K-DCF has obvious advantages in fitting time and accuracy as well as simulation efficiency and accuracy. The results illustrate that the E2K-DCF is effective and applicable in dynamic probabilistic failure analysis. The efforts of this paper provide a novel viewpoint for the transient reliability evaluation of multicomponent structures, which is likely to enrich mechanical reliability theory.

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.

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.

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

Welding defects are known to cause crack propagation and reduce structural fatigue performance. Based on the Paris theory of fracture mechanics, research is conducted on evaluation methods for analyzing fatigue crack propagation by adopting random loads with long-term distribution that follows the Weibull distribution for the stress ranges of fatigue loads. This approach is combined with the corrective stress intensity factor (SIF) equation and the method for calculating the reference stress and failure criterion. A large container ship is selected for a simulation, and fatigue crack propagation analysis is conducted on typical critical locations. A detailed comparison of the forecasted fatigue life is carried out between fracture mechanics theory and the S-N curve. The results indicate that the fatigue life values obtained using the two methods are of the same magnitude. In general, for the welded structure, the fatigue life value obtained via the fracture mechanics method is shorter than that obtained via the S-N curve method, while, for the free edge of the structure and the unwelded structure, the predicted fatigue life value is closer than that predicted via the S-N curve method. Moreover, the influence of initial crack defects on the fatigue life is investigated, and the results show that the depth of the initial crack will greatly affect the fatigue life of the target ship in typical locations, but the influence of the shape ratio on the fatigue life is limited. Therefore, in the actual ship construction process, controlling the initial crack depth of components is effective for limiting crack propagation and improving fatigue life. The above conclusions and suggestions can serve as a reference for the structural design and fatigue life evaluation of large container ships.