An efficient method for estimating the parameter global reliability sensitivity analysis by innovative single-loop process and embedded Kriging model

The surrogate model-based sampling method has been an active area of research due to its evident efficiency over direct sampling method. The fusion of the adaptive kriging (AK) model with the adaptive radial-based importance sampling (ARBIS) method is developed as an improvement of the AK model combined with Monte Carlo simulation (MCS) method especially for estimating the small failure probabilities. In the AK–ARBIS method, the number of candidate samples in each updating process of the kriging model is reduced through partitioning the whole MCS sample domain into different subdomains and removing the samples inside the last subdomain from the participating candidate sampling pool, which can avoid the time-consuming matrix operation involved in kriging predictions in order to find the best training sample in each updating step. In the existing AK–ARBIS method, kriging model stops updating according to the learning function-based stopping criterion, which cannot directly reflect the error of the estimated failure probability. In this regard, this paper proposes the error-based stopping criterion (ESC) enhanced AK–ARBIS method, where the processes of finding the optimal hypersphere and accurately identifying the sign of candidate samples are decoupled in order to successfully embed the ESC. In addition to embedding the ESC into the AK–ARBIS method, two target-oriented candidate sampling reduction strategies are investigated, respectively, to improve the efficiency of finding the optimal hypersphere and accurately identifying the sign of the participating candidate samples. Based on the candidate sampling pool reduction strategies and ESC, both the computational time and the required number of calls to the real limit state function are reduced over the existing AK–ARBIS method. Three case studies are analyzed to demonstrate the accuracy and efficiency of the proposed enhanced AK–ARBIS method, especially for estimating the small failure probabilities.

This study proposes an improved adaptive kriging model-based FE model updating framework to increase the updated FE model’s accuracy and reduce computational costs. The proposed adaptive kriging model uses an efficient hybrid expected improvement and minimizing surrogate prediction sampling strategy to generate new training samples. The k-fold cross-validation is introduced to assess the kriging model’s accuracy. Benchmark functions and model updating of a full-scale bridge structure validated the proposed adaptive kriging model. The results demonstrate that the hybrid sampling strategy balances the global and local exploration of the design space and provides reasonable training samples, increasing the accuracy of the adaptive kriging model. The cross-validation significantly saves computational costs. After model updating, the frequency relative errors of the continuous bridge are under 2%, and the modal assurance criterion values are over 0.96. The updated FE model can serve as the baseline FE model of the bridge.

Sensitivity analysis is used to find the key variables which have significant effect on system reliability. For a product in early design stage, it is impossible to collect sufficient samples. Thus, the probabilistic-based reliability sensitivity analysis methods are difficult to use due to the requirement of probability distribution. As an alternative, interval can be used because it only requires few samples. In this study, an effective global non-probabilistic sensitivity analysis based on adaptive Kriging model is proposed. The global accuracy Kriging model is constructed to reduce overall computational cost. Subsequently, the global non-probabilistic sensitivity analysis method is developed. Compared to existing non-probabilistic sensitivity analysis methods, the proposed method is a global non-probabilistic reliability sensitivity analysis method. The proposed method is easy to use and does not require probability distribution of the input variables. The applicability of proposed method is demonstrated via two examples.

Global sensitivity analysis (GSA) is useful to recognize important inputs for assigning priority and unimportant inputs for simplifying models by exploring whole distribution ranges. Meanwhile, regional sensitivity analysis (RSA) is also studied for finding the contribution of the critical region of an input, which can be viewed as the complementary of GSA. However, there is a lack of GSA and RSA research in presence of fuzzy uncertainty. Thus, a new global sensitivity index (GSI) under the fuzzy uncertainty is devoted on the credibility distribution function (CrDF), a comprehensive distribution description under the fuzzy uncertainty. The CrDF-based GSI is defined by the fuzzy expectation of the difference between the CrDF and the conditional CrDF of the output on fixing the fuzzy input over its whole distribution range, which can quantify the contribution of the fuzzy input to the output CrDF. Then, a new fuzzy RSA technique, the contribution to this CrDF based index (shortened by CCI) plot, is also proposed, and it can assess the effect of given regions of important inputs on output CrDF. Besides, mathematical properties of the CrDF based GSI and the CCI plot are discussed, and their solution are established by use of the fuzzy simulation with the same set of samples. After the accuracy of established fuzzy simulation solution for the CrDF based GSI and the CCI plot are verified by an analytical example, other examples are used to demonstrate the reasonability and applicability of proposed CrDF based GSI and CCI plot under fuzzy uncertainty.

The moment-independent global sensitivity (MIGS) analysis can help decision makers to efficiently reduce the uncertainty of model output. This article proposes a novel single-loop simulation (NSLS) method for MIGS analysis. Through an interval discretization strategy, estimation of probability density functions (PDFs) in existing methods is transformed to estimation of the marginal probability of the input, the marginal probability of the output and the joint probability of the inputs–output in NSLS, which avoids the computational complexity and error resulting from PDF estimation in MIGS analysis. To drastically reduce the computational cost of NSLS to estimate the MIGS index, an NSLS-based adaptive kriging (NSLS-AK) method is subsequently developed. In NSLS-AK, a rough global kriging model is first constructed, then this kriging model is adaptively updated until the convergent condition is satisfied for accurately and efficiently predicting the responses of the samples in estimating the MIGS index.

The quality and reliability of wind turbine blades, as core components of wind turbines, are crucial for the operational safety of the entire system. Carbon fiber is the primary material for wind turbine blades. However, during the manufacturing process, manual intervention inevitably introduces minor defects, which can lead to crack propagation under complex working conditions. Due to limited understanding and measurement capabilities of the input variables of structural systems, the distribution parameters of these variables often exhibit uncertainty. Therefore, it is essential to assess the impact of distribution parameter uncertainty on the fatigue performance of carbon-fiber structures with initial cracks and quickly identify the key distribution parameters affecting their reliability through global sensitivity analysis. This paper proposes a sensitivity analysis method based on surrogate sampling and the Kriging model to address the computational challenges and engineering application difficulties in distribution parameter sensitivity analysis. First, fatigue tests were conducted on carbon-fiber structures with initial cracks to study the dispersion of their fatigue life under different initial crack lengths. Next, based on the Hashin fatigue failure criterion, a simulation analysis method for the fatigue cumulative damage life of cracked carbon-fiber structures was proposed. By introducing uncertainty parameters into the simulation model, a training sample set was obtained, and a Kriging model describing the relationship between distribution parameters and fatigue life was established. Finally, an efficient input variable sampling method using the surrogate sampling probability density function was introduced, and a Sobol sensitivity analysis method based on surrogate sampling and the Kriging model was proposed. The results show that this method significantly reduces the computational burden of distribution parameter sensitivity analysis while ensuring computational accuracy.

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

Interval multi-objective optimisation of structures using adaptive Kriging approximations

A novel training point selection strategy guided by the maximum reduction of structural state misclassification probability for time-dependent reliability analysis

The increasing use of surrogate models has widened the range of application of classical reliability-based design optimization (RBDO) techniques to industrial problems. In this paper, we consider such an approach to the lightweight design of an automotive body structure. Solving this problem while approximating the complex models (nonlinear, noisy and high-dimensional) with a single metamodel would require a very large and non affordable design of experiments (DOE). We thus investigate and propose a methodology of adaptive Kriging based RBDO where an initial DOE is iteratively updated so as to improve the Kriging models only in regions that actually matter. The nested reliability analysis is expressed in terms of quantiles assessment. Two stages of enrichment are performed. The first one seeks to gradually improve the accuracy of the metamodels where the probabilistic constraints are likely to be violated. The second one is embedded in an evolution strategy optimization scheme where, at each iteration, the accuracy of the quantile estimation is improved if necessary. The methodology is applied on an analytical and crashworthiness design problems showing good performance by enhancing accuracy and efficiency with respect to a traditional approach.

Collecting enough samples is difficult in real applications. Several interval-based non-probabilistic reliability methods have been reported. The key of these methods is to estimate system non-probabilistic reliability index. In this paper, a new method is proposed to calculate system non-probabilistic reliability index. Kriging model is used to replace time-consuming simulations, and the efficient global optimization is used to determine the new training samples. A refinement learning function is proposed to determine the best component (or performance function) during the iterative process. The proposed refinement learning function has considered two important factors: (1) the contributions of components to system nonprobabilistic reliability index, and (2) the accuracy of the Kriging model at current iteration. Two stopping criteria are given to terminate the algorithm. The system non-probabilistic index is finally calculated based on the Kriging model and Monte Carlo simulation. Two numerical examples are given to show the applicability of the proposed method.

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

Efficient sampling methods for global reliability sensitivity analysis

Global sensitivity analysis and seismic response analysis of buried structures consider the uncertainty of soil parameters using the Kriging model

Despite being a common procedure, abdominal hernia treatments still require improvement due to the number of relapses and other postoperative issues. In silico testing can be employed to predict the behavior of the complex abdominal wall and implant systems. Here, uncertainty quantification and sensitivity analysis are required in order to optimize the parameters of hernia repair models. This paper concerns the modeling of an abdominal wall and implant using the finite element method. A Gasser-Ogden-Holzapfel (GOH) material model is used for the abdominal wall and an orthotropic material model for the implant. The parameters of the GOH model and the orientation of the implant are assumed to be uncertain. Regression-based polynomial chaos expansion is used as a meta-modeling method for uncertainty propagation and global sensitivity analysis. The maximum force in the connection between the implant and native tissue is considered as the quantity of interest. A failure risk criterion is also defined and presented. It has been found that the significance of the material parameters depends on the type of implant that is analyzed. Likewise, the risk of connection failure varies considerably depending on the implant used. Models with different types of implant produce very diverse results. Moreover, these differences also appear in the global sensitivity index and the risk of connection failure. This would indicate that specific implant designs and material properties are crucial to the success of hernia repair surgery.