Reliability Analysis Problems Research Articles

Global sensitivity analysis for multiple importance sampling centres using a novel adaptive line sampling method

To achieve more efficient resolution of reliability analysis problems in engineering, it is essential to enhance the line sampling (LS) method, which is typically effective for rare events. This article proposes an enhanced method for rare events by combining LS with kriging. In this method, the updating of kriging is conducted from a one-dimensional perspective along the important direction. The samples used to assess the failure probability are obtained through importance sampling (IS) from multiple IS centres rather than Monte Carlo simulation (MCS). During each iteration, both upper and lower bounds of the failure probability are simultaneously evaluated to determine whether to halt the iteration process. Finally, global sensitivity analysis is conducted by filtering the samples generated at multiple IS centres, rather than generating MCS samples. By comparison with existing methods, this article demonstrates the efficiency and accuracy of the proposed method through three numerical examples and an engineering problem.

An active learning Kriging model with approximating parallel strategy for structural reliability analysis

With the ever-increasing complexity of engineering problems, active learning functions fused with Kriging models are receiving significant attention and are extensively applied in various reliability analysis methods. It is argued unfavorably that the existing fusion-type methods usually obtain only a single optimal sample point during model updating process. Meanwhile, the information of the used sample points is not sufficiently utilized. To these gaps, this study proposes an adaptive Kriging reliability analysis method based on an approximate parallel computing strategy, namely AP-AK for short. To start with, a new Kriging model update strategy is proposed, where the first selected sample points help to introduce the intermediate model and further search for optimal points closer to the limit state surface. An improved learning function is then proposed to limit the locations of points based on the information of used sample points. The new function is characterized by setting the acceptance and rejection domains of the sample points, which prevents computational waste incurred by local sample point aggregation. Superior performance of the AP-AK method is demonstrated against other Kriging-based methods through five numerical cases and one solid attitude orbit control engine case. The comparison results show that the proposed method exhibits high efficiency and robustness for solving complex reliability analysis problems.

Fatigue Reliability Assessment for Orthotropic Steel Decks: Considering Multicrack Coupling Effects

Multiple fatigue cracks are generally present in practical engineering due to the existence of welding; the size and number of cracks of orthotropic steel bridge decks are greatly uncertain. The component failure conditions caused by these cracks may have correlations. Currently, it is still a challenging issue to develop a physical model of multiple fatigue crack propagation in bridge decks and perform a fatigue reliability assessment, which is also the motivation that drives the innovation of this study. A fatigue reliability evaluation method is presented for orthotropic steel bridge decks, considering the coupling effect of multiple cracks and the randomness of vehicle loading. A numerical simulation method for multifatigue crack growth is developed by combining the ABAQUS and FRANC3D programs. The equivalent crack depth under different spacing and depths of collinear cracks is calculated by using numerical simulation and the multicrack equivalent characterization method. The critical damage accumulation function of multiple fatigue cracks is established using linear elastic fracture mechanics. Subsequently, the critical damage accumulation function of multiple fatigue cracks is established based on linear elastic fracture mechanics. In order to solve the time-consuming problem of traditional Monte Carlo method, the iHL-RF method and AK-MCS method are developed for fatigue reliability analysis. The results show that compared with the single-crack model, the fatigue reliability of orthotropic steel deck will be crucially reduced considering the coupling effect of double cracks. The MCS, iHL-RF and AK-MCS methods can effectively solve the fatigue reliability analysis problem. Compared with the MCS method, the reliability calculation time based on AK-MCS method is significantly reduced. The AK-MCS method-based method reduces the time for calculating the reliability of orthotropic steel decks by 50% compared with the iHL-RF method. The reliability analysis of orthotropic steel deck bridge based on AK-MCS method is proved to be efficient and accurate.

Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy

Efficient structural reliability analysis method is crucial to solving reliability analysis of complex structural problems. High-computational cost and low-failure probability problems greatly limit the efficiency in structural reliability analysis problems, causing the safety and reliability of the structure to be questioned. In this work, a highly efficient structural reliability analysis method coupling active Kriging algorithm with conjugate first order reliability method (AK-CFORM) is proposed. Specifically, the resample strategy is considered to reduce the number of samples evaluated in each active learning process; the uniform sampling is used to better balance global and local optimal problems; the conjugate map is used to improve the robustness of analytical first order reliability method; and the approximate numerical differential formula is proposed to solve the problems of non-convergence when solving the gradient of the Kriging surrogate model. Finally, three numerical cases and four engineering cases are used to illustrate the effectiveness and robustness of the proposed method. The results show that the proposed AK-CFORM has greater advantages in the number of calling system response and surrogate model with robust and accurate performance.

AOK‐ES: Adaptive optimized Kriging combining efficient sampling for structural reliability analysis

AbstractThe pivotal problem in reliability analysis is how to use as few actual assessments as possible to obtain an accurate failure probability. Although adaptive Kriging provides a viable method to address this problem, unsatisfied Kriging surrogate accuracy and reliability modeling samples often lead to an unacceptable computing burden. In this paper, an adaptive optimized Kriging combining efficient sampling (AOK‐ES) is proposed: first, to enhance the Kriging approximation ability, a high‐fidelity optimized Kriging model (OKM) is established; further, to ensure the samples quality of OKM modeling and reliability calculation, an improved Latin hypercube sampling method and an optimized importance sampling approach are developed correspondingly. Six different types of case studies demonstrate the superiority of the proposed AOK‐ES. The analysis results demonstrate that the proposed AOK‐ES holds the potential to reduce computing cost while ensuring accuracy.

Operational reliability analysis of remote operated vehicle based on dynamic Bayesian network synthesis method

In this study, we propose a reliability framework that combines the GO method with fault tree analysis and integrates human factor reliability analysis. Taking the application of remotely operated vehicle (ROV) in underwater oil and gas production as an example, a reliability model of ROV operation process is established. The human reliability in the ROV operation process is analyzed on the basis of Cognitive Reliability and Error Analysis Method (CREAM) extension approach. The influence of human factor reliability and equipment reliability on the system is compared and analyzed. The importance of each operation step is also compared and analyzed. A sensitivity analysis of the ROV during operation is performed. This study provides a theoretical basis for the improvement and maintenance of the operational reliability of ROV. The proposed reliability modeling approach solves the reliability analysis problem of large and complex operating systems.

Dynamic pruning-based Bayesian support vector regression for reliability analysis

Adaptive surrogate-based reliability analysis methods have garnered significant attention due to their potential to enhance computational efficiency in accurately estimating failure probability. However, the candidate sample pool remains constant for most surrogate-based reliability methods, and traversing the candidate sample pool one by one will reduce the efficiency of surrogate modeling. More importantly, maintaining a static sample pool may lead to the inclusion of samples that contribute minimally to the construction of the surrogate modeling, thereby impacting the accuracy and efficiency of the reliability analysis. Accordingly, this paper leverages the robust performance of Bayesian support vector regression to propose a dynamic pruning strategy for the candidate sample pool to estimate failure probability efficiently. A dynamic pruning strategy is presented to streamline the process further, iteratively reducing the candidate sample pool. An adaptive learning algorithm is then introduced, integrating the U function and the sparsity of training samples. This is complemented by a formulated convergence condition, contributing to an ideal surrogate model. The proposed approaches showcase superior efficiency and accuracy through illustrations using well-known benchmark problems and complex reliability analysis problems involving small failure probability and high-dimensional limit state function.

Reliability evaluation of phased-mission systems exposed to random shocks

The paper aims to examine the reliability analysis problem of phased-mission systems that execute multiple consecutive non-overlapping mission phases in a random shock environment. Each phase is carried out by several subsystems which consist of non-repairable components connected in different topology configurations. The random shocks, modeled by a Poisson process, significantly affect the failure rate of components within the dynamic subsystems. The system configuration, success criteria, and component failure behavior may differ from phase to phase. The paper presents technical methodologies to evaluate the mission success probabilities of subsystems in various configurations and proposes a modularization method to compute the reliability of phased-mission systems by combining the mission success probabilities of all subsystems. Finally, a numerical example is provided to illustrate the proposed model and method.

A comparative study of various metamodeling approaches in tunnel reliability analysis

Various metamodeling approaches are applied in conjunction with Monte Carlo simulation and or the second moment-based method for reliability analyses of underground tunnels. However, there is no study regarding the suitability of such metamodels for reliability analyses of tunnels. An attempt is made here to make a comparative assessment of different metamodeling approaches for tunnel reliability analysis to comprehend the performances of various metamodels from the subset of machine learning methods. In doing so, the least square method based polynomial response surface method (RSM), mostly used in tunnel reliability analyses, and its improved version i.e., moving least square method-based RSM, are taken up for comparison. Further, the most successful empirical risk minimization-based Kriging model and the structural risk minimization principle-based support vector regression model are considered for comparison. Also, the sparse Bayesian regression found to be useful in solving various structural reliability analysis problems, is taken up for the present comparative study. Two numerical examples demonstrate the effectiveness of the selected metamodels in tunnel reliability analysis. It has been generally noted that the Kriging and SVR-based metamodels outperform in reliability estimates of underground tunnels.

Network reliability analysis through survival signature and machine learning techniques

As complex networks become ubiquitous in modern society, ensuring their reliability is crucial due to the potential consequences of network failures. However, the analysis and assessment of network reliability become computationally challenging as networks grow in size and complexity. This research proposes a novel graph-based neural network framework for accurately and efficiently estimating the survival signature and network reliability. The method incorporates a novel strategy to aggregate feature information from neighboring nodes, effectively capturing the response flow characteristics of networks. Additionally, the framework utilizes the higher-order graph neural networks to further aggregate feature information from neighboring nodes and the node itself, enhancing the understanding of network topology structure. An adaptive framework along with several efficient algorithms is further proposed to improve prediction accuracy. Compared to traditional machine learning-based approaches, the proposed graph-based neural network framework integrates response flow characteristics and network topology structure information, resulting in highly accurate network reliability estimates. Moreover, once the graph-based neural network is properly constructed based on the original network, it can be directly used to estimate network reliability of different network variants, i.e., sub-networks, which is not feasible with traditional non-machine learning methods. Several applications demonstrate the effectiveness of the proposed method in addressing network reliability analysis problems.

The motion reliability analysis of a series system with multiple coordinated manipulators

Coordinated manipulators can construct a series system, such that all the position error of the end-effector is required to remain within the permissible limit. This article proposed a new method to handle the problem of reliability analysis involving in multiple failure modes. The extreme value of the position error is introduced to construct a surrogate model to replace the original failure event, the moment with fraction order instead of the traditional integer is applied to derive the best-fit distribution of the extreme value based on the maximum entropy principle. The innovations mainly include: (1) the high efficient dimension reduction via the surrogate model constructed with the extreme value and (2) a better probability density function is derived through the fractional moment. A series system consists of three manipulators is used as an example to demonstrate the efficiency and accuracy of the proposed method.

A Kriging-based adaptive adding point strategy for structural reliability analysis

Aiming at the problem of structural reliability analysis with complex performance function in practical engineering, an adaptive adding point strategy for structural reliability analysis is proposed by combining Kriging surrogate model and learning function. In the process of structural reliability analysis, in order to reduce the computational cost, the surrogate model is usually used to fit the implicit performance function. Existing learning functions rarely take into account the problem of sample point aggregation due to too many sample points selected from the failure domain (or safety domain) during the fitting process. In order to overcome this defect, a new method can ensure that the added sample points are evenly distributed on both sides of the limit state function, preventing the aggregation of sample points and causing information redundancy, thereby improving the fitting accuracy of the model, accelerating the convergence speed of the sample points and saving the sample space. Through the analysis of four-branch series system, nonlinear oscillator and truss structure, the results show that the algorithm needs less samples than other methods, and the reliability calculation accuracy is higher, which verifies the correctness and efficiency of the proposed method.

Introducing a new system performance function to formulate reliability analysis problems of wind turbines

Consideration of safety is one of the current requirements to design a new system that is often implemented by defining the system failure probability. Renewable energy systems (RESs) do have the same requirements when it comes to safety and reliability. When designing a wind turbine, as a RES, its reliability is of the highest importance. So, efficient reliability models are required to ensure the turbine is working safely to generate electricity. A new model is introduced in this paper by taking into account the wind speed and the wind angle as two effective factors. These two random variables are reported to follow the Gaussian and Weibull probability distributions, and so are employed to define a limit-state function for the turbines. This limit-state function, which is also called system performance function, will then be used to find out the system failure probability.

PINN-FORM: A new physics-informed neural network for reliability analysis with partial differential equation

The first-order reliability method (FORM) is commonly used in the field of structural reliability analysis, which transforms the reliability analysis problem into the solution of an optimization problem with equality constraint. However, when the limit state functions (LSFs) in mechanical and engineering problems are complex, particularly for implicit partial differential equations (PDEs), FORM encounters computation difficulty and incurs unbearable computational effort. In this study, the physics-informed neural network (PINN), which is a new branch of deep learning technology for addressing forward and inverse problems with PDEs, is applied as a black-box solution tool. For LSFs with implicit PDE expressions, PINN-FORM is constructed by combining PINN with FORM, which can avoid the calculation of the real structure response. Moreover, a loss function model with an optimization target item is established. Then, an adaptive weight strategy, which can balance the interplay between different parts of the loss function, is suggested to enhance the predictive accuracy. To demonstrate the effectiveness of PINN-FORM, five benchmark examples with LSFs expressed by implicit PDEs, including two-dimensional and three-dimensional problems, and steady state and transient state problems are tested. The results illustrate the proposed PINN-FORM not only is very accurate, but also can simultaneously predict the solutions of PDEs and reliability index within a single training process.

AK-HRn: An efficient adaptive Kriging-based n-hypersphere rings method for structural reliability analysis

With increasing complexity of engineering problems, various traditional reliability analysis methods are facing rising challenges in terms of computational efficiency and accuracy. Surrogate models, especially Kriging model, have received growing attention and been widely used in reliability analyses by the virtue of their advantages for achieving high computational efficiency and ensuring high numerical accuracy. Nevertheless, there have been still two significant problems in the Kriging model-assisted reliability analyses due to the absence of prior knowledge: i.e. (1) the size of candidate sample pool tends to be quite large in order to ensure prediction of a convergent failure probability; and (2) local prediction accuracy of limiting state surface by Kriging model is generally excessive. These above two issues can often result in high computational cost for Kriging-based reliability analyses. To enhance computational efficiency, a new method that combines adaptive Kriging and n-hypersphere rings, named an AK-HRn method, is proposed in this study. First, the n-hypersphere rings, which can update its position and radius adaptively, is adopted to divide the design space into potential safety domains and potential failure domains. Second, these potential failure domains are used as the sampling domains for implementing importance sampling method to generate a suitably-sized candidate sample pool. Third, a novel learning function is presented to enrich the design of experiment (DoE), which avoids excessive local prediction accuracy of Kriging models by establishing the rejection domains. Finally, the efficiency and robustness of AK-HRn is compared with other Kriging-based reliability analysis methods through four illustrative numerical examples and one 6-DOF industrial robot case study. Comparison shows that the proposed AK-HRn method has high efficiency and robustness to solve complex reliability analysis problems.

A dynamic Gaussian process surrogate model based on the grasshopper optimization algorithm for non-probabilistic reliability analysis of complex structures

In practical complex engineering structures, the performance function (PF) for reliability analysis is commonly implicit and highly nonlinear. Commonly used surrogate models are appropriate for structural reliability analysis with an implicit PF. However, these methods require hundreds of PF values, which are time-consuming to obtain by adopting numerical analysis, such as finite element analysis (FEA). Therefore, since non-probabilistic reliability analysis does not require a large number of samples, it has great development potential. In this paper, a dynamic Gaussian process (GP) surrogate model based on the grasshopper optimization algorithm (DGP-GOA) is proposed for the non-probabilistic reliability analysis. First, with the help of the scale factor of the convex set model, the non-probabilistic reliability analysis problem is transformed into an unconstrained optimization problem. Second, the DGP-GOA fits the PF by constructing a GP surrogate model with a small dataset. Third, the GOA is used to search for the global optimal solution to obtain a non-probabilistic reliability index. Then, a dynamic retraining strategy is proposed to improve the fitting accuracy and efficiency. The results demonstrate that the proposed method is highly applicable to the non-probabilistic structural reliability analysis of complex engineering structures.

The Reliability and Exploitation Analysis Method of the ICT System Power Supply with the Use of Modelling Based on Rough Sets

The article describes a new approach to the reliability–exploitation analysis of the critical information and communications technology (ICT) system power supply. A classic approach based on statistical indicators and a new one founded on uncertainty modelling based on the rough set method is presented. The main advantage of the uncertainty modelling approach is the simplification of the calculations and the fact that, unlike statistical analysis, uncertainty modelling does not require complete information on the used data sets. An extensive study of world publications was carried out, proving that this is an entirely innovative approach to solving the problem of reliability and exploitation analysis. Calculations, analyses and syntheses are also exhibited in a specific example. A sample of the ICT system power supply was simulated, and the simulation results are shown. The simulations were prepared by one of the co-authors for the purposes of this article.

Active Kriging-Based Adaptive Importance Sampling for Reliability and燬ensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like high-nonlinearity, multi-failure regions, and small failure probability, which brings in unacceptable computing efficiency and accuracy of the current analysis methods. In this case, by fitting the implicit limit state function (LSF) with active Kriging (AK) model and reducing candidate sample pool with adaptive importance sampling (AIS), a novel AK-AIS method is proposed. Herein, the AK model and Markov chain Monte Carlo (MCMC) are first established to identify the most probable failure region(s) (MPFRs), and the adaptive kernel density estimation (AKDE) importance sampling function is constructed to select the candidate samples. With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF, the failure probability and sensitivity indices are acquired at a lower cost. The proposed method is verified by two multi-failure numerical examples, and then applied to the reliability and sensitivity analyses of a typical stator blade regulator. With methods comparison, the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

Structural Interval Reliability Algorithm Based on Bernstein Polynomials and燛vidence Theory

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic reliability index method, the extreme value of the limit state function is obtained using the properties of Bernstein polynomials, thus avoiding the need for a lot of sampling to solve the reliability analysis problem. The method is applied to numerical examples and engineering applications such as experiments, and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method, especially for some reliability problems with higher nonlinearity. Moreover, this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems.

Multidisciplinary Reliability Design Considering Hybrid Uncertainty Incorporating Deep Learning

Multidisciplinary reliability design optimization is considered an effective method for solving complex product design optimization problems under the influence of uncertainty factors; however, the high computational cost seriously affects its application in practice. As an important part of multidisciplinary reliability design optimization, multidisciplinary reliability analysis plays a direct leading role in its computational efficiency. At present, multidisciplinary reliability analysis under mixed uncertainty is still nested or sequential execution mode, which leads to the problem of poor disciplinary autonomy and inefficiency in the reliability analysis of complex products. To this end, a multidisciplinary reliability assessment method integrating deep neural networks and probabilistic computational models under mixed uncertainty is proposed for the problem of multidisciplinary reliability analysis under mixed uncertainty. The method considers the stochastic-interval-fuzzy uncertainty, decouples the nested multidisciplinary probability analysis, multidisciplinary likelihood analysis, and multidisciplinary interval analysis, uses deep neural networks to extract subdisciplinary high-dimensional features, and fuses them with probabilistic computational models. Moreover, the whole system is divided into several independent subsystems, then the collected reliability data are classified, and the fault data are attributed to each subsystem. Meanwhile, the environmental conditions of the system are considered, and the corresponding environmental factors are added as input neurons along with each subsystem. In this paper, the effectiveness of the proposed method is verified on numerical calculations and real inverter power failure data.