Reliability Analysis Problems Research Articles

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.

Structural fatigue reliability evaluation based on probability analysis of the number of zero-crossings of stochastic response process

Structural fatigue failure is closely related to the number of stress cycles. Therefore, the number of the intersections between stochastic response process and zero-boundary is a key problem in structural fatigue reliability analysis. In this paper, the relationship between the number of the multiple intersections and the fatigue cumulative damage index is derived according to the Miner rule-based high cycle fatigue random cumulative damage index. Then, use random walk to approximately simulate Wiener process, and get the first intersection probability between Wiener process and the zero-boundary. Next, further utilize the renewal process to solve the distribution law of the number of intersections between the Wiener process and the zero-boundary in a period of time. Finally, based on the fatigue failure criterion considering the randomness of the failure threshold, the calculation formula the structural fatigue reliability is derived. As a practical example, the fatigue reliabilities of the key part of Metro Bogie under different operation periods are analyzed using the proposed method.

Reliability analysis of boom of new lifting equipment based on improved wolf swarm algorithm

Aiming at the low accuracy or inability to solve the problem when the traditional reliability optimization method deals with the practical engineering reliability analysis problem, this paper proposes a structural reliability analysis method using the improved wolf swarm algorithm (IWSA). Firstly, the reliability optimization mathematical model is established with the minimum reliability index as the objective function and the limit state equation as the equality constraint. Then the augmented multiplier method is used to transform the constrained optimization mathematical model into an unconstrained optimization mathematical model. Finally, IWSA is used to solve the problem. The proposed method is applied to a numerical example and an engineering example. The computation results of the proposed method in solving the numerical example are compared with the Monte Carlo simulation (MCS), which verifies that the proposed method in this paper has good calculation accuracy. The maximum deformation under the working condition is used as the target to establish a limit state function, and the reliability index is obtained by the proposed method combining with the finite element analysis software, which provides a certain theoretical guiding significance for the reliability analysis of engineering structures.

A Novel Reliability Analysis Approach under Multiple Failure Modes Using an Adaptive MGRP Model

In this paper, a novel MRGP-SS method is proposed to deal with the reliability analysis problems under multiple failure modes. First, a random moving quadrilateral grid sampling (RMQGS) method is proposed to improve the randomness and uniformity of initial samples. Second, an adaptive procedure, which combines the multiple response Gaussian process (MRGP) model and the novel active learning functions, is proposed to efficiently and accurately produce surrogate models for failure surfaces. In this regard, two novel learning functions are introduced to adapt to different iterative cycles, one is employed to correct the quality of samples, and the other is used to search for the samples closest to the limit state surface. Third, the subset simulation (SS) is integrated into the adaptive MRGP model to estimate the failure probability under multiple failure modes with fewer function calls and time consumption. Numerical and engineering case studies are finally provided to demonstrate the effectiveness of the proposed method.

Reliability analysis of underground tunnel by a novel adaptive Kriging based metamodeling approach

An adaptive Kriging based metamodeling approach for tunnel reliability analysis strategy is proposed with due consideration to accuracy and efficiency. Based on a preliminary design of experiments (DOE), an initial Kriging model is constructed. Subsequently, a reduced space is built from the Monte Carlo Simulation (MCS) points located near the limit state surface. The MCS points closer to the existing training points are removed from the reduced space to avoid clustering. Finally, the MCS point having the highest joint probability density value is selected from the reduced space. The inclusion of such a point in the DOE is expected to improve the prediction accuracy of a maximum number of neighbouring points. The selection of new training points and updating the Kriging model iteratively is continued until no point is left in the reduced space. The estimated failure probability is considered final if its coefficient of variation is less than a predefined threshold; otherwise a new set of MCS samples are considered for further iterations. The effectiveness of the proposed algorithm is demonstrated by three tunnel reliability analysis problems and noted to be quite efficient and superior over the AK-MCS method in most of the cases.

A Grasshopper Optimization Algorithm-Based Response Surface Method for Non-Probabilistic Structural Reliability Analysis with an Implicit Performance Function

Non-probabilistic reliability analysis has great developmental potential in the field of structural reliability analysis, as it is often difficult to obtain enough samples to construct an accurate probability distribution function of random variables based on probabilistic theory. In practical engineering cases, the performance function (PF) is commonly implicit. Monte Carlo simulation (MCS) is commonly used for structural reliability analysis with implicit PFs. However, MCS requires the calculation of thousands of PF values. Such calculation could be time-consuming when the structural systems are complicated, and numerical analysis procedures such as the finite element method have to be adopted to obtain the PF values. To address this issue, this paper presents a grasshopper optimization algorithm-based response surface method (RSM). First, the method employs a quadratic polynomial to approximate the implicit PF with a small set of the actual values of the implicit PF. Second, the grasshopper optimization algorithm (GOA) is used to search for the global optimal solution of the scaling factor of the convex set since the problem of solving the reliability index is transformed into an unconstrained optimal problem. During the search process in the GOA, a dynamic response surface updating strategy is used to improve the approximate accuracy near the current optimal point to improve the computing efficiency. Two mathematical examples and two engineering structure examples that use the proposed method are given to verify its feasibility. The results compare favorably with those of MCS. The proposed method can be non-invasively combined with finite element analysis software to solve non-probabilistic reliability analysis problems of structures with implicit PF with high efficiency and high accuracy.

Statistical inference of dependent competing risks from Marshall–Olkin bivariate Burr-XII distribution under complex censoring

Dealing with competing risks is an important problem in reliability analysis and attracts much attention from scholars. It is more practical to consider competing risks with dependent failure causes in reality. In this article, statistical inference of the Marshall–Olkin bivariate Burr-XII distribution under adaptive type-II progressive hybrid censoring is discussed to show the procedure of dependent competing risks analysis in the complex data structure. The maximum likelihood estimation and lognormal approximation confidence intervals of parameters are computed. The existence and uniqueness of solutions are proved with Cauchy-Schwarz inequality. The Bayesian method with Gamma-Dirichlet prior and Metropolis-Hastings algorithm are further considered to find satisfied estimation of parameters. In addition, dynamic cumulative residual entropy is derived to quantify the information uncertainty of data. We finally compare the performance of various methods by conducting a simulation study and real data analysis.

Comparisons of some memory‐type control chart for monitoring Weibull‐distributed time between events and some new results

AbstractMonitoring Weibull time between event (TBE) processes is essential to avoid deterioration of quality characteristics in various reliability analysis problems. Statistical process monitoring (SPM) charts are widely used to monitor the possible decreasing mean shift. For monitoring such data, many control charts have been proposed in the literature, such as the Weibull exponentially weighted moving average (EWMA) chart, the Weibull cumulative sum (CUSUM) chart, and Mixed EWMA–CUSUM (MEC) chart and Mixed Hybrid EWMA–CUSUM (MHEC) chart. The current investigation revisits their efficacy and compares them with a CUSUM chart based on the generally weighted moving average (GWMA) statistic, labelled as the Mixed GWMA–CUSUM (MGC) chart, to monitor the decreasing mean shift in Weibull TBEs processes. We offer some numerical results based on the Monte‐Carlo simulation, such as average run length (ARL), the standard deviation of the run length (SDRL) and the relative mean index (RMI). Our findings show that the MGC chart often outperforms the existing control charts in detecting small downward shifts. Finally, an illustrative example is given to display the application of the MGC chart for Weibulll data.

Novel learning functions design based on the probability of improvement criterion and normalization techniques

Structural reliability analysis relies on the evaluation of multivariable structural performance function. The construction of the surrogate model for reliability analysis has been widely studied to reduce the number of function calls. The novel learning function has been proposed based on the probability of improvement criterion and the introduction of covariance weight by normalization technique to estimate the failure probability efficiently. Furthermore, the weights of each candidate sample are inconsistent; thus, an improved learning function of the former is proposed by introducing the joint probability density function of the variables. Moreover, a novel adaptive truncated sampling space technique is proposed based on variable normalization transformation. The truncated sampling space is directly dependent on the failure probability rather than the manual definitions. Uniform samples are then obtained in the adaptive truncated sampling space by Latin hypercube sampling. Combined with the novel learning function and global convergence condition, the adaptive analysis of structural reliability is realized. Finally, several highly nonlinear and high-dimensional illustrative applications are used to evaluate and discuss the proposed adaptive learning strategy. Results show that this strategy can efficiently and robustly solve the problem of structural reliability analysis on the premise of ensuring accuracy.

Integration of deep learning and Bayesian networks for condition and operation risk monitoring of complex engineering systems

A challenging problem in risk and reliability analysis of Complex Engineering Systems (CES) is performing and updating risk and reliability assessments on the whole system with sufficiently high frequency. The challenge stems from both operational data complexity and systems’ complexity. The data complexity calls for novel and advanced data-driven methods, e.g., Deep Learning (DL). However, the systems’ complexity cannot be addressed only using black-box models; engineering knowledge and systems modeling methods must also be considered. In this paper, a novel mathematical architecture for operation condition and risk monitoring of CES is presented. In this architecture, a Bayesian Network (BN) is used to model the system, subsystems’ relations, scenarios leading to adverse events, and to fuse subsystem-level information. Further, Bayesian DL models are trained for subsystems’ diagnostics based on condition monitoring data, and their outputs are integrated into the root nodes of the designed BN. This integration enables addressing both the data and systems complexity in a single architecture that provides system-level insight. The proposed architecture also has the capacity to incorporate human inputs and qualitative information. We demonstrate the effectiveness of our proposed approach by performing a case study on a real-world Vapor Recovery Unit at an offshore oil production platform.

РАЗРАБОТКА УТОЧНЕННОГО Р-БЛОКА КАК МОДЕЛИ СЛУЧАЙНОЙ ВЕЛИЧИНЫ В ЗАДАЧА Х АНАЛИЗА НАДЕЖНОСТИ СТРОИТЕЛЬНЫХ КОНСТРУКЦИЙ

The article describes a new type of the p-box (probability box) for random variables modeling in problems of structural reliability analysis. The advantage of the presented random variable model is that it is based on confidence estimates of statistical parameters without the need to confirm the hypothesis about the type of probability distribution function. The numerical example shows that the introduction of additional information in the form of a median’s confidence interval to the p-boxes based on the Chebyshev’s inequality is leading to reducing the area between the boundary distribution functions of the random variable. This makes it possible to reduce the level of uncertainty during further arithmetical operations with p-boxes in problems of structural reliability analysis, which is clearly visible after the discretization of the p-boxes into the Dempster-Shafer structure.

An active learning reliability analysis method using adaptive Bayesian compressive sensing and Monte Carlo simulation (ABCS-MCS)

Response surface methods (RSMs) have been developed to improve the efficiency of reliability analysis for computationally time-consuming systems. Most RSMs cannot self-evaluate the accuracy of reliability analysis results and rely on Monte Carlo simulation (MCS) for verification. Therefore, this renders a challenging question in RSM applications that how to determine whether the number of sampling points is sufficient to achieve target accuracy of reliability analysis. Adaptive Kriging MCS (AK-MCS) utilizes the advantage of self-estimated uncertainty in Kriging method and combines a learning function to sequentially select additional sampling points to improve the accuracy of reliability analysis until a target accuracy is achieved. However, extensive sampling data are required to ensure that the trend function and auto-correlation structure function of AK-MCS are reliable, and AK-MCS does not work with high-dimensional or highly non-stationary data. To address these challenges, this study develops an active learning reliability analysis method using adaptive Bayesian compressive sensing (ABCS) and MCS, denoted ABCS-MCS. ABCS-MCS can self-evaluate the uncertainty of predictions and combines a learning function to adaptively determine the minimum number of sampling points and their locations for achieving a target accuracy of reliability analysis. This approach is directly applicable to non-stationary data because BCS is non-parametric and data-driven, and thus does not incorporate a trend function or an auto-correlation function. Investigations using two highly non-stationary analytical functions and a slope reliability analysis problem reveal that ABCS-MCS outperforms AK-MCS.

Surrogate assisted active subspace and active subspace assisted surrogate—A new paradigm for high dimensional structural reliability analysis

We propose a novel approach for solving high-dimensional reliability analysis problems. The basic premise is to train the surrogate model on a low-dimensional manifold, discovered using the active subspace algorithm. However, learning the low-dimensional manifold using active subspace is non-trivial as it requires information on the gradient of the response variable. To address this issue, we propose using sparse learning algorithms in conjunction with the active subspace algorithm; the resulting algorithm is referred to as the sparse active subspace (SAS) algorithm. We project the high-dimensional inputs onto the low-dimensional manifold identified using SAS. A more accurate surrogate model is used to map the inputs on the low-dimensional manifolds to the output response. We illustrate the efficacy of the proposed framework by using four benchmark reliability analysis problems from the literature. The results obtained indicate the accuracy and efficiency of the proposed approach compared to already established reliability analysis methods in the literature.

On dimensionality reduction via partial least squares for Kriging-based reliability analysis with active learning

Kriging with active learning has been widely employed to calculate the failure probability of a problem with random inputs. Training a Kriging model for a high-dimensional problem is computationally expensive. This reduces the efficiency of active learning strategies since the training cost becomes comparable to that of the function evaluation itself. Kriging with partial least squares (KPLS) has the advantage of a fast training time but its efficacy on high-dimensional reliability analysis has not yet been properly investigated. In this paper, we assess the potential benefits of KPLS for solving high-dimensional reliability analysis problems. This research aims to identify the potential advantages of KPLS and characterize the problem domain where KPLS can be most efficient and accurate in estimating the failure probability. Tests on a set of benchmark problems with various dimensionalities reveal that KPLS with four principal components significantly reduces the CPU time compared to the ordinary Kriging while still achieving accurate failure probability. In some problems, it is also observed that KPLS with four principal components reduces the number of function evaluations, which will be beneficial for problems with expensive function evaluations. Using too few principal components, however, does not show any evident improvements over ordinary Kriging.

A classification-pursuing adaptive approach for Gaussian process regression on unlabeled data

Some areas of mechanical and system engineering such as dynamic systems commonly exhibit highly fluctuating responses over given parametric domains. Therefore, classifying some quantities of interest over the parametric domain for designing new systems turns out to be a highly challenging task. In this context, an innovative adaptive sampling algorithm named Monte Carlo-intersite Voronoi (MiVor) is proposed for design applications based on the classification of one or more continuous quantities of interest useful for parametric studies. In contrast to reliability analysis problems, no probabilistic setting and information is needed. The proposed technique is able to efficiently detect two or more classes of highly imbalanced decision regions and to accurately describe the boundary between these regions in a robust manner. To the best of the authors knowledge it is the first adaptive scheme for classification-pursuing parametric studies that combines information from (potentially) multiple class label outputs and the accompanying continuous values for efficient sampling involving (possibly) multiple class outputs. The resulting surrogates utilize only a small number of observations which are obtained in an active manner. The capabilities of the presented algorithm to provide accurate classification are demonstrated on three dynamic applications with various dimensionality and under consideration of a combination of different first-passage failure scenarios. Comparisons with two regression-based adaptive schemes show that the proposed algorithm outperforms existing methods. For instance, in the case of a quarter-car problem, more than 99% of points are correctly classified using the proposed approach at convergence, whereas less than 80% of reference samples are correctly classified with standard approaches. Similar performances (> 95%) are also obtained with MiVor for a non-linear oscillator of Duffing’s type and a three-degrees-of-freedom mass-spring system with three and six-dimensional parametric spaces respectively.

A reformulation of the stochastic load combination problem

This paper revisits a classical problem of stochastic load combination, in which the maximum load generated by combinations of various types of stochastic processes are analysed. This paper takes a fresh look at the combination of a renewal pulse with a homogeneous Poisson shock process, and proves that the problem can be transformed into an equivalent renewal process. This approach leads to an accurate solution for the distribution of maximum combined load in the form of an integral equation, which can be solved by a trapezoidal integration scheme. The proposed solution is accurate for all small and large load levels and time intervals, since this approach does not rely on any asymptotic arguments. This paper also analyses various assumptions and relative accuracies of popular approximations of the load combination problem reported in literature. The proposed formulation advances the understanding of the load combination problem and provides an accurate and original solution for an important problem of structural reliability analysis.

An improved Kriging-based approach for system reliability analysis with multiple failure modes

Reliability analysis with multiple failure modes is needed because more than one failure mode exists in many engineering applications. Kriging-based surrogate model is widely adopted for component reliability analysis because of its high computational efficiency. Compared with Kriging-based component reliability analysis, selecting the sample points that affect the system performance is more difficult than that of a single failure mode in system reliability analysis. Therefore, how to select suitable sample points is a key problem in system reliability analysis. Meanwhile, reducing the number of calls to the performance functions is challenging, especially for systems with time-consuming performance functions. In this paper, an improved Kriging-based system reliability analysis approach is proposed based on the two strategies. In strategy 1, the initial sample points are determined by considering only two different cases: (a) the candidate samples are selected from the safe regions only for series systems; (b) the candidate samples are selected from the failure regions only for parallel systems. Therefore, samples having little contributions to the composite performance function are avoided. In strategy 2, the sample points determined in strategy 1 will be further optimized by interpolating. From comparisons with three reported methods in numerical examples, the efficiency and accuracy of the proposed method are illustrated.

Reliability Analysis of a Complex Multistate System Based on a Cloud Bayesian Network

This study focused on mixed uncertainty of the state information in each unit caused by a lack of data, complex structures, and insufficient understanding in a complex multistate system as well as common-cause failure between units. This study combined a cloud model, Bayesian network, and common-cause failure theory to expand a Bayesian network by incorporating cloud model theory. The cloud model and Bayesian network were combined to form a reliable cloud Bayesian network analysis method. First, the qualitative language for each unit state performance level in the multistate system was converted into quantitative values through the cloud, and cloud theory was then used to express the uncertainty of the probability of each state of the root node. Then, the β-factor method was used to analyze reliability digital characteristic values when there was common-cause failure between the system units and when each unit failed independently. The accuracy and feasibility of the method are demonstrated using an example of the steering hydraulic system of a pipelayer. This study solves the reliability analysis problem of mixed uncertainty in the state probability information of each unit in a multistate system under the condition of common-cause failure. The multistate system, mixed uncertainty of the state probability information of each unit, and common-cause failure between the units were integrated to provide new ideas and methods for reliability analysis to avoid large errors in engineering and provide guidance for actual engineering projects.

Subset simulation based approach for space-time-dependent system reliability analysis of corroding pipelines

This paper proposes a subset simulation (SS) based approach for space and time-dependent reliability analysis of corroding pipelines. It is assumed that the pipeline can fail either due to leakage and/or burst. We propose two distinct approaches for tackling the problem. In the first approach, we treat the problem as a time-variant system reliability problem. The problem is formulated as a series system where failure at one of the defect locations will result in failure of the pipeline. This approach is particularly suitable when there are only a limited number of corrosion defects. In the second approach, the reliability analysis problem is treated as a ‘space-time variant’ reliability analysis problem. This approach is particularly suitable when exact knowledge about the number of defects is not available. In both the approaches, the time-dependent probability of failure is represented in an auto-regressive form such that the probability of failure at a given time can be computed based on the probability of failure at the previous time and an incremental failure probability. A simple composite limit-state function is proposed for computing the incremental failure probability. SS is used for computing the initial and incremental failure probabilities. To illustrate performance of the proposed approach, four pipeline problems representing different scenarios are considered. For all cases, the proposed approach is found to yield highly accurate results.

ПРОБЛЕМА АНАЛИЗА НАДЕЖНОСТИ СВАЙ НА ВЕЧНОМЕРЗЛЫХ ГРУНТАХ ПО КРИТЕРИЮ УСТОЙЧИВОСТИ

The increase in the rate of global warming directly affects the safety of buildings and structures on permafrost. The research presents the problem of reliability analysis for piles on permafrost soils by the stability criterion under the action of tangential forces of frost heaving. The two groups of piles reliability analysis methods are developed: for complete and limited statistical data about random variables in the models of limit states. Approximations of the dependences of the design resistances of permafrost soils to the shear along the freezing surface on the temperature are proposed. It can be used to estimate the freezing force that keeps the pile from buckling. The method for reliability monitoring and durability forecasting has been developed for piles on permafrost soils. The proposed method makes it possible to reasonably reduce the cost of reliability analysis in the initial periods, which can increase the number of buildings and structures being inspected by the similar costs.